{"analysis":{"report":{"acute_accessibility_barrier":{"denominator":2,"numerator":7},"acute_entry_excluded_on_validated_prefix":true,"arithmetic_method":"rational_outward_dyadic128_machin_trigonometry_v1","clock":"structural_t","cumulative_boundary_form_input":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":25582966721764084803205063639608863905},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":324216845946966576177761816148174186109}},"cumulative_boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":712373406929372934637645766637059273489},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":343418413907973474985198309308150477089}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1090557449975262370626924754643235154865},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1014724758836874871180337513306793933429}},"cycle_indices":[5,6,7,8,9],"endpoint_form_storage":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":709825091699093989053397867302297510809},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1419650183398187870577017271873387245387}},"endpoint_phase_storage":{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":10833572428250391200861660791873541787},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":346674317704012387968506969920666197397}},"forecast":{"end_time":{"denominator":1,"numerator":12},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":83569617809245040063865350978972189093},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":83569617809245029987387152132560802219}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-397450906684520716347640760042982503259},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-794901813369041444249067721773596410337}},{"hi":{"denominator":664613997892457936451903530140172288,"numerator":-865677180709544103513720452533501005},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-221613358261643296127924745213512060255}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":43313782115268665093184708519931671961},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":21656891057634325740537343521301470363}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":128394326066749548428792864859422550789},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":128394326066749542088271753411113852783}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":214486780365293385109471990586985728171},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":428973560730586760951607595973534931183}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-220420150583455967520046335302246898737},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-440840301166911945806320978150866077697}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-288804786347180390151587223796091223405},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-9025149573349387599102081808116210125}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3606877217333463375361129509482463609},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3606877217333453617882876548645580499}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":144373393305219415495021211514500654129},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":288746786610438819690072278523779778525}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":89243782300837703539164853396741800457},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":713950258406701617445976430130053863491}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-60499165190150893056651696585120064401},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-30249582595075454313700358631434878687}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2899559150125464448003532051671123111865},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-724889787531366116053109835595996349763}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":9679757040021602865102058610869863971},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":619504450561382566908311785117619076343}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":623585258866494654762543044313625406857},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":623585258866494638277570798935270698285}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":99869975208041299723760266460669999805},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":99869975208041291529809518608804894937}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-41387774673497635738614194754611814805},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-20693887336748824122674867214424919037}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":12855502534008751889067077568786413599},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":6427751267004374131766744934478694301}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":33628957543421996164247530896808307855},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":269031660347375955429513717329689541399}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2012827623622255045475867675100718307},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1006413811811121354146147315444754193}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-131356038019417366129766521970124085595},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-65678019009708686064636534571837371615}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1486937024001746859354596620627780596571},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2973874048003493705399905065564131133559}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"failed_tube":null,"forecast_start":null,"freeze_hidden":false,"initial_box":[{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":-3},"lo":{"denominator":1,"numerator":-3}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":3},"lo":{"denominator":1,"numerator":3}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"method":"full_sine_held_capacity_Picard_Taylor_Metzler128_v1","model":{"epi_weight":0.0,"phase_domain":"regular","phase_weight":1.0,"storage_scale":1.0},"neighbors":[[1,4,10],[0,2,6],[1,3],[2,4],[3,0],[6,9,10],[5,7,1],[6,8],[7,9],[8,5],[0,5]],"observation_time":{"denominator":1,"numerator":0},"order":10,"prior_admission":null,"reasons":[],"scope":["fixed_simple_connected_unit_support_and_explicit_smooth_sine_law","full_phase_lifts_not_rounded_phase_midpoints_or_normalized_phasors","held_nonnegative_capacity_uncertainty_is_an_augmented_zero_rate_coordinate","exact_held_capacity_and_zero_capacity_row_invariants_tighten_endpoints","every_initial_point_enclosed_using_whole_time_Picard_and_Taylor_certificates","propagation_starts_at_actual_observation_time_including_the_preforecast_gap","fixed_order_and_step_budget_without_adaptive_retries_or_empirical_error_estimates","global_smooth_extension_admits_tubes_while_initial_held_capacity_stays_nonnegative","no_runtime_dispatch_graph_mutation_events_or_physical_validation"],"status":"admitted","steps":[{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":26401847559627383201609815003},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":211214780476243861350340460005}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1020701948939840595079318158102037472237},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1020701948939840595084564729653630937479}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-56797846991526796343237939841182131},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-113595693983053597491699633700504509}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":28404084611804025001629408558166299},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":7101021152951006199453068440865207}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":126870492913763117415946343037},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1014963943310081868831136965451}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":88360295235538942985045993627467621},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":22090073808884735372651012467638953}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-44180011159565219889294085952032653},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-88360022319130441736107440712890937}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":18936105055798219182735184212776385},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":18936105055798219113453796003731185}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-796284759015446105102969},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-796284766011348444064219}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-18936144076729473335400987317980533},"lo":{"denominator":166153499473114484112975882535043072,"numerator":-9246164099965563180748899083723}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1020714562935585447760916606171686245123},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":510357281467792723879299209647344650505}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-10460364152403869347967687155569},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-20920728304807862204583645364449}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-7615386977038636043330315224638623241},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-1903846744259659010867611124801308955}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3807459353917953866745903486103794041},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":3807459353917953866610958266343708741}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":423807050691904460958569552769083},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":423807050691904367208248622977973}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-70637181660348930180670146053585},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-17659295415087237562296450009149}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-1269109944354137207071318501818389743},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5076439777416548828394725243459189233}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2538209428824670318208653845267446251},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":2538209428824670318131968280194191005}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":9810716814114316991412027168885},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":78485734512914526383948504728621}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":14557282147004577195164243},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":58229128585302304916080971}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-313943461882113373893976097039959},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-313943461882113404108675169162789}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":951934488413739979238348915827292383},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":7615475907309919833841070194047553269}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":460876154815665797},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-78582026930598555}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":169019001875284151},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1142623886023082159}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1060175820407323261},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-282260236194423601}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":23450965221061737},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-180366169573643733}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":850994062150297},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2363647859843523}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":99640900916882759},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-647580070961573145}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":862212427007794269},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-58273603698309273}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3968818147293915},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-61343751914457369}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3749563573424289},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-50724043211515}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":3228223990177487},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-3560587081322189}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1915879762616630537},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-402307114380313575}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-31172439370218569},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-186444081616400931}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2240005473698335809},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":489936731141277663}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-488192313765890019},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1111329847291865337}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":389869877196249631},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":685989433462708153}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-18756665433325},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-10184311150458105}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":942843589301708999},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":833392353116078739}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1149625210145335175},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1302996340291845665}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":167242202182374869},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":296295013514259903}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-174044306818621},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1532046239106621}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-60188299350442427},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-270967896473892537}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-401371013776061749},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-467092146346847543}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":1,"numerator":0},{"denominator":1,"numerator":0},{"denominator":1,"numerator":0},{"denominator":1,"numerator":0},{"denominator":1,"numerator":0},{"denominator":1,"numerator":0},{"denominator":1,"numerator":0},{"denominator":1,"numerator":0},{"denominator":1,"numerator":0},{"denominator":1,"numerator":0},{"denominator":1,"numerator":0},{"denominator":1,"numerator":0},{"denominator":1,"numerator":0},{"denominator":1,"numerator":0},{"denominator":1,"numerator":0},{"denominator":1,"numerator":0},{"denominator":1,"numerator":0},{"denominator":1,"numerator":0},{"denominator":1,"numerator":0},{"denominator":1,"numerator":0},{"denominator":1,"numerator":0},{"denominator":1,"numerator":0},{"denominator":1,"numerator":0}],"time":{"denominator":1,"numerator":0},"tube":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":59244699014397937987571272642580175},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-14811207913953618783587597709677917}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1020474949682188297807404720869746417905},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1020928842675710903197228600062349348013}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":63981191758869964541841919135259441},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-18202659113741195088509273662629441}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":72853072977571789973742526473428535},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-16065127422175820969043071079805537}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":27350318638300264234931499380459},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-85041383724503165983758357169745}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":14158195570769081941219822362748563},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-24875708914804671978301627388034453}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":12437881301839107789343732794082555},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-226531618029394099461120399315363967}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":48570848511822335683522498203901511},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-10710044906256253002619554748939211}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":44607433369590968788483284823361},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-44607433369590968788483284823361}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":1338746341232407393179882671349435},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-48570510617507658514513755916928437}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1020921748148979352864302883086087635315},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":15945426396564908862850495054786191743}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4843270485684832686453981112802031},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2484405995060792551017162196105553}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1904275479839442400375097095136823699},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-4284619829638745400843967914302039433}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":8569797873423043301157276891961079383},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-476099881856835738953182171721351941}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3755196566449150754284959393310563},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1212170186927848251137527223420863}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1305869950001766447295122298486067},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1729743065950844056018841601818217}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":634836266869816325542222488622170041},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5713526401828346929880000198576274813}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":714195771332494259855794592811453387},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-634840685628883786538484326834986961}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2781658976898439254508648833213987},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-897871951528967416174822636755759}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":275964819632055500301360295003287},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-275964819632055500301360295003287}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":897871951528967416174822636973433},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-695414744224609813627162208472001}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":17138472536736364655131380998027603847},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1904274726304040517236820355227873267}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1683549237682787280450501615241},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":105221827355124716103679250011}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-127533384987523731472739620256932572979},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1020267079900189851792731150509464282747}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-453907265116289811633260703436368379},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-453907265116289821550025949676672815}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":28389823835083622563326115526524629},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":56779647670167244914838325176338227}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":16234482039555107469870834973503},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":8117241019777529039580923722025}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":88292058855973115855522522494528649},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":176584117711946230174197283012307301}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-44145485815206109215679990104969831},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-353163886521648877762339307865374613}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":75706967908177755727314258983682381},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":37853483954088877791513410287989521}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-50875298196755351277102171},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-3179706138231934427592603}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-18926897819859033384010506858474117},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-37853795639718066829032512304037419}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":255079347563398013377382246780206808707},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1020317390253592053504774075744772932891}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-20885634536117984361469291810783},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-83542538144472105224317936483663}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-7613802908052816234021385372718244809},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-30455211632211264936857868319183538357}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":15223861921402500638559411265207320739},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":7611930960701250318906616533844912255}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3388659921116291871481334547067263},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3388659921116291612045471007906899}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-282431024425591568565008031908309},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-564862048851183190651773329909093}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-10147859681822172447306439030468208065},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-634241230113885777975334356532498597}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":2536923156873674869323658243970940753},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":10147692627494699476872071492079558951}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1255247694665675088110615636405089},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":156905961833209379431730170770795}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":232639323566361366201618097},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":930557294261741278860317819}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2510512109753055599104858028880233},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2510512109753055681666120513943091}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":7614158238251770411683375484232835587},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":3807079119125885205797266124018452027}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":76754291704721909},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-11850821138811001}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2864784622340407173},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8424076948543756019}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":7876389882852643079},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2773082331307888257}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-120126572572803179},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-335635457409773871}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":9046286332083499},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5920118205772751}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-805275319701595983},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2380686257121630685}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3199763528319190033},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":281426812919158147}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-10327319953749515},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-57112177710616401}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1094895657042709},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1458773760189737}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":47885747177226021},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":17033423512045865}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3419020105178651875},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":493363636688523647}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-54401222822626585},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-190139297087506613}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1106556951111318003},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1836920822376354625}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1830780115120372277},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2194605880019143697}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":769919323374960507},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":80420396130668929}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1339625055987119},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-23077622433115197}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":466223542493596269},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":786897408391699463}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-540567724045971573},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-643587779219026167}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":41306723648512911},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":279055183779069711}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":41307577476917},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1724977271372151}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-227771193381706651},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-134006378618172233}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-755184038458497825},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-463765736795496905}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":85070591730234615865843651857942052864,"numerator":97499763926059855},{"denominator":170141183460469231731687303715884105728,"numerator":1313724031950087517},{"denominator":170141183460469231731687303715884105728,"numerator":1203364423673887403},{"denominator":85070591730234615865843651857942052864,"numerator":26014865864556421},{"denominator":340282366920938463463374607431768211456,"numerator":12689009058794851},{"denominator":340282366920938463463374607431768211456,"numerator":749142293266732645},{"denominator":340282366920938463463374607431768211456,"numerator":981421555191529259},{"denominator":170141183460469231731687303715884105728,"numerator":17843090700367149},{"denominator":340282366920938463463374607431768211456,"numerator":3829234707914583},{"denominator":85070591730234615865843651857942052864,"numerator":7539793730477257},{"denominator":340282366920938463463374607431768211456,"numerator":1161309272126348677},{"denominator":340282366920938463463374607431768211456,"numerator":86441589326987087},{"denominator":340282366920938463463374607431768211456,"numerator":198066874232138869},{"denominator":85070591730234615865843651857942052864,"numerator":47794054077340601},{"denominator":85070591730234615865843651857942052864,"numerator":16609963651193911},{"denominator":340282366920938463463374607431768211456,"numerator":13882442360501519},{"denominator":340282366920938463463374607431768211456,"numerator":76680498728138205},{"denominator":85070591730234615865843651857942052864,"numerator":27065171682261859},{"denominator":85070591730234615865843651857942052864,"numerator":6739367891430485},{"denominator":340282366920938463463374607431768211456,"numerator":1896593519828583},{"denominator":340282366920938463463374607431768211456,"numerator":21159849315212521},{"denominator":340282366920938463463374607431768211456,"numerator":91512754825615073},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":3},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":118505211020488020646562320361102665},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-29625287635193078321996533214604389}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-510004190040984364061363348527557856603},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1020779012146270802524768955742246324127}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-53289161150370778027671938750117107},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-656354489477198924615709149049333103}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":41052896958364890933785026906319875},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":13314362031620076026997825665119247}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":45183373416723362124445397099293},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-24737236793685007949146438737465}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":255314244217639636853459657518817559},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":41441607102234460133235442738296383}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-5180236474154600038294886085107735},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-510623197052173195028647721889640583}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":27369845368183846062772243350963163},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":8875741009471867431494087512244849}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":80935107412472573528061419152171},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-80935606853304298811131213353021}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-4437864795491371374051289175055275},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-109479874448450048621084469005554821}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1020784941397319984370498195854526294483},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1020081156779974618274682301225149056435}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3287247593534097804895189058259549},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-876003429663473475029781728426765}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-13326907395180264121855119245673231623},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-2022848311509396485619389317668132791}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":16181245693954626505062860167184224187},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":3331552299133580601508683497814816393}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":4344270277566937016764829871895931},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-494496672023870040161041393029743}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1076135024703080666759278284140959},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-317620220033277164274896834170547}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-555240924168865325039276794995876565},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-5393525617003592440012404317004610741}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5393498572127194454232075049842249531},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":4441910159137668606019468145019562831}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":804641764909043436503666498436017},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-366411637639529604074843424622095}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":938836455480973312373063327753775},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-234707912040614978667156170849243}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":45802079524504743729811277617199},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6437184344585475287483973935582363}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":16183181894398853694174045779384252579},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":13327017150822298809830367791462144963}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":8471100457605822630358722314581},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":16942200915209181475616641452429}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1019544247989609681046471984024624320141},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-509772123994804840531690755232031602921}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1019512438996805244945821019458575971},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1019512438996805260468796092322820889}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":255294828586515175921338309929550515},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":127647414293257587626262208495122595}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":41072706322539162779873007810711},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":20536353161269561116096258785411}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":396803514665035939540911664931445791},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":396803514665035937145259638080429323}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-99198145273862571878041139684682339},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-198396290547725145333893846032744365}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":85100196887393125683026972215541811},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":85100196887393125568846653805448687}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-288927759116485569696211685},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-288927759128726300364831843}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-170203541484134821267708634227526753},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-85101770742067410730032000886720659}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":31864278187571298303588776536752455303},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1019656902002281545707441987981787903663}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-70292165733998607585118567936219},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-70292165733998689008749981977617}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-11416750431379789810030478459966451459},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-45667001725519159241631908606439503117}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":5705219475805503526996747033463336249},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":5705219475805503526631392758440252837}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5713318919246017335471671354678919},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":11426637838492034162566924363236595}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-476271562208024476914048862555865},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1905086248832098010677430379235109}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-3802313866541203694450250303893107331},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-15209255466164814778381912778157231361}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":15208693362258848374789235270604658519},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":15208693362258848373963758292277942067}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":1058379287413787767261194409068817},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":4233517149655150966169126004007387}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":7052419031724996427303120963},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":14104838063435594877389067221}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-2116790184578902306977224002363487},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-4233580369157804694180534554013941}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":5708973738456123706390915999829325761},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":45671789907648989650439931356677028685}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":387446730595052029},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-23177856907074557}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-3031043572088538463},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12135485274943964241}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":11373434895443018849},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":2894489409840922173}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-251341472570315049},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-485163516913461489}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":2841155431371187},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1470198235361915}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1722583541094798647},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1715065028777954475}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1155046082132686753},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2359864105045678243}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-21681671763058693},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-10330307006335069}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5074317643131437},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2708735933497559}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":138456443079841611},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":9021524159107113}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4878906348958068069},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":280812098182767451}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-42244946788999667},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-383319413487042299}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2135597248416525399},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":818416408799055657}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1631640250967569653},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2114801152611315799}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":741802811947902687},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":573714512095153037}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3466561300372891},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-26726140483657083}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":451535423487085485},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":355703918257528871}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-484766730980889975},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-310558960594911933}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":318908029564703261},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":62736771925822015}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":422775070242087},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1943801721672909}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-206659717490059295},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-259616433535492551}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-339477990918030177},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-226281050115967903}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":798090105992387223},{"denominator":42535295865117307932921825928971026432,"numerator":677258019291999899},{"denominator":340282366920938463463374607431768211456,"numerator":4969259498551535207},{"denominator":170141183460469231731687303715884105728,"numerator":108747962149039721},{"denominator":340282366920938463463374607431768211456,"numerator":27712860529393225},{"denominator":85070591730234615865843651857942052864,"numerator":385469692155115329},{"denominator":85070591730234615865843651857942052864,"numerator":506365755396056247},{"denominator":340282366920938463463374607431768211456,"numerator":74901205885529957},{"denominator":340282366920938463463374607431768211456,"numerator":8349203880305659},{"denominator":10633823966279326983230456482242756608,"numerator":1969861214670779},{"denominator":340282366920938463463374607431768211456,"numerator":2383225815397368785},{"denominator":5316911983139663491615228241121378304,"numerator":3414448632666309},{"denominator":340282366920938463463374607431768211456,"numerator":505615167877641597},{"denominator":170141183460469231731687303715884105728,"numerator":244564049612146875},{"denominator":85070591730234615865843651857942052864,"numerator":42536014811671449},{"denominator":340282366920938463463374607431768211456,"numerator":34680985922304391},{"denominator":340282366920938463463374607431768211456,"numerator":194624276062844403},{"denominator":170141183460469231731687303715884105728,"numerator":138193649477212167},{"denominator":42535295865117307932921825928971026432,"numerator":8611897587695035},{"denominator":85070591730234615865843651857942052864,"numerator":1208102954168089},{"denominator":170141183460469231731687303715884105728,"numerator":26873864263285169},{"denominator":2658455991569831745807614120560689152,"numerator":1801673528631899},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":32,"numerator":3},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":118497282695774438216124864675063319},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-118469005753014465028579312244753243}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-509624800834325703716052600008020176909},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-127547516629628432090211198712189246239}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-11420089121878086627225386145313031},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1250086984062009167691693625490275309}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":156520613374749712392031136308903003},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":45697318147435859639594557326983499}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":324800319368830143268473270945413},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-42317902445131003914952919827399}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":243240705582073393728788663389462503},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":284302170212292336507643200851671161}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-284300581493847777418924256761186457},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-486466815885929370242039349261826405}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":208704226383591242543077713680224655},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":30464747372121461849288238503128345}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":73304940275207871058936244353563},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-73306493445253839873187464684411}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-30464875478960640414349993318526865},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-52177038543267451975529548895556389}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1020420679999160162640869806760074545907},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":254846945635869767831865403141656172669}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":8321337742005455215524215592524893},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-9545006923347982939326485482778901}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-28552434074603957016722671563859711855},"lo":{"denominator":2658455991569831745807614120560689152,"numerator":-371720387895914345393370067460696329}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":11890473025632471828165882312503594113},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":7136537397931114595655586880714877851}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":9567428168070175628537959702107721},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":204885317708646734213563772938861}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":67580042781476773293588968482401},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2105848388878470016012017026156185}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-2378552516022561038945215370686712005},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-7925353120704763535518317380468596457}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":495322260731387767249534509679854869},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":4757034107307921456485311578445387675}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":3544989424766965862530486111131291},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1213888466027293028772520428394053}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":689993321453753047390914716336771},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-344987661083513034019437253000179}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1213870979702745284705121368132201},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-1772535285025731053587536119044621}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":47583891907537094138524899109829212297},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":28553604180281524702806265401402632701}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":414758968218945264310130508809},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":26544573966010775016899231632255}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1018536360722792334765984002208888928913},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-509268180361396167394860407316374731231}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1808054881371499098768486413713229517},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-452013720342874780146663618459492283}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":453327093295602282062569690663739633},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":453327093295602281113372835183486011}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":259436017366209987665343872409155},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":32429502170776233394596082795983}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":704161073555701362157172867462898191},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":704161073555701358808071523446682339}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1408253691776319902552854549102933017},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1408253691776319911406732146960926265}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":151114965056401200892231773369875093},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":302229930112802401459460827946446395}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-3233874935114974843130424999},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1616937467575607123658367865}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-302239842707356886049024967330840661},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-151119921353678443160731200167817159}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1018735286653943244758853670317676295799},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1018735286653943244748524709610687751257}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1327743581612981542258082719761309},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-331935895403245656224530714266461}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-60859882647391160938347881080669051055},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-15214970661847790235217141770721751031}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":7600015556072523897873963152433981001},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":15200031112145047794526636134119283255}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":27051960454409804620318530239529471},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":27051960454409803770225023863065969}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-4511373936086384104455731762534585},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2255686968043192137476123410427091}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-20255654020368621482020006077804468829},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-10127827010184310741492664153066673461}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":20254327259955488680312381424814640205},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":20254327259955488678935708509548750227}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":20050508725501011696761143071921475},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":20050508725501011353643015163499615}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":29636524251948001384917499449},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":7409131062984004151960986083}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-10025519208742018427118029919839289},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-20051038417484037120829093888540843}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":30435601693344687799361732887238828559},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":3804450211668085974849010750628719871}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":467424422630003803},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-5355627656589329}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-8808760082069639549},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-3898578241004605655}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":14626488302543583657},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":8372732993814123335}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-182904962046329845},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-312272431001776055}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":27407191083243133},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-284606838961341}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2526941688256424599},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-551848422152753377}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5943513258809978717},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":428443073937950267}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-7935439107918725},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-26640265306408845}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":363540374338407},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1316673521515289}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":178581975918381467},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":26540968889278829}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1564404667043825221},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1674656865921448539}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-53394039282633975},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-94905953005232329}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1002114275326121289},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":42725278107210855}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1362929953893281091},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-990405812601972945}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":694681201804113085},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":479701294965391601}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":2958960680559487},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-30813685962614329}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":213248419459853361},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":76186209718674573}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-409445411260547085},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1166488809952209815}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":299493470983675693},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":26623004014427511}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":410784906123601},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1083857183017061}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-178120271171972701},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-245327904989743661}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-577065029116855171},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-864129007063299805}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":1243763271177749059},{"denominator":170141183460469231731687303715884105728,"numerator":4237814885477937619},{"denominator":170141183460469231731687303715884105728,"numerator":3891103187848819823},{"denominator":42535295865117307932921825928971026432,"numerator":43153869848085075},{"denominator":340282366920938463463374607431768211456,"numerator":46266085224437737},{"denominator":340282366920938463463374607431768211456,"numerator":2405178499533414643},{"denominator":340282366920938463463374607431768211456,"numerator":3168954465275808333},{"denominator":340282366920938463463374607431768211456,"numerator":119423811034366315},{"denominator":85070591730234615865843651857942052864,"numerator":3473676394233205},{"denominator":42535295865117307932921825928971026432,"numerator":12501208290220469},{"denominator":340282366920938463463374607431768211456,"numerator":3710327885328070367},{"denominator":21267647932558653966460912964485513216,"numerator":25306384583801349},{"denominator":85070591730234615865843651857942052864,"numerator":235458293874557231},{"denominator":340282366920938463463374607431768211456,"numerator":912349335093346347},{"denominator":10633823966279326983230456482242756608,"numerator":9923649992777219},{"denominator":340282366920938463463374607431768211456,"numerator":63923493186733659},{"denominator":340282366920938463463374607431768211456,"numerator":360909114119430615},{"denominator":170141183460469231731687303715884105728,"numerator":257268731958693583},{"denominator":340282366920938463463374607431768211456,"numerator":128304344520083127},{"denominator":5316911983139663491615228241121378304,"numerator":140554576488653},{"denominator":85070591730234615865843651857942052864,"numerator":24923175028886413},{"denominator":340282366920938463463374607431768211456,"numerator":426114893235847273},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":9},"tube":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":29617911414830855546057120210144181},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-59185141656380555262811597228330811}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1018206238805373546986069621427447452699},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1019692915676747029294193942823578651253}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-903194025791039180309976358259084463},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-516594539462174956667105192807685997}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":518133015466323819261669302719075845},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":56522646399967442590654796337781125}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":600567271931195974906518394068507},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":14017960465855992554921830301165}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":804660501045288441839742906439821279},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":351486071733896769956983597205871575}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-351478853471930662612449449077466285},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1609232259414253823219198892356938437}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":345434500652407627310406751416781215},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":150729937455050542674058236185437441}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":233905694393288665812354091710789},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-233917378633382484866196209919103}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-75366020521561909716524181317017473},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-43180880681654229722456109943212183}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1019792820316683043585123587222706138909},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1018433637172668064882296208955453702337}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":9677200320011586338185460290513367},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12430913755647190838377130238839527}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-43766100507841523490779339531811901589},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-62775112684617880984205080413327688503}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":31362037146753830487690853757311600929},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":21871860209496256730840539375697250777}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":37466093289238472794684764625435949},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":8533365010631318758998031109297161}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1311596709246057421320072800387713},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-7246492105106462284679100275489625}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-14577093156898943123841502752871206807},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-20898716249557659663436485180860176423}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":10448797666311316990298431134100633447},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":14576593143329538862115635383950544247}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":13886391863883494521247626336878803},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":1580487757370445285580140788420405}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1819343667506128210715398879116817},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-909602617949589565901289910477165}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-395123229568089325361705515935401},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-27773862325351229427001166776586177}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":31392497498021240680180935603438231381},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":10942580668901317087334373337801960237}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":128189081601428651925591308183301},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":64094540800712049205294221498497}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-508623727232234841702481146367354082967},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-508623727232234841718221218325148063891}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1408132569114373285373177777689977319},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2816265138228746599704087665266743879}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":44203832438461723946997780608266617},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":353630659507693790939060551364595187}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":79101502252007539091906536360153},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":632812018016060142597282198823319}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2195431403313809653412104728979613933},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2195431403313809644555835937276787967}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1097633157780014214729133977473805259},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2195266315560028441202305136752153819}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":471535668561287244943937550330370127},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":235767834280643622252925882473070679}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-12273332854055990201651739165},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12273332854106976103803292793}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-471559757737361629990787425580958543},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-14736242429292550948630464350057459}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1017555586508688506164780992562999938219},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1017555586508688506151140887956396996635}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1290126749677314571643315075043997},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-40316460927416105970090441809225}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-38013833434196190390632790400036069295},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-38013833434196190392544446370307772209}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":18977790454430192027752556118974160381},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":18977790454430192025899506721619299013}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":26376120454275117330561058484722277},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":13188060227137558342757019163186401}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-8800279450756435996334496185179451},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-4400139725378218126968087011950527}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-25282128654085710553245051147812484991},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-25282128654085710554707227555890565847}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":3159943924899065743334063934937819475},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":6319887849798131486146038889951990693}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":2444519904289679041905058292849019},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":39112318468634864149713056825871487}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":45061006726046950345158692727},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":180244026904151374432509911993}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-39113922796990980623427462673640563},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-39113922796990981027270647233649425}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":76049705118943531393795779550839675695},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":38024852559471765696036364993535293829}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1087923318244118671},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":8514447500924255}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-10969141506438600531},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-9322065417637711481}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":545832417867367325},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":10394956806056444897}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-458430161489670101},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-373767594195252795}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":7999249115258235},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1082447760620433}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-3183200995013905663},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-331883571396510399}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3562308583004932537},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":267384027493484933}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-160411704096350379},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-128154736259155513}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":825557914729225},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-682090040711003}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":107586870398376361},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":134742093660802385}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3762038303931858899},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":4248489348865478265}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-16748588277044527},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-183833754437256711}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":227113389383451471},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1038987243186172309}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1035852282934985607},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-894396871241858317}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":313440548902290599},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":365284005431619259}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":8545841581107233},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-35037990032401549}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":392153299070651697},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":121150891737188989}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-317465751875523315},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-530461631061912635}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":272740760489999701},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":166565631564726699}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2537507061646311},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4775563277162443}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-35772689178709649},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-112905892558503837}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-452974844553539007},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-806441328461689701}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":42535295865117307932921825928971026432,"numerator":217663786226432259},{"denominator":340282366920938463463374607431768211456,"numerator":11902577293375569707},{"denominator":85070591730234615865843651857942052864,"numerator":2735756443023434967},{"denominator":85070591730234615865843651857942052864,"numerator":123092295012780001},{"denominator":170141183460469231731687303715884105728,"numerator":34805855347911349},{"denominator":170141183460469231731687303715884105728,"numerator":1682333161093141311},{"denominator":340282366920938463463374607431768211456,"numerator":4448782227845218577},{"denominator":85070591730234615865843651857942052864,"numerator":42773502120283515},{"denominator":340282366920938463463374607431768211456,"numerator":20826539335437907},{"denominator":340282366920938463463374607431768211456,"numerator":142477893242464903},{"denominator":340282366920938463463374607431768211456,"numerator":5182258673802351025},{"denominator":170141183460469231731687303715884105728,"numerator":326157206451319509},{"denominator":340282366920938463463374607431768211456,"numerator":1522696034330983183},{"denominator":170141183460469231731687303715884105728,"numerator":738289333790247927},{"denominator":340282366920938463463374607431768211456,"numerator":514248473971868505},{"denominator":340282366920938463463374607431768211456,"numerator":102736002322052793},{"denominator":85070591730234615865843651857942052864,"numerator":145309172110691677},{"denominator":340282366920938463463374607431768211456,"numerator":831182080660907193},{"denominator":340282366920938463463374607431768211456,"numerator":207296373467219907},{"denominator":42535295865117307932921825928971026432,"numerator":1819617361628135},{"denominator":340282366920938463463374607431768211456,"numerator":160561078078919891},{"denominator":340282366920938463463374607431768211456,"numerator":684791539930468671},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":16,"numerator":3},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":118443746842047374561636393895587847},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-118188619657258547148997016000730681}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1016882468882338719586459490226900697079},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1018720126482842736478972073144401909233}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1664300483369524604249143018172438653},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1550922231694634774721287387278545869}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":779076552539807768251759151689092201},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":417132708935135004764663000124723595}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1105007847340748728248825756537791},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":41370897953370831758796162330147}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2417755109042382940684881535360103177},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":648081464559535790859808151919460447}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1296109704775620552548634258276996991},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2417549574782614052590834967513101695}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":519401118798728874679397845992110629},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":278099798036588348879467581605455307}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":171292604398713996978702358773497},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-85655142718627836258795247478471}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-278107522040753638901038428297092557},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-519430728706786110380901619611318043}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":509451722044758223065398555379918462107},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1017221869733784432411362708537253895621}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10517740757012253119017080468907435},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-7887552664579990696455219747990775}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-58961637733945263618202662745973446817},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-77944086868404236819654843893906233641}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":9729669417628370058507964426564617309},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":29453549396931941739611206975233771145}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":66161006820565675154650108040147969},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":22706510858170262505288659063028463}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1837414978118236377040472873110567},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12040269754735586257826606886100091}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-19625598944856806250721053662017699645},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-25926149699974958563710575620862135929}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":25923797872237867665045447796965640555},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":4906096520203250531230878752763850171}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":49061512553542783744423759326151067},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":8413531927859296099555788515866085}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":70502960559891799369953362740007},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-563924268231416233135950966800673}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-4206836761439295947616404352627625},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-49064260763025714428167842678935723}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":4872781211632570847517737599090249959},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":29485974137820701245308773128673773581}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":262237780720242321600992701563645},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":131118890360118277407649495095761}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-507841330461305848136184740656074990635},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-507841330461305848156044655893509005857}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-504998683683364717862091135458037805},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4039989469466917779428877056140112879}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":254148444697100565463144423272596753},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1016593778788402260217931060898752319}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1310740685543082961576375805670093},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":655370342771541365329646750943731}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1576269437363864993496690365373626369},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3152538874727729975815783425502943105}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-197012603749220403709823417912521657},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1576100829993763237098242606701480089}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":338892677693311514267318538117791397},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":338892677693311513984324547033884789}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-36419837655028377178459979735},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-1138119926721792908169286799}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-169458756530108425119291717422931681},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-677835026120433700947199411558121089}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1016121676480875084365588814680204943275},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":254030419120218771087096840979666454133}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-4431421809935796407044768180157101},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4431421809935798704510602848156953}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-91164264629074690558998801355690842463},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-91164264629074690564357037408857191131}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":45481692977102133681909856499809619353},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":45481692977102133676717464733464593085}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":45489977531508498294092050530696837},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":90979955063016994780265618851925627}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-7591849305216809956203024585427501},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-7591849305216810137180107800071249}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-7570953510264192137085748534556880965},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-15141907020528384275196955246540384541}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":7569847518848503637750607966971150835},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":15139695037697007274036789451256329409}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":33741651142296050743705981482561139},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":33741651142296050378165269052401501}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":111640147298607204498948914093},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":13955018412324293133229160331}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-33743628842527141871043962515218907},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-33743628842527142154409787999101135}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":45601097150053113236700082362044336363},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":45601097150053113235492114661527894259}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":596473560761554449},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":37685601816634029}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-12457578878981516947},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-20596317534952396715}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":2405678622772319973},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":11771435262767687581}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-262839007709956851},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-104149332933581219}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":35333102261140417},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":160869266374629}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-458446239528878149},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2971285994017799599}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3954101579601567241},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":2438945686788879997}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-46471804076252993},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-72005489612620567}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":7119418336747077},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2774849924122719}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":60714999856254301},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":156956774675610451}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":4213363920846562097},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":614761000886018827}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":18126495213664517},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-164177815885314651}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":757439371101217795},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":84502052344584021}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-336754670009172541},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-741042723109636821}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":519128670904889139},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":238468355940280887}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":20571804887090717},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-37160851056390107}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":336350038986379223},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":344836249151587393}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-430158590410019127},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-445870075077355049}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":7190671180100095},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":57385944163295759}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3191047315185363},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4844454786915613}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-103720071131556853},"lo":{"denominator":2658455991569831745807614120560689152,"numerator":-1518528040401629}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-158406242613805257},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-705374166788876497}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":170141183460469231731687303715884105728,"numerator":1152881043501224313},{"denominator":340282366920938463463374607431768211456,"numerator":15790545909448575337},{"denominator":340282366920938463463374607431768211456,"numerator":14529077126532469117},{"denominator":340282366920938463463374607431768211456,"numerator":663564992071449321},{"denominator":170141183460469231731687303715884105728,"numerator":49539472076159069},{"denominator":340282366920938463463374607431768211456,"numerator":4451297616719867813},{"denominator":85070591730234615865843651857942052864,"numerator":1476124842647154897},{"denominator":340282366920938463463374607431768211456,"numerator":231926620011171459},{"denominator":170141183460469231731687303715884105728,"numerator":14775403674082009},{"denominator":340282366920938463463374607431768211456,"numerator":192064658558493805},{"denominator":170141183460469231731687303715884105728,"numerator":3423202731733538291},{"denominator":340282366920938463463374607431768211456,"numerator":966428606235020757},{"denominator":170141183460469231731687303715884105728,"numerator":1129843432430146311},{"denominator":340282366920938463463374607431768211456,"numerator":2191907830072048853},{"denominator":340282366920938463463374607431768211456,"numerator":763629083622429897},{"denominator":340282366920938463463374607431768211456,"numerator":152110755242903335},{"denominator":85070591730234615865843651857942052864,"numerator":215381565754009271},{"denominator":340282366920938463463374607431768211456,"numerator":1233635702813626775},{"denominator":85070591730234615865843651857942052864,"numerator":76968979427963469},{"denominator":340282366920938463463374607431768211456,"numerator":21701115180212401},{"denominator":170141183460469231731687303715884105728,"numerator":119020033231978199},{"denominator":340282366920938463463374607431768211456,"numerator":1013686859735809111},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":15},"tube":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":59166163190205400347079721050098407},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-58899737464528500956770335332713479}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1015283621371232841221979734695051596535},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1017465658141495999238049403778548104093}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2645606806814881178455622267843357107},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4352190120953535101362952944186076863}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1095336667542618686111549749316048037},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":166035458961423809240823863304238893}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1850762503360483574260019997889335},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":124371046577781051436405637974675}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3395776666776061698237508697021881547},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1031029853686779708184491582040152365}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2061921250367189414971988933052480221},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-848842975573894889958694238245131909}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":730247063180526660631280604461203649},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":55348744756004802561489372860791033}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":435848590576003938467520427834965},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-435932333361860146632024600160189}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-442810129445850238463490463230026761},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-730306412360964153736457887716089023}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":63609717577678258661192114068268689489},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":31742391684412994201129546937447854729}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":1339778910408602294430876945992647},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-9837606436306443535731156944432095}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-74132848020697919302074285770133647141},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-93081036497642534093987233870495306077}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":46445122163638365139126841234105717397},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":18506149273609193076603516166625389295}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":3364360688566887064376365721332955},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":46651429672373549738914984935727325}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-7669726857929152533978477393444615},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-4743813196550496789384116571884355}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-24654794269669764634527053618982610625},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-7732034528457305955426756677064524683}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":15461970440148949828807433695762597079},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":12326198506201519988234815889307287667}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":19966869532104711558757778211615133},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":17291983697662766403449847577166599}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1342851335887725525621886203677515},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1342372643909867409530260902012589}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-17292538872331996993415124419626995},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-39936764133966930176400094079932083}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":46558649517211884510061630367473122599},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":37076652897500641383366890940929798657}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":239041198620988489002646236865165},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":239041198620984964001943538869851}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-506924082488461976590286320966531663083},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1013848164976923953228873699833044222601}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-5474226108850538005493183875449284665},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-684278263606317256238795387284139523}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":690357299618603391550614996264542425},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1380714599237206781069790168819239587}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2425124543144768346718233214471291},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1212562271572384021382903528476243}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":534594057511300907231354564585741947},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":2138376230045203622115951608940337711}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-4276138769345516942980961363028962619},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2138069384672758480533626899289086797}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":920575798444478389306993848749762775},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":460287899222239194299002722450883157}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-45581322204228802863378736471},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-91162644408548242240129930559}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-460333605228839687140686709544295251},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-14385425163401240232308847070840639}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":507219118656255534042665122804817986811},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1014438237312511068064397675192415216383}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-3493103815785684532647737945073951},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-3493103815785686058495799810730317}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-106263706838730763470540357837895690093},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-106263706838730763477655635993170592251}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":52972772200025687479564768436049046161},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":26486386100012843736335517616070447717}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":144144193635141883644900977852984499},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":72072096817570940621632221758465417}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-24067737993614441095208760086319129},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-12033868996807220788778973462705401}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-17627960359831086030263507161615147443},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-17627960359831086031626672992271131631}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":35248950614312469922134834068102435511},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":35248950614312469918242276001065493731}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":106968869726841492915437593923601367},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":53484434863420745971259486463975583}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":960261132465433963166108260063},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":960261132465364881937164615371}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-106977326146501210955162543020986157},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-106977326146501211709191614024053173}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":26580913392014841954367294024773774643},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":106323653568059367814259470723051165469}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1247846565445173639},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":44501290291453777}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-13230169297737827691},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-10836990173179906679}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":20207651458507439359},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":1557492672484414747}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-282727882381182039},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-888192591134718271}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":1179585745198173},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3682711189201911}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-3966472559615742573},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6343868148152986233}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":8366272262274608793},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":5208699717270847795}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-202633653196382851},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-309778685568142371}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":7479264779091427},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1428319076092441}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":131221657887121801},"lo":{"denominator":2658455991569831745807614120560689152,"numerator":1345039268274171}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":8998787812664929261},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":2669887697357281135}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":104025766816172959},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-139362231564305637}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1171100830385789403},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":292634269869650957}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-290181016553251033},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1136146649544601393}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":398056999527112635},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":52087632446746471}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":22941296716746241},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-37947590336684457}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":541482047336220245},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":12216290354494451}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-106293045396541775},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-174423454349153253}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":45283181130964259},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":7448652902719775}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3775090806334387},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4802369270617621}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-61477260655577449},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-9837127888426369}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-21601179448769907},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-291230507332871871}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":170141183460469231731687303715884105728,"numerator":1461664032560567691},{"denominator":340282366920938463463374607431768211456,"numerator":19928623425679455383},{"denominator":340282366920938463463374607431768211456,"numerator":18334734572095855067},{"denominator":170141183460469231731687303715884105728,"numerator":427175749334372767},{"denominator":340282366920938463463374607431768211456,"numerator":134944196750189589},{"denominator":170141183460469231731687303715884105728,"numerator":2810384427567004123},{"denominator":85070591730234615865843651857942052864,"numerator":1866089986318181247},{"denominator":170141183460469231731687303715884105728,"numerator":150460842869059235},{"denominator":340282366920938463463374607431768211456,"numerator":40150305220590653},{"denominator":340282366920938463463374607431768211456,"numerator":248057252005030339},{"denominator":340282366920938463463374607431768211456,"numerator":8636778999635195123},{"denominator":340282366920938463463374607431768211456,"numerator":1334472946893264249},{"denominator":340282366920938463463374607431768211456,"numerator":3118405797379381855},{"denominator":340282366920938463463374607431768211456,"numerator":3023883785458400183},{"denominator":340282366920938463463374607431768211456,"numerator":1053877399851216985},{"denominator":340282366920938463463374607431768211456,"numerator":210730149892830487},{"denominator":340282366920938463463374607431768211456,"numerator":1190155129823829673},{"denominator":170141183460469231731687303715884105728,"numerator":851862585108353079},{"denominator":170141183460469231731687303715884105728,"numerator":212843779923387841},{"denominator":340282366920938463463374607431768211456,"numerator":30251884433346341},{"denominator":21267647932558653966460912964485513216,"numerator":20566008920119455},{"denominator":85070591730234615865843651857942052864,"numerator":350006724621043577},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":32,"numerator":9},"tube":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":59181001220406304730699295886237225},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-117390632859589232238626585770889437}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1013415888261136255645323508177831961621},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-507967262275832261526420533993965078393}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-960764505154008155656592840944461135},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-363273281820305239083121647726197999}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1466322104164190463186136988284565269},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":966623964857759126554796824631078041}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":394987471081533908183437185871295},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1105278565197617337902582056516523}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4540490394950660011386166625143249625},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":187395127446712776019247676603214763}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-187376688923603524843982735989374141},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2269886697438178508019115342255166631}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":244397994434117341857684396398544571},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":322236754229431161791986175336681219}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":586570775536034938634990846248621},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-293386387232836757083177729981187}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-644516889790396439034194662928816175},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-977698253090769053463914531534666113}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":254088180689206399022070530465917344153},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1014042259997320478861349052228048298797}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5088485813832080594657123851412893},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-378764875101101976126806566587795}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-89273627940355693828569059281155833461},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-108179994827545661132866477827482667925}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":53935744468723026086369226748158030195},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":22271176961238795037822523243748035839}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":164364241908532815775998216349516083},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":82826145413515236891850641460720515}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-13708350267180647731662596128560179},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-7115458424927592384773731882063213}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-29659805355893979342091329900158897561},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-35899892207521871404607970081821904993}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":8973282962784845848077918239320016607},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":29655640989200084676491568207647029577}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":121995848044316686198465024202288253},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":61426352755733813484982017535831801}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3114235226375780321164892646625597},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-778055687643504279395061365380807}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-30714717282462696728091621646135257},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-122007665766214296315227861650687955}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":108238379905720324136598790177423231333},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":44654642394185663365180194491895077683}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":400263612769973751785928033834433},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":800527225539939111104430479373273}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1011751154492477685113609711319978208577},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-31617223577889927661584968799517291123}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-1778292092619388249773709481905790589},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-7113168370477553051604982316337267801}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1798911123345657752271280623931471947},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1798911123345657749806926730129787507}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1032726670012618776229514650369755},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":4130906680050474714400798981580785}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5564704840887936209732604553548475243},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":5564704840887936193586658893508931795}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-5563679307080468032687979851003889103},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1390919826770117013531480513674302759}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":299858638911969939680600862023863753},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":599717277823939878927594892839944403}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-201408821602313389658814187355},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-50352205400607413772291488967}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1199589313165321334768076165565819399},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-599794656582660667741263682092745297}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":506255361782568714178424104645137032447},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1012510723565137428332059330105635784251}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-5170933988920776982688082998383847},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-10341867977841557865136070072049839}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-30330041745203677001314049124070770499},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-60660083490407354007172605805178524359}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":60423327893515744004528176884481046479},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":15105831973378935998930757976924698917}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":3353168118198999384175114699620957},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":214602759564735957517225678846831253}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-8962901614731529536150159510037063},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-17925803229463059381827545016583019}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-20096874525178259978950597823381473741},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-20096874525178259980693624434387807093}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":40183438546964955680487092383271528785},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":40183438546964955675511008572100809229}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":79672154310789591978674042679990141},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":159344308621579182711810103946054431}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1861179100360237260412353698429},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1861179100360147778231063576697}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-159360589559289009224492038833065939},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-159360589559289010189639678569403099}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":121409164401413226398549094160064252645},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":121409164401413226394446850495198564037}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":632945695234250337},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":27655944941802223}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-13276812494609021771},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-21908109415258746875}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":20370206944158368059},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":6227522366143589963}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-577093523595191415},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-912271237587444213}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":19669623047392433},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":4247820146823599}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-4072660341574294697},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6516187484988147707}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":4250464998155470893},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":5265715466761251435}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-210314427276868657},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-321158394240007869}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":7685042154112711},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2982260026008925}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":68402753238920883},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":90013650337194573}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":9263470379405156037},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":2750276385885297801}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":170163691322310227},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-225315646318924895}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":809081759124384701},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-2993068346114919}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":97873399856193677},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-386501755662090663}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":135503418985318191},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-31843338916565467}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":3136505225841505},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-19108015104465675}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":400219405111800037},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":10471347078619475}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":8928714993917077},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-122912083311886021}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":128904129435920063},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":823590302441267}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4296328420700889},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1170233517141455}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-17908926591051233},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-14673658901650923}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-3067838840702603},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-224593781994470025}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":170141183460469231731687303715884105728,"numerator":1788557995015399285},{"denominator":170141183460469231731687303715884105728,"numerator":12119498335981345563},{"denominator":340282366920938463463374607431768211456,"numerator":22297491088421458655},{"denominator":85070591730234615865843651857942052864,"numerator":266147022476178955},{"denominator":340282366920938463463374607431768211456,"numerator":177712916835968483},{"denominator":170141183460469231731687303715884105728,"numerator":3425604629156422609},{"denominator":170141183460469231731687303715884105728,"numerator":4550681918535907895},{"denominator":42535295865117307932921825928971026432,"numerator":47273105965776687},{"denominator":340282366920938463463374607431768211456,"numerator":52799064085823437},{"denominator":85070591730234615865843651857942052864,"numerator":77608435792297101},{"denominator":340282366920938463463374607431768211456,"numerator":10512980788501860103},{"denominator":340282366920938463463374607431768211456,"numerator":1752140283217023511},{"denominator":170141183460469231731687303715884105728,"numerator":2046038791968476153},{"denominator":340282366920938463463374607431768211456,"numerator":3967134032800937903},{"denominator":42535295865117307932921825928971026432,"numerator":172945717815106759},{"denominator":340282366920938463463374607431768211456,"numerator":277873189988677197},{"denominator":340282366920938463463374607431768211456,"numerator":1563859602607672283},{"denominator":340282366920938463463374607431768211456,"numerator":2237753381464629197},{"denominator":340282366920938463463374607431768211456,"numerator":559964106593885427},{"denominator":340282366920938463463374607431768211456,"numerator":40252459400427511},{"denominator":42535295865117307932921825928971026432,"numerator":54104205944636313},{"denominator":170141183460469231731687303715884105728,"numerator":919399702900592345},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":21},"tube":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":14807164625531218138634595897950987},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-116832847795620020619330390596621749}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-505643321702068728547298642042286857513},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1014132778485011341688237746271654640727}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-5251756441740845792558610497246175805},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-7476453112837767921904342080254008851}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1891291389746869268243216401088098951},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":82748990296008323211490854778340565}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1273806036300038366709011763370133},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2128446809583058551202202721420975}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1462110365365242276235003216409603969},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":4102120348827011481931001901571675865}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":-64087011953219963588668313702725829},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5847268808400470402736662738496293131}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":630469513153842979353720657847191809},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":441378831007616551515145051905556887}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":378816120758711526933763029863273},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-758067429575194405619258419375959}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-441419835410009956104782292148371171},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1261115067196614532927650733191968385}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":507349872167974565088032503703923058453},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":506042337050784254634358695812383969809}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":4392646855227426506782995017969373},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-7389364293265275354613340368958079}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-52188996206079389362456280264304465947},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-123235136677878626181190531422453258329}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":61385056144666088603699980115750577409},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":52038073983954531791445596667403902375}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":119309732004993956787364484350120079},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":133646941371270099873101474160645847}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-22197962786352856079241932054131875},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-5111964357371088279863501669093607}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-34635832624708790050521143073896187613},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-20418356787121305075289926684107002393}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":5103322221215119895592128128077439749},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":17314607131855763334315874043722897987}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":44303037732535111412674410468466321},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":99164060704252719308276654264710091}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3538002245834871110636435512188617},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-441769525519371985557388376507765}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-99171087763623017792326771869228127},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-177233471592404949420682284363552869}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":30830705840273887998559985080422624927},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":104434856924388680683150529412199766603}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":627664928284670430694417953181617},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":156916232071166384858006483102637}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-126174970359871967442615777874139960247},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1009399762878975739606957964755184432421}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-4475126962081775132966780227188778773},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-4475126962081775163318076108316271029}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1135185892658181387795252151676179137},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1135185892658181386331251789434283187}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":412850628728849734117767866712781},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":6605610059661595254120855413204361}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":7012577560005546355832425621227606069},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":7012577560005546337100889142033628195}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-7010973005793539975635457421963397511},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-3505486502896770000245250164300579415}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":378455471797873890292629467939067763},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":94613867949468472508097101241497305}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-50550681539073279036998708711},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-404405452312732488192760724147}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1514067647300348181396771675254422913},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-757033823650174091125589777485390613}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":252586331701063720374786671964242431109},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":505172663402127440735208828247171977779}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-14586959974476025889942466708487491},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-14586959974476030729115307671429525}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-136327981861011040302196412741010730049},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-34081995465252760078366991659868094401}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":67828024593264761966092987381837513681},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":2119625768539523811099206848348291625}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":304654667673936456791343034203566457},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":304654667673936452981117584129007341}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-25463266489763460116160833941785511},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-12731633244881730251107409227767107}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-45092702538059899970821777446832054481},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-22546351269029949987574922941104255093}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":45078172039472863019726492156400477209},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":45078172039472863013550777780934076203}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":113175148854905287157835313390660827},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":226350297709810572767375438623512921}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3331628740140080683182519378921},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3331628740139967871359616790353}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-28297402610604858640929391759344945},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-226379220884838870327151677613993775}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":68226960921472973301269440373730390383},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":136453921842945946597447475434019742567}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":312007212968018391},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-5617391529054839}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-12623588773204747273},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-10663732212697138163}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":19753073808974448661},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":1472675832616632771}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-140433291868791197},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-901474613647539829}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":40028545408239687},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":267711934793155}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-3990859956843332123},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6471643800720194511}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":8330087383112981043},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":1264681568038488821}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-209064869535756201},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-80628415132837079}},{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":60559240287937},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3162764530129069}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":17290227067759393},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":180576020746756537}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":9230053344180771567},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":5406055936801437909}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":28999248818827675},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-21374729497758005}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":445488352630207023},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-472601928737112099}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":236838104393985675},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-408751462692459427}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":143329108813615317},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-163536344618745447}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":26959799159915451},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-18931643747453063}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":128001731111538395},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-55062827536748859}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":112676794506898689},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-283754107596093885}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":76098492711409685},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-25937438752484641}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1190122020771161},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4515088587927411}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":25399017165944903},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-76414691291871469}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":30651366974603193},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-311912630972877233}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":4261630574555679447},{"denominator":340282366920938463463374607431768211456,"numerator":28663933054937610695},{"denominator":10633823966279326983230456482242756608,"numerator":823920697097087469},{"denominator":340282366920938463463374607431768211456,"numerator":1294129639155708429},{"denominator":340282366920938463463374607431768211456,"numerator":228009138001325463},{"denominator":170141183460469231731687303715884105728,"numerator":4062688158829278871},{"denominator":340282366920938463463374607431768211456,"numerator":10791840897839367779},{"denominator":85070591730234615865843651857942052864,"numerator":115939432612090257},{"denominator":170141183460469231731687303715884105728,"numerator":33835387371017363},{"denominator":42535295865117307932921825928971026432,"numerator":47396266711185285},{"denominator":340282366920938463463374607431768211456,"numerator":12452516977623217609},{"denominator":42535295865117307932921825928971026432,"numerator":277261313401891037},{"denominator":42535295865117307932921825928971026432,"numerator":647091476068395527},{"denominator":340282366920938463463374607431768211456,"numerator":5017970281605875451},{"denominator":340282366920938463463374607431768211456,"numerator":1751679998321099175},{"denominator":170141183460469231731687303715884105728,"numerator":176821220593168957},{"denominator":170141183460469231731687303715884105728,"numerator":990484829519970299},{"denominator":340282366920938463463374607431768211456,"numerator":2833303339428254871},{"denominator":170141183460469231731687303715884105728,"numerator":355080454485357441},{"denominator":10633823966279326983230456482242756608,"numerator":1617753847368383},{"denominator":340282366920938463463374607431768211456,"numerator":548951417540708921},{"denominator":21267647932558653966460912964485513216,"numerator":145527725455304631},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":8,"numerator":3},"tube":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":59322385208313970294899090694671143},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-116101290409504699905793372357063271}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1008904136530951074766219820722642741301},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-506033744910768098718942788740106315201}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-6865989672160741883361480681698376491},"lo":{"denominator":1329227995784915872903807060280344576,"numerator":-36475690059878332190215042741886639}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2369420641525291112545526402747585759},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":867760588440627021417985483307057431}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":7836616340562563871201825267629271},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1859580581107899070711331418051279}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":7315756334991384735367121394112596329},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":2685071781882665400027748074552970337}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-5369204462508255389526786222729706563},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-7313952908230381821138720306448276405}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":789870100247731844537697693859381281},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1157178372887037098830722252228541105}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":474272974086681892602042588723479},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-949404530846548092088226163151993}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1157319799734174374293996481963114151},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-790007467022821989517395559483455537}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":506400954267352337308154324229389678461},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":126236257354879026502713032371593711525}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":6448213029640155224987421621773139},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-35706865267652643606624028779501755}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-29860024021956714995124159435208673041},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-69120402508852670114046111548147667465}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":8598465951236457753152889564725359701},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":29746975073625876551778177797786767973}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":332712048789702879475217191541961251},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":25184938150800787440236630526431885}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-8384700125642029649718737760818731},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-56666860066148114056129621988752647}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-39578164564280653085045681395276330807},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-22867004712519660906800410855559620999}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":45719600946917059077955914672351945409},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":39568309391414721964128240983292543481}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":30906212236518104398559338075987375},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":74788521573535943996090229768299431}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3956399419051078002671844508681641},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-987394321442985806532727668165101}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-74795560978925257373609683634203309},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-247285797972235459519943883891744271}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":69182914237751141200786360785049799779},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":119525090615403331282543975686984753917}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1868111382641248128066094887358763},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1868111382641236915668830410727683}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1006803005248530649993512884151263806813},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1006803005248530650068490349497313698879}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-5489109740555598138474108986598832359},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-5489109740555598172927113734956153059}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2794190451608431003337315807878211047},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2794190451608430999916033165347679049}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5024406780610044575771218005829385},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":5024406780610044271349376810666767}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":8616127898510106088859856058625381013},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":8616127898510106067505787146635019339}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-538359125317470966999728781357141687},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-4306873002539767750150990870355173763}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":931566475686555205497150601692542279},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":931566475686555204882065588548203695}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-376418330470612481949068253843},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-752836660941405925401391469541}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-931751971397436443621080349184753623},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-931751971397436444124150312709317541}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":503974467222184215377787763718458987629},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":503974467222184215361427835215764278269}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-4950116037883945689095809378795907},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-4950116037883947155837435362031377}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-75640835525691993269702495318209060623},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-151281671051383986553058986177338213037}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":37590850234744534124052672353946960103},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":9397712558686133529360099303996357781}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":208266548821870545851096221578580545},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":52066637205467635885309345041260299}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-69674714678879810517076434565301197},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-69674714678879811458728372706636897}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-24974150218034503207661741327237347693},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-24974150218034503210286602762397264781}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":49928595481998110106461621194782370343},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":49928595481998110098974632611055490185}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":309688651158612750915042493378934497},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":309688651158612749034696364857128865}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5600407047747472360235645081499},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":2800203523873666563122368751909}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-154868428946604930215701132510894173},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-309736857893209861888586166692277685}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":37863312114570811954425038288190697051},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":37863312114570811952881456163369763263}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1197988979091652685},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-18165395013307907}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-11328521493342940809},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-2501617278285574453}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":1152691789122406147},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":10505184664174944409}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-520742467081238579},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-430728138770475807}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":39882383975047631},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1905162427181367}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-3727655766584261843},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1555638714585086011}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3939519839503004367},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":575579428089714933}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-99727350102455655},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-157058128838613253}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1920103713904079},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3383707788299625}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":135820707639530143},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":87094772953558163}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":1114284741610728221},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":5063419865087145409}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":71787021474080339},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-118596480961706183}},{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":753575658647779},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-51448779069243797}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":411240075192002713},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-60052758015184181}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":21095236678188357},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-142897088097325225}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":28586819837480797},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-18531414753170797}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":114437108446928091},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-255136015396914239}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":214237902252711143},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-82764523830009913}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":12440037037982297},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-6490120345538493}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2572757844541983},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2155326641744047}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":66915893775130209},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-9004410993482123}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":263590189729210085},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-87937845227719637}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":4970873352665873383},{"denominator":10633823966279326983230456482242756608,"numerator":1035828884579816207},{"denominator":21267647932558653966460912964485513216,"numerator":1905253922966596483},{"denominator":340282366920938463463374607431768211456,"numerator":1540284416035409481},{"denominator":42535295865117307932921825928971026432,"numerator":35798226454352521},{"denominator":42535295865117307932921825928971026432,"numerator":1178698113764642467},{"denominator":340282366920938463463374607431768211456,"numerator":12515958492353895631},{"denominator":340282366920938463463374607431768211456,"numerator":557754234408180985},{"denominator":85070591730234615865843651857942052864,"numerator":21237172576380739},{"denominator":340282366920938463463374607431768211456,"numerator":454344028838591937},{"denominator":85070591730234615865843651857942052864,"numerator":3608624867198842295},{"denominator":170141183460469231731687303715884105728,"numerator":1365305484268728585},{"denominator":170141183460469231731687303715884105728,"numerator":3183589347876318831},{"denominator":170141183460469231731687303715884105728,"numerator":3085504341880967087},{"denominator":340282366920938463463374607431768211456,"numerator":2156414134977119945},{"denominator":170141183460469231731687303715884105728,"numerator":219000572199378327},{"denominator":170141183460469231731687303715884105728,"numerator":1220037436618997961},{"denominator":340282366920938463463374607431768211456,"numerator":3487874127695723979},{"denominator":170141183460469231731687303715884105728,"numerator":437906032229306287},{"denominator":170141183460469231731687303715884105728,"numerator":32444455483751405},{"denominator":170141183460469231731687303715884105728,"numerator":338562590980357659},{"denominator":340282366920938463463374607431768211456,"numerator":2867431309549542895},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":27},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":118950854631064482702779210849990047},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-115171415475336140562266851326089007}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1006277490666501515851219681783038495783},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-252436670503423774450509999110217474555}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-8679282794871311598752802421558841019},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-711812130487106141910023784420171921}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2899791977080293273715544666181817227},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2200436208453703828101054324831176773}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":362059666701112712756097991939311},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":3026121736787796985167289964818339}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":8938140841072823850486349141024183965},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":6798626084331404391169171120032093603}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-3398568297592652948515429876785721379},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8935500701267646683076834238467734731}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1933382696474725230213678069347758547},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1467204019493358930120206214474283855}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1158761913263142218088532528263327},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-580170115491460695953165428647927}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-183428956023082424583321617026718593},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1933791639341547243968558127597234881}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1010665320086085182129785296219569633719},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1007465387267782175823399214792593796441}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3080722717652415619283892903730389},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-42762156032671481971400230256673187}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-134454254405580170416642415946992900285},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-4787235279996527164755699427754623199}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":1189665720939213625852978761672203919},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":33452313321807663749841974918078278535}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":448862457671790955802506875912915649},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":288631579896397063778740751817100245}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-48123249543733702781866107437750823},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-9519510487708234660802439109087157}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-44482191173282937094873540261704815401},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-25293652410526282927177954956976975323}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":6320956528944475220999979684611894203},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":22234114897954046020417107674079019603}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":83450644974161929450052878397802673},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":107205577622303222770752259645592387}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4368893285567326929708321927519517},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-544686951393005521387154198292967}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-214436845603837267150242373101205643},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-333860598413853286922167783813489261}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":153362724163120000451518021100633685201},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":134575166029593273946995192337837831657}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1331602979319984966236324729868771},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2663205958639957261973701665616465}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1003970709097214245027866522509097126115},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-125496338637151780638963788462566498285}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-6594580034244636103455785531038115169},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-824322504280579517746231410518483763}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":421171397239600866606526853706791285},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":421171397239600866113648860609566985}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":14681567814020933413474712700524531},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":14681567814020932670600086956966969}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5185359100525462437184343023427208541},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":10370718201050924850379901815298807919}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-1295916460576455887172584466204537355},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-10367331684611647129135237374916331035}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1123350110905608125970427196927115333},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2246700221811216250506262367079489655}},{"hi":{"denominator":166153499473114484112975882535043072,"numerator":-643551458503521313178162897},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1317993387015432358384880180971}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2247237667510273883740960610098232395},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-561809416877568471227551539361492941}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":502664542383633842444419492409209279507},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1005329084767267684852115607434183442261}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-6512759709566917421922941073148527},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-26051038838267676667215259884272085}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-41543988725816617879376115941087478375},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-83087977451633235766865263864763370875}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":82479384359125959799312244156519411059},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":20619846089781489945899637275560061397}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":276199422342905205760473958685129131},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":276199422342905203012725471101516611}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-92468298734695740650915114318917017},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-46234149367347870889342705556277343}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-54756189557470231640153926811919372957},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-27378094778735115823200833932135698197}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":54730292152802801794710255686982581149},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":27365146076401400892902827522782534239}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":411018318510929710423778422928655419},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":411018318510929708183147296856915141}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":8946054916287605475345124027965},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":1118256864535929571417675126043}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-411094599291008557105675035882448697},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-411094599291008558842502936160900171}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":83201303724903170841765849833871417373},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":83201303724903170838092143998816696283}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":560040316196913701},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-37217248757493945}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-9513464598760195843},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-4518932341704931883}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":16552345532575512451},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":1092672623454508749}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-228859430937579051},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-795894123149549839}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":38950067181374325},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1434327336685759}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1653299402019266665},"lo":{"denominator":2658455991569831745807614120560689152,"numerator":-45231869297918521}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1796179346653893341},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":986448379355766525}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-181938728151839159},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-296402670648684555}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1868537379784235},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3625056481981481}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":258816891971105807},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":80628456341314635}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":8343632802592957887},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":4504477688999359403}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":20840203985011863},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-17594868774825199}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-28040490158861179},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1134454094748949577}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1131351579620960401},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":259283753227978101}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-90847047620552535},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-197065344975150355}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":14981851519917857},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-8954257134309409}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-9701241477638725},"lo":{"denominator":664613997892457936451903530140172288,"numerator":-758001019321473}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":610855057769318657},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":103690176552022059}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-11424002989674675},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-150722863505927261}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5436260091368747},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2035705936953507}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":26305762487045237},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":74704639575371}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":393629464102206161},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-22919657100723039}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":5700774660185158947},{"denominator":340282366920938463463374607431768211456,"numerator":37640760211687664237},{"denominator":340282366920938463463374607431768211456,"numerator":34608583480640033705},{"denominator":340282366920938463463374607431768211456,"numerator":1802424341751701331},{"denominator":340282366920938463463374607431768211456,"numerator":353396606617777377},{"denominator":170141183460469231731687303715884105728,"numerator":5376425941365142951},{"denominator":340282366920938463463374607431768211456,"numerator":14257818888043762465},{"denominator":340282366920938463463374607431768211456,"numerator":660064042138947807},{"denominator":170141183460469231731687303715884105728,"numerator":52402447500362373},{"denominator":340282366920938463463374607431768211456,"numerator":535842784029631415},{"denominator":170141183460469231731687303715884105728,"numerator":8221055567660379567},{"denominator":170141183460469231731687303715884105728,"numerator":1643925189183046843},{"denominator":340282366920938463463374607431768211456,"numerator":7657966895849384051},{"denominator":340282366920938463463374607431768211456,"numerator":7420813613943091585},{"denominator":1329227995784915872903807060280344576,"numerator":10141041665698197},{"denominator":340282366920938463463374607431768211456,"numerator":530994782608282159},{"denominator":340282366920938463463374607431768211456,"numerator":2939523506707353355},{"denominator":85070591730234615865843651857942052864,"numerator":1049679470025027009},{"denominator":340282366920938463463374607431768211456,"numerator":1056378134272581183},{"denominator":340282366920938463463374607431768211456,"numerator":79698165878871929},{"denominator":170141183460469231731687303715884105728,"numerator":408498849699170599},{"denominator":170141183460469231731687303715884105728,"numerator":1726985722951447485},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":32,"numerator":15},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":119400897579464237614846426264778499},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-114020102461080218474235468764468459}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1003416632144644976906521425876097717635},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1007179268926740169308709119032895836301}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-5342226243756927628269969783971831771},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13622122423487265460622721421460419749}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1740699161079970025581978207702632765},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2717834021547152216444041448783141045}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":16566299734172338451607592627602327},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":9324648430892060775041971618053051}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5355454891582173310511747236731474953},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":8383374355770746006003819421540443103}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-8381140164769328419232385850850480927},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2676799641967849736716282540116271505}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1160595679098119471577277982520880431},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1812237572837207239387417067433228609}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1387667180538771561265128553524245},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1390404895535142483099777287670341}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1812584711787497729612793706788077367},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2321777021861249305906461423579120601}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1008296785224245119649055975977779312347},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1004818277425478230714251492768189197011}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1391425383157131915813813298884727},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-25393221197922485864948693723775551}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-74707481601937143347350798185110800145},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-168082041678971285141735536833163554295}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":10429091601074020474869677387117451863},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":37132459549238806586102806834652541779}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":294609156622068656120541262306489085},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":397345851465919284287073653296065577}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-16583697436592247971608705964828061},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-99734039071477178192848731895946215}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-24671708329186488810879419346916350905},"lo":{"denominator":2658455991569831745807614120560689152,"numerator":-432751987776041137167228719540854547}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":55366323614682989262573560146566855587},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":24662201733627672873731820209164710595}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":438521714622275130207261003172090471},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":295373866329316928904411160708438069}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4775027076820674035344918348439029},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1189224522186783568696517633710319}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-295417512223364869979423802680411927},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-109652742230453693624801556767730141}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":21038622779975984741892925517589931131},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":149580389149224955575568315577227536213}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":228904747813319799736628441258867},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3662475965013102651804289331036413}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-500456720243505658627169369665409462045},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-15639272507609551833545647972682255377}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-973412001748768021085885962918996491},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-3893648006995072105601681794116682329}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1997416664251738104059055241001343143},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3994833328503476203626548458479361307}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":10372877082139950999771409337980205},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":20745754164279901104545321007154255}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12271347277660623774851378719114128587},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":12271347277660623748238028391670728561}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-12266703576660224007055456251057973251},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12266703576660224042235216965803890381}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1331898051104721856934834886869951865},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2663796102209443712215514311439273857}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1096454868874219342952024745763},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2192909737748704532583299113149}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1332274270470625000559424827230500467},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1332274270470625001231264703986374071}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1002493918660615237816086567213727974031},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":501246959330307618887691003737414861649}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-16698206609714006115596201073392007},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-33396413219428020404866553479896247}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-90502885511053754806144492255002108879},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-181005771022107509631269084655592857757}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":44858155656655206309634976363529923317},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":89716311313310412600891341065143336035}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":357167152593002032931512508610868289},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":714334305186004059427492570476633463}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-59834200787429389953034819120004895},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-59834200787429390618273224232602255}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-29756077615095102646664346906133628933},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-59512155230190205300647723924478263047}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":929359310721127908447148302043052299},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":7434874485769023266274128309821254365}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":265975830138743841893256633697368869},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":265975830138743840579046985273920615}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":1712416795654450637454636885751},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":3424833591308850772099648399137}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-532067263684558930866236261595151777},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-532067263684558932904194118478493083}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":181297614856198583325577696477545258237},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":181297614856198583316970785408666628625}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":509568044400664367},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-234156088615929915}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-3641428164463271205},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-1959511590541833807}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":14237074838927074729},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":1647340898354626263}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-47225266653518823},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-88702988381616367}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":37335736819731621},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1483604126885561}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-689586558722981673},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-650797143926075097}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":6305450109299236319},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3122874119362929071}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-79072140864833505},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-271167042300581747}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3580103005542009},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3893671063292965}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":119780519557515199},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":35703875778573217}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":118154052089768837},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3769529496168077613}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":370124716244963765},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-14211599680683755}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-31559375758030491},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1399379589025228525}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":696691733832012949},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":537382748372806305}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-94177785876370639},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-243018382106936997}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":31062630631195183},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-34164573660711813}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-70414737791177737},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-252626836140495787}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":192017460718880293},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":4199553615692187}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-32659143921943969},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-191359486421329409}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2818088550053209},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1913978228464249}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":139195104843704659},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":18732036563607537}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":127246485982837295},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":36878715729769631}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":85070591730234615865843651857942052864,"numerator":1611336198538980851},{"denominator":340282366920938463463374607431768211456,"numerator":42094747262718645995},{"denominator":340282366920938463463374607431768211456,"numerator":38692420262127107891},{"denominator":340282366920938463463374607431768211456,"numerator":2079870124849272313},{"denominator":340282366920938463463374607431768211456,"numerator":429572682487980047},{"denominator":170141183460469231731687303715884105728,"numerator":6041329852731681485},{"denominator":85070591730234615865843651857942052864,"numerator":3999648090601201235},{"denominator":340282366920938463463374607431768211456,"numerator":770566350864857567},{"denominator":340282366920938463463374607431768211456,"numerator":127396401087622319},{"denominator":170141183460469231731687303715884105728,"numerator":311733554377752419},{"denominator":85070591730234615865843651857942052864,"numerator":4614028737665140347},{"denominator":170141183460469231731687303715884105728,"numerator":1943781558931695239},{"denominator":10633823966279326983230456482242756608,"numerator":282588602635810927},{"denominator":170141183460469231731687303715884105728,"numerator":4380652735656322751},{"denominator":340282366920938463463374607431768211456,"numerator":3068925627141985199},{"denominator":340282366920938463463374607431768211456,"numerator":632624802966643861},{"denominator":340282366920938463463374607431768211456,"numerator":3477302957756184539},{"denominator":340282366920938463463374607431768211456,"numerator":4962583220357045505},{"denominator":170141183460469231731687303715884105728,"numerator":625594524567363759},{"denominator":340282366920938463463374607431768211456,"numerator":96273552472227271},{"denominator":85070591730234615865843651857942052864,"numerator":242028353145856465},{"denominator":170141183460469231731687303715884105728,"numerator":2042920639101704923},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":33},"tube":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":30004468101407320260719212533218497},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-56313414779610427579131952993458659}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1000332216249613150755537895168814011861},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-502187493040140516686753621335307172583}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-6436832916713071214836903772810949349},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-8014304092028720101025720255570979773}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4113148573881190558391787311267096725},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1643364622515937707261117741026389251}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":23021702787615710742805374462904053},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":3438721537572044887866480446764169}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12629018591601339513399814711282909189},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":10119795935434212110044355693631323827}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-10116593269697480497257807575031828993},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-6311988709419573249243243461026635955}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2742431314907386325168549963287532349},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":547904747311243782774835319680114129}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1634586026450424401674052184957235},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-819554784316271699333039230167715}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-137007869202971683941021105662056979},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-685810877468704087475641171655715855}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1005703767111745654302755626373287404443},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":62622308979185372510224325813976387857}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-7031084039205991587106162976907807},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-59832393326491559970884606677371459}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-41079229229710655327136214894127514939},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-182907296763081123398140899255885341643}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":90665357914543682291569188827819148937},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":81569831741857323949379588888395561265}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":47240529621212499349289435985287227},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":264896665162150226148104235957915613}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-88546971779653634482058768160940887},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-63880120665037348085310015358723315}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-6769683918495746013627130233725399019},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-30072326721504301710192944545970872325}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":60111359819643861412655464773684102121},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":27066197872688008691411171304607962617}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":563011169012620534654422010129325763},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":394130224010741838575227639935174455}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5174425508791971075651906207489231},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5146748751322851652310849566347211}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-394200282287612555873872123696470607},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-563143452321572568191899046532995953}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":91600114777369168280284679442925313295},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":164536204993702786689030390987940004835}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2442059627276302607039133462582861},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":4884119254552589584558715884891497}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-997642426734829813693096584447637737729},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-997642426734829813794216865770933428911}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-18125518849221127415355265719385956107},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-18125518849221127508201588608188988049}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1167354250490344333078829796897475197},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":2334708500980688663623750926856785571}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":28503390354853310850025119055595745},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":14251695177426654891871552640661993}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":7156341747174682167567719058514114639},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":7156341747174682152958988508703430201}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-14306509927757095307839389403816745509},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-1788313740969636918299275440482216077}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":778408928395157619166355419289672719},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":389204464197578809347056037210445767}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-436919810645741623036883475695},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3495358485166249705208909100833}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1557329608593300080152972187144398937},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3114659217186600161835317859349509217}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":124931516080992018091206464096761349807},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":999452128647936144685009298298812816935}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-20941462039507230074095407136806059},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-20941462039507234797170280332311969}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-195766289118928311266320993927709657085},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-195766289118928311288226732559802918491}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":96887936578860144918366901504339668343},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":96887936578860144897157925268228111525}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":452169013598581029618819159715143153},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":452169013598581025900413079854145257}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-75812084262726519059838384281047925},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-151624168525453039669738619122167817}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-32106065671251572422596120716057965625},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-8026516417812893106706641374663013389}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":64170601686059162123510181672160304673},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":64170601686059162111468755829142901223}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":674051015846462544370447034397730033},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":674051015846462541327748896783650923}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":2530611621479196786784491665521},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":20244892971833335536536398522909}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-674219928132476931734172551349070709},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-674219928132476934094281468870213709}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":98067025389519075674157879761892969739},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":98067025389519075669182915537374745009}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":112882105860744275},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-330523299223921363}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-2400828655439062039},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12953979173199996497}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5814894756298271563},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":4217349722134093853}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-284477402198966497},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-608856748017908623}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":549114663990411},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-211979077727573}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-131824234891228411},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4511264079016921691}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5294212653745547011},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1097750752144971647}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-129581218382551193},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-240163076805824861}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3384147380713689},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4166821728561773}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":215084922720493705},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":120055882047849741}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3309737164410297957},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2894552168120911049}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":396121264632726481},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":5694680034695937}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-737122345243568133},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1608024366384125697}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1598159700505694199},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":191509213190553259}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-268521143712141431},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-278957211728891501}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":31943236528044845},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-32415898591585313}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-30770414230228649},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-150982777506922165}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":447391417563781159},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":407556320616886385}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-101257234340714411},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-112173248213811359}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5741527735429721},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3592819479647105}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":84077399477765217},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":68133703134804973}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":607444594023143917},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":11191415937040231}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":170141183460469231731687303715884105728,"numerator":3598984851232599665},{"denominator":340282366920938463463374607431768211456,"numerator":46483979730486909381},{"denominator":170141183460469231731687303715884105728,"numerator":21358470774585145667},{"denominator":340282366920938463463374607431768211456,"numerator":2371718994028693759},{"denominator":85070591730234615865843651857942052864,"numerator":128865837025144735},{"denominator":5316911983139663491615228241121378304,"numerator":209495193584875795},{"denominator":170141183460469231731687303715884105728,"numerator":8864025742646344847},{"denominator":340282366920938463463374607431768211456,"numerator":889195760525925535},{"denominator":85070591730234615865843651857942052864,"numerator":38223224668913265},{"denominator":340282366920938463463374607431768211456,"numerator":717172222194033689},{"denominator":340282366920938463463374607431768211456,"numerator":20458746157289148327},{"denominator":340282366920938463463374607431768211456,"numerator":4527861580896490637},{"denominator":21267647932558653966460912964485513216,"numerator":657338644092271995},{"denominator":170141183460469231731687303715884105728,"numerator":5094213347092018913},{"denominator":340282366920938463463374607431768211456,"numerator":3573709439988177109},{"denominator":42535295865117307932921825928971026432,"numerator":92856419715027613},{"denominator":85070591730234615865843651857942052864,"numerator":1012890221125289549},{"denominator":170141183460469231731687303715884105728,"numerator":2888549832126681879},{"denominator":340282366920938463463374607431768211456,"numerator":1459804437763585401},{"denominator":42535295865117307932921825928971026432,"numerator":14338962019982777},{"denominator":340282366920938463463374607431768211456,"numerator":1130043910850208769},{"denominator":340282366920938463463374607431768211456,"numerator":4760773255002974619},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":16,"numerator":9},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":120342408149576905220849509790810623},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-55292331538652195359449072972773995}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-498517931531885349243009476894154768957},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-500672141211463470832399763940408731051}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-15238530749242845371502404044923728867},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-9299571768308637515110057731851311601}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4793720191497993923657699064303865271},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":244129257594005334115331828621295085}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":15346880112961975349836981561641055},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":2455052519678820282580236776736179}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":7343434460581423730403626123156456923},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":6001477991969077223420723859520617567}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-11998536131057723385885675274503819889},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-14680210587082729597583482841022097951}},{"hi":{"denominator":332306998946228968225951765070086144,"numerator":3121240080047666617584991894175217},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2604645686680625167305345468414895645}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":763471074011610728386442496206503},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-383471726135067684009253017205993}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-651339950139497098190962068710910383},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3197247204390604476313859871993979993}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1002894296308412178125831475849049391239},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":998890519830442775028382391694858474711}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-18111348303316835563334231625104085},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-65641967009886963342613294199693481}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-89577596522040632325641950760090822439},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-197660972824343714261334729219384118123}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":97831138486582691048163641074625172729},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":88814663849613492773416640819753881341}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":947538799413314284663578410152222395},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":344211347358151461645074727532825371}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-115293380776990836697921720764835569},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-79521794377835134389699348246661113}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-58920200721998064441353028979538296787},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-64839745803919472961109675107804652023}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":16199488854588462269645100641598893459},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":14722000095643555895093051667230042217}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":706413331182357228412618010721509415},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":256283515088473310176017749762980407}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":634505684889137382609344012320581},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5035697570787420304090633595976903}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-128168734643061811020453437118521871},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-706598189695364111926036680661474861}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":99015282822013488836657534266087373623},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":179438398101995428388488087039496475939}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":6341494520501993524639047785351083},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":6341494520501976403785055522193525}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-994169476624198375678765713739169593785},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-248542369156049593947052351344884774477}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-20832498944001718784544326732813162947},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-5208124736000429721251743076512529445}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5391888706185338802803385015449387269},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":1347972176546334699282784017158421839}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":19117943347841121446205648712187007},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":38235886695682241634528176972945939}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":16489099156832881141386775947571957337},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":2061137394604110138700374503558766629}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-8240554736701540741108809883792919653},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-16481109473403081524093790908158767339}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3595379828021770540426490161388729333},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1797689914010885269143213254019545101}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-5370599786571849549495925807617},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5370599786572223237241192582529}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-449592264120653367412294544284175083},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3596738112965226941025140556286343763}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":498106452897314178391928388912159165487},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":996212905794628356735345105911665730879}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-51545198723787433131582633975141833},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-12886299680946860981501749625588795}},{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":-1644163470116260603753005126615435117},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-210452924174881357305381822530892668209}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":25997486988450886884225465514307843611},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":103989947953803547512702447437898147593}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1124319848122445942541677422620197359},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1124319848122445934043636585385568013}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-188671876789701251282748949058176747},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-188671876789701253069506362539719943}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-68852209436821873712336357244556342645},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-17213052359205468430501696334862269599}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":68801175241458243963715310242552623643},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":17200293810364560987490728196877731989}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":419412788383823461662249750991467049},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":838825576767646919841389379018425191}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":14511050448195266102983590918297},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":29022100896390252803009865846483}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-26220773742522242407672138423574505},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-839064759760711759748133838143589203}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":105453934794604518989402930399290193737},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":13181741849325564872964562331603921703}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":195433623115612819},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-212763840807921109}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-545444218428477749},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-1260454837599003957}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":1113177885443643327},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1733229861573337691}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-182550829844867655},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-498114888483042427}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":4067919618336909},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1089648331269893}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-699938421775794021},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-934587856001848103}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2104392641705556059},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":149679259808476681}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-24218141193896443},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-102492890688648225}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":6320852175739129},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4440753145598161}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":93416992365691483},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":93861541638917723}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5562941749667695301},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":482454047003774569}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":411066943289490743},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":30341814060017201}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-912346380698545121},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-439519257892324381}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1743679931880321825},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":936651009110196633}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-164193770539532831},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-609051386069275673}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":32728446181501287},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-30394080055809205}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-166302195642901771},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-340768127664924513}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":123675750090032143},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":515557369583200733}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-4048835501920009},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-15589809497356979}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5786099302863713},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3384562659036549}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":95603141407000259},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":23404429372137299}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":85780219787925763},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":267593909647293853}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":7956795909092432031},{"denominator":340282366920938463463374607431768211456,"numerator":50770914906645691731},{"denominator":340282366920938463463374607431768211456,"numerator":46645226175630572953},{"denominator":170141183460469231731687303715884105728,"numerator":1339171222044381285},{"denominator":340282366920938463463374607431768211456,"numerator":611580233421096507},{"denominator":340282366920938463463374607431768211456,"numerator":14722652669323009967},{"denominator":42535295865117307932921825928971026432,"numerator":2429051245976851835},{"denominator":170141183460469231731687303715884105728,"numerator":507987609186982113},{"denominator":170141183460469231731687303715884105728,"numerator":90731534986359405},{"denominator":340282366920938463463374607431768211456,"numerator":816905879460238927},{"denominator":170141183460469231731687303715884105728,"numerator":11219636587750000767},{"denominator":170141183460469231731687303715884105728,"numerator":2603424808824434951},{"denominator":170141183460469231731687303715884105728,"numerator":6037858918311555207},{"denominator":340282366920938463463374607431768211456,"numerator":11696192848281550829},{"denominator":340282366920938463463374607431768211456,"numerator":4108688496122209667},{"denominator":340282366920938463463374607431768211456,"numerator":861817443622116351},{"denominator":340282366920938463463374607431768211456,"numerator":4660748115424345133},{"denominator":340282366920938463463374607431768211456,"numerator":6639274411952319637},{"denominator":340282366920938463463374607431768211456,"numerator":1681617953534118765},{"denominator":340282366920938463463374607431768211456,"numerator":135116147677044923},{"denominator":85070591730234615865843651857942052864,"numerator":325629605407969215},{"denominator":340282366920938463463374607431768211456,"numerator":5477107822130763987},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":39},"tube":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":30329716587910441754690584920483405},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-108645742713009577087900416640862935}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-993538836270703034607069218462391324941},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-998098381230843900370566604605107357747}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-2221256494927711161474874756658915287},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-21324720857416070527361672515394404849}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5522165470233275309608925479397799505},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":2287333586076694331270338381039703131}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":40879677037081111855992971980566303},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":13564123695080665887857548989412111}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":263738126401283577097151177309491245},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":14027510539312388236106899180804212087}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-14021601801960976699666211847938498677},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-16870683059922162781397985207697711439}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3681811454170556310745310877325641925},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3050505075737305381891018877831862653}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1780816634987607571890305002584295},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1791502083847810421375349048985177}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-3051481618807355539105510778483481941},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3683257602599801751109844537513385715}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":499938542133055905632632575534231593167},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":497813764042177572954565385161881281555}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-26172554805785177715046592003261871},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-76909265350496022345323989062663145}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-24240574169874741075227761746013736909},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-106170775479150877623405545682542128923}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":52463717799488778973392539823485883161},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":47997329454979105056933009490904782965}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1172647451183444664397464680925122845},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":874525868976463983734532746348280749}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-73290913785259766466983376653807761},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-49251309279963646197766176707290811}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-63627362100843970943133395308201630891},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-34737527258717854981860927174160689463}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":34711816760789698658897629936528598057},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":63586931482112469310765810691038728951}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":437546990256420306483411162986262665},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":81464113582663677782092561706121227}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":682758574034504898211441213091573},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5404184566027648822256644354778833}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-651871776485160860737164292042603149},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-875353292958321570707244686084023195}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":212799368431858797716707748519756915461},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":24285293602201704384263202222621037905}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":4020994870628148511599127789703535},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":8041989741256278415482478780936233}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-990506899144135722782393395907279542393},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-990506899144135722899864064390892700791}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-11842857240093606427343794226363406089},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-23685714480187212962492921789584999411}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":6160947225015393486901000632631720913},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":3080473612507696740298462400578688859}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":50243256657553199845565371923944339},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":50243256657553198374726512582226325}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":18794705790844653691515400471430641597},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":587334555963895426787644548404576157}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-18784607992249616699803372077954549907},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-18784607992249616744920775522147816417}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4108137922722025745311917811517230705},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":4108137922722025742904325872269360271}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-7993781370567432531015293934059},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-7993781370567869634400250654789}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-513737794498909356242582316573896113},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4109902355991274851877103906916464339}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":992785885077856335133390995107062917139},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":992785885077856335081085511408220403273}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-31202992052593606215577727522051345},"lo":{"denominator":332306998946228968225951765070086144,"numerator":-60943343852721899068259092721309}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-225061347877216646326715236866195221533},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-225061347877216646354958211220712607577}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":111018276478226481406527066098084354871},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":13877284559778310172398538744132870537}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1376096634411764244976635511893315939},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1376096634411764235360670084611190353}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-231134084340954978726718836836261031},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-115567042170477490383685349783767563}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-73428646820726024592591079813762987377},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-73428646820726024603536692755166953583}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":4585435082001861123246309806357848375},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":73366961312029777956388810165445737577}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":513864287413930408947591635623924077},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1027728574827860813946495935434816491}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":40525059849265944817732381200751},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":10131264962316405153459148395403}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-128507268823638047636442209012952055},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-514029075294552192078431275704812207}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":112807604538715611971994717194659459501},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":225615209077431223931116022479274617923}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":41007214072468195},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-514570108860550409}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":194652128839428701},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-3591972574573440481}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3084502983244664545},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-689328654096017243}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-79122079448748529},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-95842058039135005}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":29603593862206377},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4260080366671397}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-659584856078809429},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-366611858849945471}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":387730218939444055},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":101910001696178967}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-62314778058710715},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-167118373592675301}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":182526818417899},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4696705949255361}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":155915698030253415},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":65223574959175687}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":556895548616331981},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":459662571958471945}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":207354632591969043},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":46213008218234369}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-515757720395680007},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-922559330963270379}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1826003995136466193},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":32839967189843735}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-46066972020574107},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-79763732379538095}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":33222431341036921},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-28179277817184775}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-397582514902574085},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-23023798796717049}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1049049347837583143},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":295913865192656765}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-149904716618977973},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-66425208171139677}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5745840149608465},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3208793270451383}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":52028025626620609},"lo":{"denominator":10384593717069655257060992658440192,"numerator":3451057082621}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":744120591843419785},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":336239347292259151}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":8718515121389214653},{"denominator":5316911983139663491615228241121378304,"numerator":858573586537401719},{"denominator":340282366920938463463374607431768211456,"numerator":50473499358136420449},{"denominator":340282366920938463463374607431768211456,"numerator":2999914839383275851},{"denominator":340282366920938463463374607431768211456,"numerator":718487592556420119},{"denominator":85070591730234615865843651857942052864,"numerator":4004683113470431279},{"denominator":340282366920938463463374607431768211456,"numerator":21109690848035036001},{"denominator":340282366920938463463374607431768211456,"numerator":1151394171856952923},{"denominator":85070591730234615865843651857942052864,"numerator":53320727602261575},{"denominator":85070591730234615865843651857942052864,"numerator":230719156406777213},{"denominator":340282366920938463463374607431768211456,"numerator":24384822226914400953},{"denominator":340282366920938463463374607431768211456,"numerator":5923122799468407003},{"denominator":340282366920938463463374607431768211456,"numerator":13714685566691102649},{"denominator":170141183460469231731687303715884105728,"numerator":6640907774989980975},{"denominator":42535295865117307932921825928971026432,"numerator":584149459025650855},{"denominator":340282366920938463463374607431768211456,"numerator":989625076786526199},{"denominator":21267647932558653966460912964485513216,"numerator":331451059212862335},{"denominator":85070591730234615865843651857942052864,"numerator":1886865639853445851},{"denominator":340282366920938463463374607431768211456,"numerator":1916445609873725463},{"denominator":85070591730234615865843651857942052864,"numerator":39406157795944911},{"denominator":21267647932558653966460912964485513216,"numerator":92821781727589077},{"denominator":170141183460469231731687303715884105728,"numerator":3116382666373285111},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":32,"numerator":21},"tube":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":61253742973486543976767072891160871},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-106432505702524954897833162999153901}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-989853801647288445287570064434523009647},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-994648996066077256954947110173321247221}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-20458860654693876274965733837108781125},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-24195243547772301370751660595129343793}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3148516682577715243555947856279364473},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":5291317077410884164911051419417209895}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":13347877213021529555752431795723021},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":9137982169576008281174162320091993}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":19200000905945881846992325563681008303},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":16187887851375881027670848057999674051}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-16180204924336455699361533596140772273},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-9594625207501356763961196555784093525}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2099185306822574220805103879914833889},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1764190425920697607847447506752109927}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2051238333449143462392894427493853},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2067159659963942476148829713446985}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-220605160457996445798926868064182037},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2100119011850390598969046171234268879}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":498330613858175017233917188515422763529},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":248044502124783314407014596791149205443}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-35514549548641662790932157629884335},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-89292817662453600145282519787786127}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-208620671941453420097969718469763045515},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-113471597137866395961059546820433142283}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":6996835521528957166429398489371568947},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":51552783955198453359119672019445173179}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":357429133795185141197394830251902277},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1090386882893746530627420481536090607}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-182922273000385186692907460833044229},"lo":{"denominator":664613997892457936451903530140172288,"numerator":-469567013463956704279922156369363}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-4267194150534643542829778389227186359},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-18511534172807516738968870549456333799}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":73983927347119603186227528638773193785},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":68225313896384759590377955226368092247}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":33376432428553237029383151705818519},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":406678329442375867415201707587489097}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5840776333815134379346512199886761},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5759904485318426928069065655936123}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-203395759243792199267434880657801903},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1068400264830598396827426392839717539}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":227501078526674635389365359512522160133},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":104532089853634208015831367296949003155}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":4992978499539171560174450690813273},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":9985956999078323035019490430243321}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-493333710864928151979055878773905723531},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-986667421729856304083317243421986062295}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-6668760106046089377750712067792406257},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-26675040424184357625892096480831824641}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1743807404914166132070678150699664889},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":3487614809828332260658894352380187649}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":64843285933799333603208657461055131},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":64843285933799331896945512291299415}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":21223389928405796821478783445206331671},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":21223389928405796784702213429095751893}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-21210895216534512864203937253655976703},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-5302723804133628228119437807326897227}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2325485663938108309209799298730294987},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":4650971327876216615727418580693420199}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-1446486880181966480809237568043},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-5785947520728119583545837119765}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-2326610414460992464039631638586406701},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4653220828921984930237564121793825369}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":123647636225200740121403808843045139027},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":989181089801605920915242306301382408455}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-18619029949924620177261495618893611},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-74476119799698494413279674197537455}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-239587498306314910495420722019956718481},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-239587498306314910527058018210622669705}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":29492276360619452514072363401155395725},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":117969105442477810025667519319848651017}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1661388630737800910514736702655014023},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":830694315368900449862596989676448657}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-139659413503110288725439104808758047},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-279318827006220579762911167549018075}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-77937873675230075994314224352389356547},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-19484468418807519001649266373966984395}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":38932195483658485513284265964567927031},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":77864390967316971009131367636727407261}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1242154790739728433416573703639638137},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1242154790739728428977643170323996537}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":55301796675137182646778168214537},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":55301796675136809212868878237589}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1242598162409306883075380056803977421},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-621299081204653443261385370280513547}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":120126199262352541964223643505962776269},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":240252398524705083914000357289587553411}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":134126769657835901},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-593228572565362357}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":707583300699284937},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2211858281178593605}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":896017670930962921},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1489334890324642393}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":21463083811905705},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-271557998564243209}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":13233287879961875},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6443530457009445}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":65224948115821277},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2121274951162725457}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1016073469637014891},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-374373491758954999}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-27553735482498535},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-128729286727365687}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1335471381070173},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4923079144022935}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":61830996420458459},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":36038919628193513}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3329822068076166833},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-74855447163538581}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":408237976691338379},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":53012351952951927}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-546489617575254799},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-937421063783063151}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1851362614663066515},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":276770050007091431}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-388336330056378063},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-647247110296028853}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":33585084696556401},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-12940244401153099}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-441634513230312091},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-768763568031381123}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":537872216351093567},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":635858446667175283}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-162095973678428121},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-273613779692530109}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5626482703120327},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3065970470017303}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":218421289265967069},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":126714510135462965}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":12183103591772339},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":385780195576734537}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":9477796879877338631},{"denominator":340282366920938463463374607431768211456,"numerator":58975718054510144137},{"denominator":170141183460469231731687303715884105728,"numerator":27081626936322265785},{"denominator":340282366920938463463374607431768211456,"numerator":3335951407831067671},{"denominator":85070591730234615865843651857942052864,"numerator":209169129869102815},{"denominator":340282366920938463463374607431768211456,"numerator":17295035058416016521},{"denominator":85070591730234615865843651857942052864,"numerator":5686615006607459053},{"denominator":340282366920938463463374607431768211456,"numerator":1295502232761151311},{"denominator":340282366920938463463374607431768211456,"numerator":248527826552695779},{"denominator":42535295865117307932921825928971026432,"numerator":129417360713018035},{"denominator":340282366920938463463374607431768211456,"numerator":26291743463869499173},{"denominator":340282366920938463463374607431768211456,"numerator":6674504033491788279},{"denominator":340282366920938463463374607431768211456,"numerator":15427716649125167259},{"denominator":340282366920938463463374607431768211456,"numerator":14938825935069115545},{"denominator":340282366920938463463374607431768211456,"numerator":5265315971531232959},{"denominator":170141183460469231731687303715884105728,"numerator":563141846108159845},{"denominator":10633823966279326983230456482242756608,"numerator":186808001385586125},{"denominator":170141183460469231731687303715884105728,"numerator":4249319576593358737},{"denominator":340282366920938463463374607431768211456,"numerator":2163706363650769805},{"denominator":170141183460469231731687303715884105728,"numerator":91185364029209829},{"denominator":21267647932558653966460912964485513216,"numerator":104865122019579549},{"denominator":340282366920938463463374607431768211456,"numerator":7026495644020651983},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":45},"tube":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":61955081977376267880918348324965459},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-103946160388135161045632217740506997}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-985993534642566020416804671614026668099},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-991008384088754578731315108277102621707}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-23295177007898283789949994526127352419},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-13600275865393787218662965796549347225}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":444809589797391701424401001545827977},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":756840539074939827544150413719684361}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":34274280755744743861769252706304829},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":48209333896004721780413824598488671}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":5410753161579408180620389342049182563},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":18478227251347655983284966213582709381}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-18468477922953505837363834168850076851},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-10814889307957307230879605530435775929}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4744882976946037991396584914001534307},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":2018694236126345524313703978314934047}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2337334239591677146647659072491509},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1180200391381042947899501231071527}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-1009771443456279150156143083241736881},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4747251595486699093785432130185905769}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":993256313405349852382561857073944450847},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":494276015065207339945426619802076184661}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-23075777993067640892153554674424955},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-102800032687577663843746521371973215}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-223239067904901753545583935126124476807},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-241461867628050681356896950327808668513}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":118893145526841208717470248233028487117},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":110143291028380400563823649899841988921}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":860225863819497389441091695405401845},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1337834957386516397191612806253093809}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-224639111667211125809545007338666053},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-36198604800581206872660137911420035}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-72859669877843707744235170028520375981},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-78549439306666876227794265681923234385}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":39237643189545148633695201665789352625},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":72799369637911942477388632902650601663}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":321663641176038769530709502806250695},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":998959020397161451260235460455545175}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":6212137206579554840603485325265517},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-3050864755759599663114102702567953}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-999272609475666800220252410681965067},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1287128020610042608933102825875223241}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":242132043675222901464757996392001547435},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":111890002616616074324800123677873409791}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":6082867407167560201492407533040359},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":6082867407167549428300275023327131}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-491332054466689885830522703786984876475},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-982664108933379771793633250555048278989}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-29790112985572623970529723856109036015},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-7447528246393156023045084903654954881}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":7833317309495775508056576947781427253},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":7833317309495775500402910497433544353}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":41185332042469956618260856049601811},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":41185332042469955635685029307092221}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":5942212255414652548742216551796077069},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":2971106127707326269473006368515718181}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":-371151276453157689706721595962935411},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-23753681693002092192560521545808854519}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5222896442544182423979328541266797551},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":5222896442544182420984913496152604435}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-4086300786437591780719788595909},"lo":{"denominator":2658455991569831745807614120560689152,"numerator":-127696899576179311204786434273}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-5225717284338856420605629325421624115},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5225717284338856422998874968745014241}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":985408875622445411113412513750018819649},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":492704437811222705526925428251045097441}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-43877325156624089937747140684280405},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-87754650313248195134674193401746397}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-63506896968491257998851601244607053731},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-63506896968491258007643708023398084565}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":124838877714683545836525144482082552991},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":62419438857341772901244027347707645977}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1981816419057365305123555951294627651},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1981816419057365293108315058193241861}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-83379716425624756005375355022574901},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-333518865702499026622548528605515657}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-82376499151081184665874548727205496995},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-82376499151081184679554831620847054947}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":82290087674754483249614432238514514229},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":82290087674754483230212047644489122679}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":185429798222284444583794704085589215},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1483438385778275551717342471194240985}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":36976333325268963019129453214957},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":36976333325268749314669664232041}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1484022285313841735228244927420064033},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-185502785664230217384622192704167835}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":254815965679737976009937298359637784015},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":127407982839868987996922997593385768961}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":425613949908679839},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-656616167928428521}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2504779338840644401},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1870963471399995051}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":605307039387621779},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2498399025155387039}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":57378268852585787},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-164474809519190081}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":23187760067167485},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2145303947765169}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":379714591847845663},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1344416451367142117}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":64387344548662449},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1619777878365176825}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3021372026652911},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-11399232025843331}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1213781580557019},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5114151107561801}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":45989014462981557},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":1803546882187699}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1121427608638527093},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-517439815112413141}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":196071795485441561},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":51853932010340365}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1103366231052312107},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1847956764228383329}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1819763626334110443},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1112312835641291461}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-97584132742213935},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-318190796370331151}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":526823694918477},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-23464785331208167}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-116182265257914691},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-779815874623559141}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1070861665727010277},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":325207938566833569}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-83405953020870175},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-17096921410534427}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5456167958631031},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1480706045628301}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":111416131437675209},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":134317715301477787}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":795541828802778189},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":51931889249358849}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":10232077073591159047},{"denominator":85070591730234615865843651857942052864,"numerator":15713415103999655273},{"denominator":340282366920938463463374607431768211456,"numerator":57721601814712382935},{"denominator":170141183460469231731687303715884105728,"numerator":1843608775780880311},{"denominator":340282366920938463463374607431768211456,"numerator":966691338813395509},{"denominator":85070591730234615865843651857942052864,"numerator":4635121202999466173},{"denominator":170141183460469231731687303715884105728,"numerator":12170091003259303051},{"denominator":170141183460469231731687303715884105728,"numerator":724294611213535161},{"denominator":340282366920938463463374607431768211456,"numerator":287371028039706715},{"denominator":340282366920938463463374607431768211456,"numerator":1154240900963088903},{"denominator":85070591730234615865843651857942052864,"numerator":7035490300053343037},{"denominator":170141183460469231731687303715884105728,"numerator":3729722563268160707},{"denominator":42535295865117307932921825928971026432,"numerator":2151489786374253257},{"denominator":170141183460469231731687303715884105728,"numerator":8332409748993610513},{"denominator":340282366920938463463374607431768211456,"numerator":5884597915664789613},{"denominator":170141183460469231731687303715884105728,"numerator":635966401677306339},{"denominator":170141183460469231731687303715884105728,"numerator":3341299020012414393},{"denominator":85070591730234615865843651857942052864,"numerator":2372742350679006051},{"denominator":170141183460469231731687303715884105728,"numerator":1211569081240915563},{"denominator":340282366920938463463374607431768211456,"numerator":209495669764039099},{"denominator":340282366920938463463374607431768211456,"numerator":1880109033319703007},{"denominator":340282366920938463463374607431768211456,"numerator":7855608229029169347},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":4,"numerator":3},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":125520842854275241113937468410002711},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-101195991572712835818936587872796123}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-245492784360294852771390538918009852863},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-987189231095264847749734475638538274117}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-26268905415374333499738959132269526447},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-30330255503474573612377848322247256699}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":7980500374507733584351946433032936751},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":3431766434558828423823663245308197815}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":86686909904315360395110757456999907},"lo":{"denominator":2658455991569831745807614120560689152,"numerator":487626692216734339040227575028419}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":24201952138515149473759723498931534073},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":20892438571726979819251378732555858811}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-20880332551930052791905834512725985471},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-24185959197974653514886859723002642239}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5320359685595830751384884939424563067},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":4576594843685148378432144296498487041}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2638170491733054313930857670157459},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2670772311533921312321504719689819}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-2289382865073173260015140229187553485},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5323316717902730600520106447328915731}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":989672323420533606602195730260055242339},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":984759987231256750292543137302137196663}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-58085484232484613447864803572097317},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-58713522195320588336938885723841357}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-118887842814001640524349726247218785621},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-255893812411119575515912145550605788079}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":125755237623413710843079665827269233929},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":117103979644596043268177280574688224521}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1023229541565380818727717481393171359},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1618603024916360817755166959079930541}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-272042308218833894421568897191133845},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-344807496092700724714659822431700777}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-77377460773668936580045749382352320309},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-82981589789280330722730496883699427137}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":82894354069644243768808196892345073133},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":4831594136135593516128510258860456555}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1532245160225565701344816412026817933},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":302480631865881071900878141449719219}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":6576208598479081707780303356637743},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6428516066956013675733613964870641}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-605173154437495831722917046974771261},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-766432422109071929870645761735317977}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":128344405867090099453551584079742370321},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":238426130390318960025877822504151948657}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":7282388285787667289082987591124671},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":7282388285787655796184960643002245}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-978510282390981654906908771226348839075},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-978510282390981655046496090721212131049}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-2063774794696569623685939643647676483},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-8255099178786278526761588545126523171}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":2183435544809521706407107552905782611},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":4366871089619043408628540222060226007}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":103176082911683788877556744418758945},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":51588041455841893314515261796280171}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":13212313561888923834174426362947453271},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":1651539195236115476676846903226763469}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-26406535212228308187055470938966693539},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-13203267606114154120663888468209420601}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2911443996606665832849531094536356641},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":5822887993213331662384471872821840715}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-11294029648907077299815748515459},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-11294029648907412107706624044999}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-5826373506793588552584064146790532855},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1456593376698397138806330855491412245}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":981479874727518013304934463536734565645},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":61342492170469875827620901837382141055}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-6389316886623663580958382854989263},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-51114535092989317085481431049570035}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-134189054766201787772122369335240029927},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-134189054766201787791535641505689836465}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":131624301408244950507553630002324590047},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":131624301408244950469978287870925441399}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1169449240657341664039448958265934075},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":584724620328670828697015713027418999}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-394010985469902793585139740235828401},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-394010985469902796493073054293310331}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-86741316454234391705694488460103808917},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-86741316454234391720828570551541256309}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":86640872244548627216177310647340416619},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":43320436122274313597367406124402004149}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":219106381921796862595988750339987205},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":54776595480449215477434085172295615}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":97128002866086138424006997320743},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":48564001433042825997906422184397}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1753605510354935973729584845395040481},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1753605510354935977998153252055955013}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":269302642641300942031481292982998503937},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":269302642641300942013679440896724019885}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":324752903132176321},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-706012213688413309}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":6845949487218929793},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":22658984876221521}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-209504821813868751},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6676732383375703805}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":198935471538651683},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-33151394967903849}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":9964017306602369},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2648500857538131}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":693170803417647657},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-619376953984874627}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":66691355833394253},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2372656715087254253}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":37348594149594551},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-55403180044405735}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4383116072764527},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2618978005031177}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":30589814444201949},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-5009599721139257}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":152857209776107025},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1904691400703599571}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":367824458713985471},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":21983756022290709}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1065804660228107957},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1770810954419627029}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1738371934440853491},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1069344048512368547}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-375445657293181185},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-304109460837040415}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":1049615018335699},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-10552481913632389}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-468855006943866999},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-48118194259172669}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1036822912743863269},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":318828151109902633}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-41153070162002697},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-66519202753650703}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5223550525849945},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1436753667502639}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":110634500971289529},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":34138060040325125}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":790691382815945537},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":426928118830700125}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":170141183460469231731687303715884105728,"numerator":5488757734268913805},{"denominator":340282366920938463463374607431768211456,"numerator":66551956882831953257},{"denominator":85070591730234615865843651857942052864,"numerator":15279075848252880019},{"denominator":85070591730234615865843651857942052864,"numerator":1013263938253527381},{"denominator":170141183460469231731687303715884105728,"numerator":554501045695710335},{"denominator":85070591730234615865843651857942052864,"numerator":4939197964180815137},{"denominator":340282366920938463463374607431768211456,"numerator":25883133285349052451},{"denominator":85070591730234615865843651857942052864,"numerator":402729817757109035},{"denominator":340282366920938463463374607431768211456,"numerator":329997354834116099},{"denominator":340282366920938463463374607431768211456,"numerator":1280020623701077599},{"denominator":10633823966279326983230456482242756608,"numerator":935507579057935203},{"denominator":340282366920938463463374607431768211456,"numerator":8275885894874953903},{"denominator":340282366920938463463374607431768211456,"numerator":19060769023354047001},{"denominator":340282366920938463463374607431768211456,"numerator":18453157122735331851},{"denominator":170141183460469231731687303715884105728,"numerator":3264515450010323127},{"denominator":340282366920938463463374607431768211456,"numerator":1426620334821737391},{"denominator":340282366920938463463374607431768211456,"numerator":7416522995117275843},{"denominator":170141183460469231731687303715884105728,"numerator":5260832947003087579},{"denominator":340282366920938463463374607431768211456,"numerator":2694277373419922967},{"denominator":170141183460469231731687303715884105728,"numerator":119582784073024181},{"denominator":170141183460469231731687303715884105728,"numerator":1045962911219908993},{"denominator":340282366920938463463374607431768211456,"numerator":8719044411144619319},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":51},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":127324630049860656683222170519494895},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-98200222576586313528120731039955603}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-977799959127125897035667314494675019229},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-983204570022963535655629465917203447357}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-29369703113194021923791805372156177557},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-33573801836980042391170988012661506585}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":4443100052403288029986952651309089779},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":7716330332239019882672799719188223157}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":54079248309584086845693419848137147},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":79505349358914548780256838602479397}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":13435173696984219018590759227984303673},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":23424238091401962613406554314029510175}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-23409496812180741393659736601243258665},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-13425672810197124434682094903033039749}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2961885313615733184571196899806271753},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":5145021533134484204522970995876693921}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1476377628767218970401969945250911},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1498915669844746406022696256384895}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-2573875700806772130777076803486215751},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1481852557216666463017227148110275519}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":985919579195155974244014559133521120875},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":980812543468050342937994107497521364171}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-35653089214491707516534607620283337},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-133158955407213951583593625169322467}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-252226702910896779520628162595113034527},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-135117776270789652134205292114620791469}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":33133095556760690603502774016006410627},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":61992021939988483089492747149505778971}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2409242669113333036054814989144122761},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1934324613495591099447592599307226699}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-162713319029677599315117388056606269},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-101587228622698363135724754215206911}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-20456266404045047625070493667318367701},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-43669700482595066078103856524785238579}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":87237972633126985577198116858168584407},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":40870161339689880373606797632649965935}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1806080153565920196141179065825035727},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":723794650234268628946235747060784365}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1733283772141162246718126557509859},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-3369553912086322762348460445786755}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1448149594680955688981794984873301713},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-903438250504908075723146105658834679}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":33896017051883319394675201047599445307},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":252999057820257022753450926809766284579}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":17156900735325946623726292059618371},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":8578450367662961109102927614548735}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-974219442881244077163145302092220673333},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-974219442881244077309337629744204932817}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-36355249575723466866324085179010184689},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-18177624787861733500233105143615825561}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":9674992662281305818979284825532182005},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":4837496331140652904930737417604730225}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":127625305694514948065193573950176347},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":127625305694514945507759412799043533}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":29184149999323607751182647260060439763},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":29184149999323607707407312740738942099}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-29162916453234840643062558212509417905},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-29162916453234840700150316066947004739}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3224941155426450597500481698885643545},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":6449882310852901191347597966891190245}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-15304529911314800113057284775587},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-30609059822630362618175797871789}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-3227066249408036308768380734684990995},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-3227066249408036310219868022664751985}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":488702470337496460716133398443424712181},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":488702470337496460682986307514346121481}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-29468923405585458671324510355915607},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-58937846811170926617794086407912779}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-282635841291511209607273906387424434427},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-141317920645755604824938038215453096873}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":17290294240907236425460384694145083907},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":34580588481814472840613838022040848535}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1367024676702123866802440056656039199},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":341756169175530964873870884389656433}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-461055347626481386999984909367977365},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-461055347626481390233012299957682055}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-11378663366429051509624351420396898235},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-22757326732858103023409025416088679307}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":90913766650835330535616897334597020669},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":90913766650835330512064405616608460015}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2051600500558848441926879862388010459},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":256450062569856054484730344591571051}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":31381264501044523742477892449735},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":125525058004177544132617982129845}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2052558713853809687694535594191358891},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2052558713853809692401008570370271653}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":141854685326898624456689091156498711811},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":283709370653797248893802975745805771295}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":118139722316740987},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-46653775092035719}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":4164310825445803861},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2246347929306232351}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2551028274621722437},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8017119416552603799}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":16921676353243169},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":10389218122038465}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":16807106244987313},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12432049102146131}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1925648425183855307},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":10881824439510693}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-317065627810690429},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1493146365384026915}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":32820228676598683},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-22507763610580729}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3937953750426177},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5309275020842549}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":8101169240394333},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-5660082907957627}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":313527608728243071},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2657830685311131055}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":337773194735734733},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":15413624011280123}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-247145511040797513},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-826344093151842805}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1616609872204182891},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":61699033163737641}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-346876631348954489},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-282949956722677171}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":33163993753657435},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-9474436106124903}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-227469554486825261},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-741271512871651945}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":489016506462079529},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":300617308472063129}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-78184168815184405},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-63045941137708313}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4952976188516223},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1408775522741527}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":214345733202736929},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":66777563499714359}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":767265759156372159},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":420436247636943893}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":11711390295362233711},{"denominator":42535295865117307932921825928971026432,"numerator":8756878370649930257},{"denominator":340282366920938463463374607431768211456,"numerator":64338016983145292535},{"denominator":170141183460469231731687303715884105728,"numerator":2216960401228726945},{"denominator":85070591730234615865843651857942052864,"numerator":316024375725499921},{"denominator":340282366920938463463374607431768211456,"numerator":20935724871508331871},{"denominator":170141183460469231731687303715884105728,"numerator":13683899094822728465},{"denominator":170141183460469231731687303715884105728,"numerator":891304302479079687},{"denominator":42535295865117307932921825928971026432,"numerator":47071552028565743},{"denominator":340282366920938463463374607431768211456,"numerator":1412644617867141815},{"denominator":85070591730234615865843651857942052864,"numerator":7915352945514725909},{"denominator":340282366920938463463374607431768211456,"numerator":9121672092339494321},{"denominator":42535295865117307932921825928971026432,"numerator":2621128993833828985},{"denominator":21267647932558653966460912964485513216,"numerator":1268696878856653015},{"denominator":85070591730234615865843651857942052864,"numerator":1799361219512303385},{"denominator":85070591730234615865843651857942052864,"numerator":397614315577974681},{"denominator":170141183460469231731687303715884105728,"numerator":4088739474320382481},{"denominator":170141183460469231731687303715884105728,"numerator":5793923330502131963},{"denominator":85070591730234615865843651857942052864,"numerator":744152709841872201},{"denominator":85070591730234615865843651857942052864,"numerator":67883345794208727},{"denominator":340282366920938463463374607431768211456,"numerator":2312841184987802275},{"denominator":170141183460469231731687303715884105728,"numerator":4807094263918056015},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":32,"numerator":27},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":129297039191456198841937882443398959},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-23746688881243005065900693324117693}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-973493518037685825208482005226655776893},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-979067700652458969472942100464943198795}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-2036690470744482425559358847048300701},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-36920539364245670509202666809649680781}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":153633372951920337643341446398114557},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":8611653991495329618155216630300214771}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":133330201913182475887432406246492447},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":49912812622425299466826146147547523}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":29641612627167088644361708258470788271},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":26067184290067931958214866006532012357}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-26049551481423557331971070100918927621},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-7404847197367766470703769070593332811}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":6554047712221773941098717818877430289},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":2870824012217307926819222150573206739}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":410005283761712471327391247678971},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-835287257341578916273883179267711}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-5745029386309604804946878080596590423},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-3279235295574721140659368271756379595}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":982008685601334824370828264404405992275},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":976720576863166713711890257926714981531}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-42895896829112353493561486819552585},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-149970199909214079754464360373393847}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-133294288699454870741037166846856698003},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-284483898733848082103778381262356778933}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":139221587859028983342807680158563632813},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":65390079234634473408720844241759306979}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":175637674112586490991251442536981719},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2286531336371716588002289249053532989}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-385070979704667047322429297877741635},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-237235518678512254974765761217676871}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-21549813598058694624860168019251365575},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-91619875012230910561978833708965672917}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":91503186711032552192143170952673357053},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":43050307540802984430844719407574637243}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1054679056691790031198854939564607889},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1713239160040018765597910575220236163}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":910393220384821059553662458198929},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-7032339141376275613574067645185065}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-428491401215128147086852710473159205},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-131897791237796652635571792368338617}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":285566981936255837444208306573152395881},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":267495493830750398076954011132784949713}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":19905675460861389366521525923067643},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":9952837730430681782956831203602349}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-969805195184859679208701676534407397509},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-242451298796214919840280092524325130383}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-39783985381284315487496462322112732329},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-19891992690642157813688989158883889663}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5327759876904144450584333668285157277},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":10655519753808288891272184083400135697}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":19512276424505336158884910500324253},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":19512276424505335797271683032522837}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":32040759353386339558382121043246175449},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":32040759353386339512437641632073666925}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-16008106761739674123044274689425278435},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-16008106761739674152938062885203596223}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3551390301777343759447550509839647077},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":1775695150888671878720948614276459921}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-10187618916238504600212966010759},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-2546904729059680113080450123743}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-7107901668909109658829456299525693937},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-3553950834454554831004014324230482947}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":973195094369740115884551652180252361585},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":973195094369740115815119447482331168099}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-134660138881645954246285337345670785},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-2104064670025718351982103550904993}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-74199462274435591013912495904595166347},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-148398924548871182051069350690405103411}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":36232571110841469700834654129557553759},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":72465142221682939379175275014990842021}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1584289176230436342996827649301622155},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3168578352460872670010440995859546193}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-133723724013306773615161154129190043},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-267447448026613549018779580753018249}},{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":-744044087311660492295763244720371863},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-23809410793973135758014135314295321695}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":95105996759044424651955064615356025745},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":95105996759044424626226107033012591029}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":297603651285743758091075552090045949},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":595207302571487514524724278563957549}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":79942146642079018339969151087445},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":79942146642078707854778794726353}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2382027348124377473218475552919047977},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1191013674062188739190146128239868159}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":149016651916989905772743428791632108769},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":298033303833979811524079294979836944973}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":163228453012767671},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-96043111143386881}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":9447052498277129931},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3741872155958276601}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1940076838908552999},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8997904593244920363}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":20646267060543725},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":93185368687685493}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":866715806090101},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-14073742679593717}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1184477523894915739},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":574133056561016285}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1262373107450225353},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1736932076098077119}},{"hi":{"denominator":664613997892457936451903530140172288,"numerator":175897479946683},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":833901980494013}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1762507626645367},"lo":{"denominator":1329227995784915872903807060280344576,"numerator":-20851319264357}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":6226979026973097},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-67518204586920441}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-239532046015656183},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3285812160527537055}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":151464700577632291},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":6301955250900811}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-876540268281205407},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1501597888630409941}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":731205003702369145},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":870742276938673123}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-38272861902486845},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-64024523117907495}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":32666347618108719},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-8499101905763095}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-106512564662475801},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-697087913749074173}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":899392421434733227},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":544183547332329763}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-142766459032382203},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-233180697469602655}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4639510890768189},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2772454208424189}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":101411133625771697},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":63133373588702037}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":91050802280932153},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":24962118280380765}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":21267647932558653966460912964485513216,"numerator":777157328792375007},{"denominator":170141183460469231731687303715884105728,"numerator":36678378305143567673},{"denominator":340282366920938463463374607431768211456,"numerator":67381882540113616315},{"denominator":170141183460469231731687303715884105728,"numerator":2414832087222291187},{"denominator":340282366920938463463374607431768211456,"numerator":1432482312082687997},{"denominator":340282366920938463463374607431768211456,"numerator":22074828709971846665},{"denominator":340282366920938463463374607431768211456,"numerator":28788042673405353345},{"denominator":170141183460469231731687303715884105728,"numerator":981979567171176219},{"denominator":170141183460469231731687303715884105728,"numerator":213636370588242681},{"denominator":340282366920938463463374607431768211456,"numerator":1552413582660689209},{"denominator":170141183460469231731687303715884105728,"numerator":16656364157356242199},{"denominator":340282366920938463463374607431768211456,"numerator":9995121899629392903},{"denominator":340282366920938463463374607431768211456,"numerator":22931830071040168449},{"denominator":340282366920938463463374607431768211456,"numerator":22198199378891232913},{"denominator":170141183460469231731687303715884105728,"numerator":3944300253255083229},{"denominator":85070591730234615865843651857942052864,"numerator":440906249194955177},{"denominator":340282366920938463463374607431768211456,"numerator":8963904138937258673},{"denominator":340282366920938463463374607431768211456,"numerator":12686874354120515625},{"denominator":340282366920938463463374607431768211456,"numerator":3269646532013658471},{"denominator":170141183460469231731687303715884105728,"numerator":153389603903382451},{"denominator":170141183460469231731687303715884105728,"numerator":1271315295871637255},{"denominator":340282366920938463463374607431768211456,"numerator":10539275038832953789},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":57},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":131403366031534999689786026119335449},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-11449222169433465160528212308537989}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-969065427007855006643094428398675535625},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-974792111311620640716697985693599672011}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-35910301699624623272785764948124459163},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-2522486278788316200510560316122403679}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10817954224848296768316572648495726171},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":9547996933107195703366463722730624753}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":81291444523320059670840946269062155},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":123741129766501037303990004047672829}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":32509082354959759836171785401263506831},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":28814713070919590804211259978566962067}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-14396982949722860664697231476111146257},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-8120867859334228616518853339017572717}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3605044071523565495261496817944807541},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":1591353749041163358970916217611084217}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3618935029066258678591068775121817},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3700313671718704235021961054862467}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-3184773550536418014611847142322729161},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-7215401078505201912354363932867439449}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":977950475646417720447035217724874822677},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":972495125932169730299351011543644095083}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-6344330764632274608465402038076909},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-167825016524088313668688788327788185}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-280858051308944532714406830619527579623},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-149317975567305650821538793049736436055}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":36455034052373604009358946738514641473},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":68744633503504694310395429540475117775}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3250634753143278782860916117311590037},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":669162743913866622418020900967713029}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-451237660148862128350731725216358075},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-137353633731263678710815341927323855}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-90496984765208304061987372223921458855},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-47910103213724692106030880708717736775}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":47843622969858613243690737378473092379},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":90383380063181786514806953245568351093}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2443212464471010013313779528643171515},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1004044030062081908081369213314403167}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":7626550609107407611960459000362933},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-7307038880631792263881089841247803}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1004506751102366741569717994563843161},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2444465618695495528690429840741156459}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":149941263300862688373708184286361122721},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":281912353326249679132290376298479134661}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":5690986749170412966872359914889585},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":22763946996681624712743979132527919}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-965281176367965960913081547564078100281},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-482640588183982980535578368532175100833}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-43295933081705304329032632912789996325},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-43295933081705304474105311562311079243}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":11673742911109236190604515115789926545},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":11673742911109236179905508742322324565}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":11811738615539873157311856214506331},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":94493908924318983630851574625173481}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":34987745899151633513159916776185291593},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":17493872949575816732567155733710460277}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-34959775110692230902342830201331113555},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-4369971888836528870584690698424692767}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3890226101696992210602545958095420867},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":7780452203393984416816293481180946899}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-53386928549642065904728713229565},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-13346732137410759721862875740617}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-3893278000453535114706091580376121321},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1946639000226767558220246269157732893}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":484430735802273092870271979541821776669},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":968861471604546185668134289541723754945}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-152537916450772133465810638867703775},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-152537916450772155524281673724151211}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-38857686017834590897799304683758403405},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-77715372035669181808213767520215721763}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":75722807435640705322614521423124532269},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":151445614871281410596400698993437409759}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3643688854642539136472733792498033473},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1821844427321269559541819684177684617}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-153938704576744413553492536699348697},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-615754818306977658153113291341521913}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-99363691181371390283077577636364940557},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-99363691181371390302880770680303474095}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":6200937124925133505947676046092012361},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":1550234281231283376050013425666882551}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":685403386270369809401001401785842469},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2741613545081479230373504987509284517}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":25123134529719162001713029050165},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":200985076237752598819914956555863}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1371545215425592432117420135264251039},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1371545215425592434934497395490357957}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":312271811855621626145229291285317056233},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":156135905927810813060967288150003072099}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":13354917804100147},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-759350999229768901}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":623959375095193577},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":4837765626404500833}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-2411668049968578937},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2345521616742742177}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":366617838834958949},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":151532862146158189}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5436426616987527},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-15089786657219681}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":339261263904437387},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1028070083684420509}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1742539387533611263},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3778866260434668655}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":13717462107102629},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":3927161153790863}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1578350432855401},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1315825019632875}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-16376582689483461},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-86377143413758847}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-571832002912340075},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1892590816359777875}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":32674696674717919},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-3625573903227499}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-745118963617483397},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1313659800470952177}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":635090674640777363},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":368344443351213837}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-259529985548522375},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-222347285910684315}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":3954271981405761},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-1834269250017981}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-192385930144594835},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-639562286981549985}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":801091422795630749},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":118355788179727247}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-125349326302562225},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-209351191648648751}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4284059586093995},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2758680833650393}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":187447566599176023},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":115193075813923611}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":676399702293836453},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":91551739851664589}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":13144277559432230171},{"denominator":85070591730234615865843651857942052864,"numerator":19116200640644188123},{"denominator":340282366920938463463374607431768211456,"numerator":70256964141243636041},{"denominator":340282366920938463463374607431768211456,"numerator":5241960698389400609},{"denominator":340282366920938463463374607431768211456,"numerator":1614661955145279799},{"denominator":340282366920938463463374607431768211456,"numerator":23169792640606646225},{"denominator":170141183460469231731687303715884105728,"numerator":15074592128291342797},{"denominator":340282366920938463463374607431768211456,"numerator":2155238013691700353},{"denominator":85070591730234615865843651857942052864,"numerator":120570340230686325},{"denominator":340282366920938463463374607431768211456,"numerator":1699400677577206771},{"denominator":85070591730234615865843651857942052864,"numerator":8721018989378115349},{"denominator":170141183460469231731687303715884105728,"numerator":5447455578413062271},{"denominator":340282366920938463463374607431768211456,"numerator":24946045886971095515},{"denominator":340282366920938463463374607431768211456,"numerator":24147425695116263863},{"denominator":340282366920938463463374607431768211456,"numerator":8601964918934908991},{"denominator":170141183460469231731687303715884105728,"numerator":973208703673184297},{"denominator":340282366920938463463374607431768211456,"numerator":9774201308623086611},{"denominator":340282366920938463463374607431768211456,"numerator":13817144612357496375},{"denominator":42535295865117307932921825928971026432,"numerator":446656172142999927},{"denominator":170141183460469231731687303715884105728,"numerator":172537762214025267},{"denominator":340282366920938463463374607431768211456,"numerator":2780950014833480711},{"denominator":42535295865117307932921825928971026432,"numerator":1436532640151483371},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":16,"numerator":15},"tube":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":33399552071022830681753688825439555},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-88070222236583834840885695852258027}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-964546009498385492256231383815407667869},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-485194774575011738964165128853145600167}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-19665779154554615751053572869246313655},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-43855829030860071356000309375670421945}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":11840870931133543627471502825693590389},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":10523814067438816142805592867698279003}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":196310428958127265265875110492672545},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":151630187222477733168428592565099873}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":35466044299444936884911751017707268701},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":31660172137157606471051629233778460555}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-7909033171034389196648189999745939325},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-17718470538777735690775325799314248723}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":7890757655296596253795237595412157559},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":3507613798902793271946816932034610207}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":992072917933095833151856768580905},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2037466452752415815886659334682609}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-1755053993013093241391298687332586581},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-3948536470309869949103904026130283451}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":973755956250782014067913663921513966547},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":968147337440363032234293548707921172483}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-118415047933301528251699107381953559},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-186678020782687522685313329323206341}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-295032154510181052935065578368295872279},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-156344550192897082070454814335060273905}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":38081395718886993934107923932793240905},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":72054292308783933991504100131645590069}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3731728241901771366869141529521980651},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1553003071261497518513070346113901429}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-131042963572149206482069031530410823},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-78925283991862438906494853881194567}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-11839425662750931921378038511754131595},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-24984446010214582949839544549188813561}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":99787606462170346259075265301205027235},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":11823227237892693055599802817081911493}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1404355301387299444225185434203307957},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2333286833342766854726510897236492277}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":497733503954191860196507695837951},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-7562034562890200124772331719814171}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2334447128280881867541242777877215361},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2810249326715837924313568329272285969}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":314112165335030202569337918183428992195},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":148123381833598217370636390523106511221}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":12836759022518447214856101239608319},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":25673518045036865962782654380888857}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-480330494008620967165424484222465554191},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-240165247004310483623500260226833943881}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-46880492455417971181840505272997185223},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-2930030778463623208220274300559926379}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12728055803013924787745494574863758463},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":6364027901506962388110440153012595053}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":226699287848083135576654052914131001},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":113349643924041565965677159870338177}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":38018381016221339636268330261114277505},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":38018381016221339586247700710728186291}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-18993471000771541322519700502103065065},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-37986942001543082709776618627403435327}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":8481737767872114986633958490998260777},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":8481737767872114981847896258710512629}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-8615411197038434716375313447347},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-68923289576308569218430172713877}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-8488941185614934798059809969039802211},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8488941185614934801834103563721529847}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":120551909068869828150599301226475413917},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":241103818137739656282391885417449494265}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-85727554545000793354917268343152837},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-42863777272500402647425304619953887}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-162412201340703621254013723593598791585},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-324824402681407242562532804520132092081}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":157866139421970223995546205737266016703},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":19733267427746277992851404685172783805}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4160478096356468955342551356367765705},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":4160478096356468936515237360241382469}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-703842061956813998498913605069446693},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-703842061956814002818807072080551161}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-25851252895065099855947304511698880091},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-103405011580260399445241258226652822533}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":25809599007481464046350322855363798141},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":103238396029925856155154664029845613735}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1567481555090927856471510394030209117},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3134963110181855705092131580455320055}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":249640854254091592186573168319341},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":249640854254090812302830295239423}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1568379911547131931609994862845234391},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3136759823094263869343216533589743285}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":326422481626935956261480604715364528029},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":81605620406733989059061727735198487277}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":575009449297779},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-728708411125414933}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":2523124536486719365},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":688364226510942997}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-5373847203494838181},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-9348607833214751307}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":385163118536654215},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":193415264761571893}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":4043685158764523},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-984055372282279}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":369254759980257735},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":686653232614268705}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1029728967658385681},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3931637516303509679}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":62185505412939757},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":12870160990062323}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":716072438181759},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5118925657431169}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-35432050068562149},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-50899200107292081}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1662469222128376467},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2071596976111855897}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":109766582358658279},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-13734767850569345}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-601532026915219099},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1113290425755890369}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1065937944062089177},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":295937123126159253}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-104604559604495561},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-186418304770204001}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":15148866777199439},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12561350042384001}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-83439681490434451},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-286418383673633853}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":694065897265946799},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":393302204471564941}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-52667605913911547},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-183185391068011773}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3914225131224959},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2745891223072673}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":84590774032107513},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":50556321173733327}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":307085260190168739},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":322364035958278041}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":13832309963731398567},{"denominator":85070591730234615865843651857942052864,"numerator":19820811016068166707},{"denominator":340282366920938463463374607431768211456,"numerator":72854561453120861857},{"denominator":340282366920938463463374607431768211456,"numerator":5666433207531743017},{"denominator":42535295865117307932921825928971026432,"numerator":226341717306213071},{"denominator":340282366920938463463374607431768211456,"numerator":24219948967886283371},{"denominator":340282366920938463463374607431768211456,"numerator":31432519021105283439},{"denominator":170141183460469231731687303715884105728,"numerator":1178292966355529481},{"denominator":340282366920938463463374607431768211456,"numerator":541752106127488447},{"denominator":340282366920938463463374607431768211456,"numerator":1853963622267852811},{"denominator":340282366920938463463374607431768211456,"numerator":36373071705954999473},{"denominator":21267647932558653966460912964485513216,"numerator":738526999417970457},{"denominator":85070591730234615865843651857942052864,"numerator":6749199866761729705},{"denominator":340282366920938463463374607431768211456,"numerator":26130452279036987795},{"denominator":340282366920938463463374607431768211456,"numerator":9331843252897483177},{"denominator":340282366920938463463374607431768211456,"numerator":2138517191707160793},{"denominator":340282366920938463463374607431768211456,"numerator":10606481069235886133},{"denominator":340282366920938463463374607431768211456,"numerator":14972931849407598485},{"denominator":340282366920938463463374607431768211456,"numerator":3886519514182454749},{"denominator":170141183460469231731687303715884105728,"numerator":193305906629695571},{"denominator":340282366920938463463374607431768211456,"numerator":3027578951091263065},{"denominator":340282366920938463463374607431768211456,"numerator":12470943645074259741},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":63},"tube":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":67912567857172477603840594827292007},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-84476084310541854164705407952497573}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-959938939831127704721173384914773717725},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-965874758205392433998932665325305728277}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-42838484033608166718198617277741609905},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-5926621814322442853317346428650277319}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":806229792197510585565175508069834415},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":2884382012109227567500341030418962207}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":29364838519351958371735042063171487},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":183884385592396000627016550774982463}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":19252885425544335240832146935748389297},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":34596854237825296018853202067076574599}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-34569401089922722829933356998791572673},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-38473141297617803554028086825163725937}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":4297446855443154245566847841380463441},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":3844979351280751982057179829445849253}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4326930507665195692376055647450849},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4464635044116518782984224750831455}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-240497331531471060136614873482543819},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8602328528007036974776745845526550993}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":242359063885797495239000203760902192311},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":963688416156752028801432257642979865739}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-68227772883431189056900118933952027},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-206474865678809207635782029034230277}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-309108206025289165935858681479514512335},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-326641027199164778401216239186018405833}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":9920984792443362775112483135338785571},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":37658899778714452821172423821386952025}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4254567121741236664285482333432310603},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3575813491631572725172323239010902909}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-302050519570237686520253960460716727},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-180159707701374546193781995164447809}},{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":-772280138629388109166706377943437163},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-51985096056329400535365013386893269119}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":103801931433267125489881845917801712703},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":98705334283861581686902971589997762709}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1603426648381778959782522114419954537},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":84060007479344563833923623080658613}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":4147579900277687884309164147410593},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1949039202776219936311822536830725}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2691353957475061188214503353186414869},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3208718691236297948417870327584031403}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":82063377801231700155876983151093221911},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":155248033741738303366435434899814738821}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":28564979081328417050733160054186099},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":14282489540664193656001485817227133}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-955958132859749438652312825021876331757},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-955958132859749438820039641031595158411}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-50527185858196511663053486864078228247},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-25263592929098255908438167747118052731}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":6908415937456749780262469630456957019},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":13816831874913499548147732639244998383}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":33706115243464110084243778494501697},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":134824460973856438304950699095453911}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":20562973393161384112883272812737888943},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":20562973393161384086916019329710682873}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-20545538380876986489543451763434674733},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-41091076761753973046091274024187077537}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":1150681552271729235432861577596777513},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":9205452418173833878258243596723788721}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-87791792827743231768230395292381},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-87791792827744451078849387666889}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-9213876697330751558316622330889044265},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-9213876697330751562412416822269795703}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":959867713535026322294389727067560578387},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":959867713535026322216504484266500277295}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-23918641399123148239356727487493863},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-95674565596492605828961304225850023}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-84671131112814317000717101723906835723},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-338684524451257268061487538287152447231}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":10261870176389747734437396937582054953},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":164189922822235963694292404284596030613}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":73749022943289576409518533585534717},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":2359968734185266434955441931849100355}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-799344906248756774321159836937234109},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-399672453124378389520493600764152891}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-26839840001951730602787067522919495003},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-107359360007806922434291620312290169191}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":13396755807007103070930500401430347455},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":26793511614014206133715920610898023219}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3561820404370692216622134134419225717},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3561820404370692208131555241631294785}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":76673468624450015224497169093017},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":306693874497799191409924311216321}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-3563979783900915855825187848246616729},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1781989891950457931227026157765532745}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":170241559001299256344259471309491802691},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":340483118002598512661297011535237251997}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":52903590555055421},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-344935192345446885}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":2484047083695763591},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":5823479474041068437}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-5591806372387117803},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-9097266834112339109}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":393288742592114525},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":221306575123541669}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":716456222904413},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-16259381267044795}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3092399543627966271},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":805134524778213883}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1118710302808645127},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3957775091106166843}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":16841707200313983},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":33134940887069179}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":657542791154509},"lo":{"denominator":664613997892457936451903530140172288,"numerator":-9644181504339}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-50490473290355105},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-56734721461077523}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1017303776028447985},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2180191833898931225}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":180332200425579983},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-23779232519738403}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-225439264029963715},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-914657542934869825}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":432932967648571461},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":440332735337055653}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-39103391368862165},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-302729379794831745}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":28883033519453313},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-10919862842181669}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-276340179763479005},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-500423697850692557}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":146118080518516505},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":153920040510430599}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-41934649707738351},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-155996626857611563}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":111926979239791},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1371174575278403}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":149053407299631665},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":42494973819829895}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":272508290342709879},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":270768495613978365}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":42535295865117307932921825928971026432,"numerator":1812247263323361415},{"denominator":340282366920938463463374607431768211456,"numerator":81807053574488420363},{"denominator":340282366920938463463374607431768211456,"numerator":75158694084216327953},{"denominator":170141183460469231731687303715884105728,"numerator":3051306113550085699},{"denominator":170141183460469231731687303715884105728,"numerator":1010514449678706413},{"denominator":340282366920938463463374607431768211456,"numerator":25226188235991436817},{"denominator":85070591730234615865843651857942052864,"numerator":8160502001478606435},{"denominator":170141183460469231731687303715884105728,"numerator":1284046312055514469},{"denominator":340282366920938463463374607431768211456,"numerator":605871313448767451},{"denominator":85070591730234615865843651857942052864,"numerator":504101940218618937},{"denominator":340282366920938463463374607431768211456,"numerator":37779733342659667305},{"denominator":20769187434139310514121985316880384,"numerator":778661441744589},{"denominator":340282366920938463463374607431768211456,"numerator":29077676188325080971},{"denominator":170141183460469231731687303715884105728,"numerator":14070103379189190341},{"denominator":170141183460469231731687303715884105728,"numerator":5037996617864159523},{"denominator":340282366920938463463374607431768211456,"numerator":2340012234114718345},{"denominator":85070591730234615865843651857942052864,"numerator":2864908337815621953},{"denominator":170141183460469231731687303715884105728,"numerator":8075922131699370485},{"denominator":170141183460469231731687303715884105728,"numerator":2104612891336449017},{"denominator":170141183460469231731687303715884105728,"numerator":215791012969731407},{"denominator":170141183460469231731687303715884105728,"numerator":1641200251906119221},{"denominator":340282366920938463463374607431768211456,"numerator":13473841499337455995},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":32,"numerator":33},"tube":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":69008256757552848958679363019398037},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-40441288915045478298169486312404259}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-477622000854376376914567116699871986183},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-961262875384851843456764019763626337603}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-11604544817209725378268683430443518763},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-25520655567314799100366223517490960603}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":3498185653232469064486579852369955251},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":12587535046356596833806942383527647167}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":69706155892095217338351181949062851},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":220907583879161161106681807843028509}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":20810774441589515037098073618370135445},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":18809014515501909210460047648417685359}},{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":-293649287176476871212651986737470323},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-10396360297032367703354729780368058413}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":2330327156497435262882065543564738367},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":8388452116970156529661188690424768585}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4693636199623502179109234653626585},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-608633684868881938975609850244451}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-8395491944051416936329859775291498407},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-9329984359686595553629359513751280895}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":965002572063912455954805719861300078787},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":479564788467187074227346310782677829917}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-155568164218688501869999268031240669},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-227152978298532311892614007430657291}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-323083814030922498025662758964322686429},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-42561212566971242856163704874256049785}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":82524378827831055755529413947049427293},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":78534035364668895995391863595594477459}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1205032448955161422578578908007250991},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":2043591731541335759713225320631198065}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-345617251641417584191473107057792207},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-204327522505655867385654481157737913}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-102903878360567096541246845137414745101},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-26978802639375031341667643008049810543}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":107728090574795056144096215926950219905},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":102739541080495945045272269130275851321}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":909643590333179503837130404915265943},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3079006304498426559508087998429875691}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":8621344854110343515016833220527679},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-500515251936140478019943535221237}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-3080754341325957048222856858449063481},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3640809159009025198194183331839860937}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":171152197993024650846649584234496680685},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":324657824475923362296574437637769208239}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":31357692609761591030501179734336261},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":15678846304880780034821946230755543}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-951185956105811564387804239208715379453},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-951185956105811564559633437207377870655}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-27112852880585232140712993761469069221},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-13556426440292616109752173172464963373}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":3734607425142373623199017981694810955},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":14938429700569494479535593092636673729}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":318263141600586861557647645161678309},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":159131570800293428522608454327552255}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":22151882114055303850182619384654033557},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":44303764228110607646653266520497353767}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-44265591412092118163794945206965261541},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-2766599463255757389556046515147713257}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":9950388798445331405950920201244713495},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":2487597199611332850076800545072571433}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-110448370627192144006727514989547},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-110448370627193500628726315694311}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-9960158799649421278012224065586248179},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-155627481244522207538191004738159941}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":955229981382942375064267554811552072177},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":955229981382942374983967808228963737343}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-212149554523933729308113673551973683},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-13259347157745859809415221189582305}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-352440069789538959380215391812319652713},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-44055008723692369930376258190348402633}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":170415297297164386857425686491070600153},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":170415297297164386796687373566115847319}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1330738317363186240978548900432153515},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":5322953269452744942111613739043086849}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-902432588926502900509275738752498947},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-902432588926502905648360547035889273}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-55612343320012663970223971113773736495},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-55612343320012663982658028582020236701}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":13877499205777305582220040185760736949},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":55509996823109222311402420663234471211}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4023060729085368862904183766149456863},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":251441295567835553359778848738235541}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":373009522898985652541184494895873},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":186504761449492343127151383710877}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-125800837118653530400326131750554229},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-251601674237307061247450556163374301}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":177225871789151340485765439938992356085},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":354451743578302680942282667981341617725}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":35482867294322237},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-641424090326139849}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":9497225166808174849},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":5817830537276868361}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-5497286650144595083},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8633538476974544631}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":391540530236876185},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":117977825764465399}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":941922125300493},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-8229493607963219}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":769580889744561773},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":109264117752809721}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-573874568275544391},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3832866141290103881}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":8706620476641581},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":76636828087896571}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2319923102782331},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-144753218081295}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-30753860023557527},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-29827284018726213}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2268677450781615387},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-544883161174108805}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":142708668296015205},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-64324753970413639}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-302244499732772451},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-360791515340983625}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":337718001532366317},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":145361054129532643}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-104074306626598931},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-236527167523127917}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":27124057132672149},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-9437252066888799}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-218071113514233293},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-210388865719029057}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":472647419078298553},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":222838388155686859}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-3901741560512821},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-63806749017404203}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":398883638096067},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2652829223011373}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":126541870581799553},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":68479960509709145}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":466625343321687255},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":217822487179372201}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":15141975164826181543},{"denominator":85070591730234615865843651857942052864,"numerator":21018725421141398089},{"denominator":170141183460469231731687303715884105728,"numerator":38611613335022941375},{"denominator":340282366920938463463374607431768211456,"numerator":6552446977717312351},{"denominator":170141183460469231731687303715884105728,"numerator":1123051015197361347},{"denominator":340282366920938463463374607431768211456,"numerator":26190937286938710895},{"denominator":170141183460469231731687303715884105728,"numerator":16891107791802556063},{"denominator":170141183460469231731687303715884105728,"numerator":1395262230354014759},{"denominator":21267647932558653966460912964485513216,"numerator":42177186647478781},{"denominator":340282366920938463463374607431768211456,"numerator":2187099410814099123},{"denominator":170141183460469231731687303715884105728,"numerator":19552339685994269945},{"denominator":42535295865117307932921825928971026432,"numerator":1714718527700932147},{"denominator":340282366920938463463374607431768211456,"numerator":31187667589759186775},{"denominator":170141183460469231731687303715884105728,"numerator":15088399757537271371},{"denominator":42535295865117307932921825928971026432,"numerator":1354383062611812389},{"denominator":5316911983139663491615228241121378304,"numerator":39863464836592417},{"denominator":170141183460469231731687303715884105728,"numerator":6166352079642293897},{"denominator":340282366920938463463374607431768211456,"numerator":17352835564347170737},{"denominator":85070591730234615865843651857942052864,"numerator":1135317069158885617},{"denominator":5316911983139663491615228241121378304,"numerator":7503460807810111},{"denominator":340282366920938463463374607431768211456,"numerator":3545355386262081539},{"denominator":170141183460469231731687303715884105728,"numerator":7249852260125194847},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":69},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":140093478994930112908495452326375393},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-77372144772994750436980342404799363}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-475242210944934062042290523357256951559},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-956566322967514029346201707311162326283}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-25030083547447298971918466930622151961},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-54730354727913735136002461690560291617}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":7559212846091502573907757886038314533},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":6836105169830666129647878245630561067}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":164227533991425724006838834981211507},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":65778726430396592169037058692316657}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":11198363725135720223670979745418169347},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":40718445884742755649292940601501969391}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-40683697386405840973633173949392046159},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-44757491139887161028170467525141823677}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10068792618152105497744626240596418445},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":9109525729287359253870867503068690357}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5067166562748874312144346524335185},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-660988268072497102860093335761631}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-9117770317225222202035695234020408285},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-5039417059140257882422482001841756263}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":960463917409970629383320540521935030739},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":954501878660527558494012408177213762771}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":-2745031663890599272334414563132801},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-248642360111596376106366383769933511}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-336956874446800653643124838953276452883},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-354233374491366797240560516177762097417}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":10703934613319056504699282175433872261},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":40851007622479298135214875717777641511}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1357322497171257396238625752713437691},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":4641120521668922123794925936345000087}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-785762911660660297449546788404322645},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-921582857541625066165675074710181733}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-26717299603704327650051821657271593197},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-111770814344713428709617119055979189471}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":27891039710534756067955589483416170987},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":106686256190936580119646051589248109917}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1026185147209192508136815357835938005},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3501495939430016894307587642882882253}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":8942873160155747803088152483897949},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8197147278246759805358318821917887}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1751800515660453132712544400039782547},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-128355892410031317794564908835213309}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":356262869804021308844652152094593483177},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":169364906123442434320462108947708654513}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":33959927517050926650528095442614871},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":33959927517050894522331609864870805}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-946357591761102683536902837871615544933},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-946357591761102683712392866382653899145}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-14491489473281582959793081865081296503},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-14491489473281583000050854730274649453}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":16091198096644082721456795161560507055},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":16091198096644082707279260594720507779}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":372977466133373845942003376494537375},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":372977466133373840950661455114910379}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":2971576224241517703156780753848707159},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":47545219587864283195172766852812098139}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-11875993243455539379188165318945752575},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-47503972973822157587768161735522232941}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":2678830010582438783974530381222866541},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":5357660021164877564897525252565783353}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-34342057622749661328222969938811},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-137368230491000148985883828729421}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-5363281733405455640305136019879215943},"lo":{"denominator":1329227995784915872903807060280344576,"numerator":-41900638542230122208565367216714837}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":950513190570968087922807069987299113695},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":475256595285484043920181939636333069277}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-29222373409253202685737045698471039},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-29222373409253206382520819525735359}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-22880595972203845627056952328108735549},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-183044767777630765049968373943479268251}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":176540858417627774034108229226113196687},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":11033803651101735873079946798357553701}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5970307884077425302537460529271174045},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":1492576971019356319799226883469535869}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-506627493887356718769175122429427227},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1013254987774713443116356090697731693}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-57499567478675456655995794300910546929},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-114999134957350913338612171412575971979}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":57387244364544920971804828436012622621},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":14346811091136230238280434751594811353}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4519492341057145702547888438611533645},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":4519492341057145692726969379280453269}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":56183794440017357265754692794631},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":449470355520137787499940592427177}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-2261254795005769561813438816454528335},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-565313698751442391413571298824131415}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":368326597620863328109535254367648768093},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":46040824702607916009778709989319713853}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":24936370826832517},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-584195413388407877}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":4418910749172042259},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":5551051487717158739}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-161368537000725101},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8005376914209320019}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":381128192464703673},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":239153917881828621}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2136439847713705},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-16436649729389761}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":740518464823888389},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1799275476721137311}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2247210001788330297},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-448868710914619037}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":139027330850232109},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":82795369365180897}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2005979251181591},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4240500597315779}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-68946347170154725},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-30185065709141517}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-595406126489304205},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2107147125377144223}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":107505626522638803},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-78904979539547411}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-158912137639334037},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-537467777720314101}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":496088109480965747},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":146141670970713375}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-26637373365515487},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-174434507314378831}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":25208251066346673},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8155741501650317}},{"hi":{"denominator":1329227995784915872903807060280344576,"numerator":-625611855326065},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-169894206861668641}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":363052808050007763},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":70241111846936461}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-20825042487907909},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-49695783663197929}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1387344521688137},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2525228693420981}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":25861058752931593},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":51911754255165915}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":96453158781956097},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":164334459565803009}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":15759532350681251835},{"denominator":42535295865117307932921825928971026432,"numerator":10762703656275714277},{"denominator":170141183460469231731687303715884105728,"numerator":39547376932646823753},{"denominator":340282366920938463463374607431768211456,"numerator":7017780146128562111},{"denominator":85070591730234615865843651857942052864,"numerator":621596103975315441},{"denominator":340282366920938463463374607431768211456,"numerator":27086463413096400079},{"denominator":10633823966279326983230456482242756608,"numerator":1088621262097040635},{"denominator":170141183460469231731687303715884105728,"numerator":1511709764568712061},{"denominator":340282366920938463463374607431768211456,"numerator":748713256050238403},{"denominator":21267647932558653966460912964485513216,"numerator":147833376626692345},{"denominator":340282366920938463463374607431768211456,"numerator":40305260484917951757},{"denominator":85070591730234615865843651857942052864,"numerator":3673482448069491043},{"denominator":170141183460469231731687303715884105728,"numerator":16661738749284446913},{"denominator":340282366920938463463374607431768211456,"numerator":32239567006941042549},{"denominator":340282366920938463463374607431768211456,"numerator":11609696617404841355},{"denominator":85070591730234615865843651857942052864,"numerator":693080231658860031},{"denominator":340282366920938463463374607431768211456,"numerator":13220475515997506739},{"denominator":85070591730234615865843651857942052864,"numerator":4642951034363827447},{"denominator":340282366920938463463374607431768211456,"numerator":4881588788490250167},{"denominator":340282366920938463463374607431768211456,"numerator":532663089606566307},{"denominator":42535295865117307932921825928971026432,"numerator":476885017307964637},{"denominator":42535295865117307932921825928971026432,"numerator":1942756017345564743},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":8,"numerator":9},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":141966068780185927963517460412060069},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-37019156411778574506756222376276459}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-118209192249843234171602362909477299273},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-951798447006596641358168385666331507547}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-26877070093024343461753788052692697695},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-58469795937266460502691688081889570355}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":16275073735391620927831710091116520075},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":14789913696700369318613802070691884629}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":384245909479954795201500479779073541},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":310931722947323752805629600860968445}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":12005522037855257650466041895586167063},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":43890617125520560651629832824845068207}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-43852577105232611188469911382432568183},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-23991360086913840470860123714368123105}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10836116759096291412902583237614597133},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":4925987290297612366120524242570278035}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5446259944307654977676884460957183},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1430208512035143139348310908487091}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-4930774246525183670974867725509446543},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-5423825779520453351287309698834594229}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":477916344037554710631901815534128743905},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":949805621153438959268442870700226587033}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-49179726790531597509590722120068079},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-270866438396073148652091338053118537}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-175362784105581360515756204364745184853},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-367870583994925104518542237358759944221}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":88688488382227993202442951883356038471},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":84820888678177104531221546094190174483}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":6082817952223593841977821372489854877},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":1309630965063995988309397606081048835}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-887857925613181647521205719976551495},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-258401139686598544350475927178192615}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-27686435952011962717044375838183129331},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-57767586063911310795440944950929409215}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":115308414268845580120391339010158227947},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":27635875616481635169657140890430776131}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":575768990073236783033748097365001761},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":989568204729660952035961911671511581}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":2315094655997887169845102022175805},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8361735261786403047306135062301645}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-247548685411335596722279749013808691},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-288078573671050237506004756447852889}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":370127199919355171624477846122384390475},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":88177506551768656605509689763666903645}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":4533642266460154414140097975452141},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":36269138131681202060934473549421173}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-235371478516576164023059723830004401149},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-941485914066304656271086069747673010541}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-30869049939867085175187816161160247921},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-30869049939867085257346404395288950733}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":17273480980548947300718194305104169619},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":17273480980548947285584731556293090313}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":217117743429263278356542969135708299},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":54279435857315818901383399178035927}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":50843788577326059258823478973578723767},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":12710947144331514800495468121992943149}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-50799806794935028556515789298516563689},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-25399903397467514314652341557098223581}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":1437375329380992426986081402956137463},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":718687664690496213081512483121187727}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-169040706327631499522447376216821},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-84520353163816580229720085701777}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-11511849208755516383823793627723975725},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11511849208755516388972459364408927811}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":945728343364005822526900756486439462585},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":945728343364005822442529213406403893961}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-256153993494687177988050864178245889},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-128076996747343604763469506079897125}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-189815846981974038485365804076084616587},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-189815846981974038521022385710060543505}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":45641364979723117545645091904144558459},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":182565459918892470113599268057081545969}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":832835168412493976578048563217455451},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":3331340673649975893855023586075440779}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-565971178103869192777788404536230215},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-282985589051934597898295645569867381}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-118681039789606519360118853537463228183},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-118681039789606519388519989035732412697}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":118435982828080240453227171210666027939},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":29608995707020060103353528420399142293}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2525928415378599774036302001428466883},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":1262964207689299884390461768463922905}},{"hi":{"denominator":1329227995784915872903807060280344576,"numerator":2097538651689377718928808946907},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":536969894832479513026592289432473}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-5055369523160653311297086820994404569},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5055369523160653319525197066301723221}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":382106134190977502461220536255451687287},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":382106134190977502427826302921895705553}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":13903379790409789},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-132094174986035093}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":4037717445902731333},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":5068576614051466189}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-579751200824211057},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-7286553484487011043}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":182174707427562493},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":115603247619639907}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":62050327791371},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-4099105352338301}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1400342194822606771},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1767204885810045229}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1053467312180451075},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3303916605799570819}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":136188715659993897},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":21258881177450223}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":896792587644503},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3895319905897525}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-4559121434788191},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-119895655632781749}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1186666992033676279},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2004627771007022867}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":77458554238889005},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-93111134320879461}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-11552683620794661},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-92859309225259235}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":167359657722802755},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":9445614361407633}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-5096446984087627},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-118499778697206785}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":23514007302056847},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-7374693120331293}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-102961013552212731},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-264419959072651477}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":131594135092010043},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":30823215641129315}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-21672991854893457},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-18390426362724273}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2426633965354427},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1217315976008383}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":40877989216387111},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":35401783776505891}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":310257280477692083},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":55115908686419861}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":170141183460469231731687303715884105728,"numerator":8174000712682309001},{"denominator":340282366920938463463374607431768211456,"numerator":87920158074950704733},{"denominator":170141183460469231731687303715884105728,"numerator":40417158147591020759},{"denominator":170141183460469231731687303715884105728,"numerator":3750079957298808533},{"denominator":85070591730234615865843651857942052864,"numerator":685578689774139255},{"denominator":85070591730234615865843651857942052864,"numerator":6976015872721472857},{"denominator":340282366920938463463374607431768211456,"numerator":35795955917120607401},{"denominator":340282366920938463463374607431768211456,"numerator":3266649151379951533},{"denominator":85070591730234615865843651857942052864,"numerator":206906010964250025},{"denominator":42535295865117307932921825928971026432,"numerator":318857251500548837},{"denominator":340282366920938463463374607431768211456,"numerator":41367810761044437723},{"denominator":340282366920938463463374607431768211456,"numerator":15684159229710889947},{"denominator":85070591730234615865843651857942052864,"numerator":8870603924786550777},{"denominator":170141183460469231731687303715884105728,"numerator":17163956464603122497},{"denominator":340282366920938463463374607431768211456,"numerator":12400469000937821445},{"denominator":85070591730234615865843651857942052864,"numerator":750839634098077619},{"denominator":340282366920938463463374607431768211456,"numerator":14119838276374372883},{"denominator":340282366920938463463374607431768211456,"numerator":19805757845083848655},{"denominator":340282366920938463463374607431768211456,"numerator":5229434107702619255},{"denominator":170141183460469231731687303715884105728,"numerator":294539479220901131},{"denominator":42535295865117307932921825928971026432,"numerator":511359753165690645},{"denominator":340282366920938463463374607431768211456,"numerator":16597103935225564685},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":75},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":143533491171449373467591567804329905},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-35492704577467235718417812191223091}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-235202356130058633489597577954664486821},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-946974054787865811462837594911878255525}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-28745001992419431188564134333002696769},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-62249543067713556997568854410180062721}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":17461030263822853693830347498141479407},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":15938994522513108153218028472226704759}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":446640968173845720164822751356506193},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":45599079071665176240858188899574195}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":25656113291706676883744392739773472105},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":23563331627512748788013271158308376757}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-11771390218207093615542831059142115629},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-25634840941383102503992346214845342399}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":11622035821777501208144451249897053543},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":10614573844613338898867339066932817551}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":364352696079498922319647980344389},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-3083779440711703430944920742885957}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-10625604594098830274796591942180884877},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11635193321219640332933390718933099409}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":14861279597229512158139770101215099057},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":945034857705481876139563123772117335671}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-27324272605679781371756983712943439},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-293742956372541940030308527616632599}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-364388357346821410193916862338713378669},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-47675017428902826072982576156244253033}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":183389716342795784401178743236572746145},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":175779874203720217254623638033512510051}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":6781382053091954886716107573669911449},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":2940094265982349883625164753671570431}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-62354492357511312916320820407790345},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1153502978265505315433302110843479307}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-57265816967415966164457655336384401951},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-119206644160021742159678087764268447905}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":1858739610287555181415666949475250427},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":28577376450902635762550891476726267371}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":321471365073578873783791826078919681},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":69533648557976032893626774959233615}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":9574539802628767609547365464534171},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8500899433116450949482460568442627}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-4453105311410853215666637359559021207},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-643393512177214036908629736754515035}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":191947934354226915281525242844448390023},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":366596678611131050024360701250850785849}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":19086190171856351353412983548486491},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":38172380343712668365797354064128851}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-234145873535145498371670841359075339875},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-468291747070290996834335149457259228005}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-32766287672133579629848268603946076137},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-32766287672133579713610936226828700045}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":18483621956720932900308603615855771367},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":1155226372295058305261026391866952537}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":251243920722258116762528218358038619},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":502487841444516227479394571828951483}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":54193058483114691825182971308944774759},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":54193058483114691766928508164356036627}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-6768349700521171811047838124495017113},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-27073398802084687281417785705985835379}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12300179161346652327078805838621946373},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":12300179161346652319989538979889116511}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-51490856953443313487193514055959},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-51490856953443770706264705681917}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-12314759789949255335358027858318031561},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12314759789949255340889835730941320901}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":470443146539331938645005460011101835513},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":470443146539331938601946119999915506145}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-279186040293766189204824835777000837},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-279186040293766222741669575562223077}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-393065586447133389476573756429198320145},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-393065586447133389552233759356774161759}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":94244103799214564714961269234606448655},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":188488207598429129356724121379046067549}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":925081657386700469147612770431735501},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":7400653259093603726654390359808537179}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-629302556001036630940888242576652151},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1258605112002073268400627422718164419}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-122268924700425951947728437208682685197},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-122268924700425951977938043401167104365}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":122003123607435458543976383705247784851},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":122003123607435458501679629661976083717}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5620829708234712857636530697792790689},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":5620829708234712846418768672043813813}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":636406261417459663647040859587459},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":636406261417458359664079440421735}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-5624881008262643789582020606552950547},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5624881008262643798370399846229606835}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":49473627439859040921645904293600883055},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":197894509759436163668826871655047701059}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":1304031379484757},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-473161698436536073}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":7250557252764614921},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":4434934458483022843}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-3982794661809294281},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-407361843615076925}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":342423497788303753},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":214575233805983849}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":133930159051649},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-1020426657073137}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2601415498618317747},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":417574305018537347}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-475092676274802311},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-746219712504526123}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":131099709496189761},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":42015705281996151}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":831407694250135},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-224191367766633}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-73928234717315001},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-58442702045351619}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2272723629468082765},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-468851060228957725}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":26313028794520715},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-52837319558334515}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":100820099037813489},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-225933842219958795}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":97098590531680235},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-114819187048271017}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":9697750627692701},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-34895327223279199}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":10968807378012815},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-875853751265147}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-48289880227116669},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-194892813806872275}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":21738898089522501},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11355633070023861}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-3057377503410213},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-25134806153232407}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2135157250004343},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2364678229066633}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":3848358838414933},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":19471540635767601}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":119932900267290587},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":28760251012575927}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":85070591730234615865843651857942052864,"numerator":4228267238806599479},{"denominator":340282366920938463463374607431768211456,"numerator":89585655341967752215},{"denominator":10633823966279326983230456482242756608,"numerator":2577974068902082989},{"denominator":340282366920938463463374607431768211456,"numerator":8002166541001105435},{"denominator":85070591730234615865843651857942052864,"numerator":753633397256981533},{"denominator":340282366920938463463374607431768211456,"numerator":28661672433022284885},{"denominator":170141183460469231731687303715884105728,"numerator":18342089567773159651},{"denominator":340282366920938463463374607431768211456,"numerator":3521099279900316201},{"denominator":85070591730234615865843651857942052864,"numerator":227953300936717179},{"denominator":340282366920938463463374607431768211456,"numerator":2744425351624950551},{"denominator":170141183460469231731687303715884105728,"numerator":21160148792502269925},{"denominator":340282366920938463463374607431768211456,"numerator":16689272021539755889},{"denominator":42535295865117307932921825928971026432,"numerator":4708328061644879333},{"denominator":10633823966279326983230456482242756608,"numerator":1138896886282112473},{"denominator":340282366920938463463374607431768211456,"numerator":13208965073344008813},{"denominator":340282366920938463463374607431768211456,"numerator":3244953246399356655},{"denominator":85070591730234615865843651857942052864,"numerator":3757875407363082945},{"denominator":340282366920938463463374607431768211456,"numerator":21055743612742748631},{"denominator":340282366920938463463374607431768211456,"numerator":5585274895472961137},{"denominator":340282366920938463463374607431768211456,"numerator":649741562970047373},{"denominator":5316911983139663491615228241121378304,"numerator":68330289366388945},{"denominator":85070591730234615865843651857942052864,"numerator":4416393217525279125},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":32,"numerator":39},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":144684536034909271472751291309658481},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-34164068844370501578100457184379631}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-935904951299825881983582256497303453069},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-471053010520178926707071024621024994883}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-30628957687261232799050295256913429523},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-66059760426639513120851006399739971453}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":9337319524177817993988478823957654725},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":17117796750792648540874483968443593125}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":129022748330972595599948577980543657},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":425140430584597236634541713699715997}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":27328677209383221993203165175871166253},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":50420059039388238670379154703216904211}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-50376233018246590117726638135313660813},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-1706624087035342953300567111509982313}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12425291012272948110182842682575354295},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":1424510213030645083095266005802658701}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1554009943282203023957286201482919},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-207118742155240807028907115193055}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-11408698939496058263214138144601352499},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12440201632090639469310690776804329201}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":473171268528185794244266026295962198511},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":940200600132713928872219093736098308209}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-241217799675667493797775261746976525},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-158592444966144964802785011764470359}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-47242997490816972561333748764220551105},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-197410560150329372645643084149394698313}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":47325078576927356044774099450287988365},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":181817142764579475217432920063404472297}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1881387676060014586707447750232463485},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":6566806974306606614474519835728411787}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1115337500816919178738987338638852277},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-160173256840638905863109980493959781}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-29556294953925674864515298060943784809},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-122783779554740898478637802981632773153}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":3828612374829284542827443595399910545},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":58991346238125849931314607753563627707}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1429394494345133657355072881298877543},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":1244471953616429465172171583731615291}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":4943036148871410649007604213276035},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-4306779557496887419322105356574609}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-4981329726513416912594239243803861091},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-715215961623222612452839102085755039}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":397567570903013053892721007315844926055},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":380388196778529107820615779967120985991}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":9886713804265782213561718284670795},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":39546855217063093455706178372138933}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-931662561829853296402574144316413708501},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-931662561829853296587532391947109973897}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-69340143499735443202523771092499313357},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-34670071749867721686613130496316521621}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":4929992155180835098738077912551916609},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":19719968620723340377776201969543055333}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":144547797867674440827189556546483479},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":289095595735348878342662525547025109}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":57586748103578815450197591206913037985},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":28793374051789407695302077145369668725}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-57538788272996342375922865866157498699},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-57538788272996342451950569833303418575}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":13117580931623294950919397819169149139},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":13117580931623294943300387482834046177}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-248635861962384455739112265331631},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-248635861962386463692141958560877}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-1641753354239212090000609097368209945},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13134026833913696725937895012985393185}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":935997710560366714717779579214080994433},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":935997710560366714630068857543599895007}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-151391230347454538440877925373112781},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-302782460694909112450027315181083193}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-406390516648830071412225529335325417765},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-406390516648830071492293021985042715261}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":194308452401436196532821817444700656445},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":194308452401436196455337612919177680799}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":8184705010213335560879061567722438769},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":8184705010213335532699728954096393051}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-696666839033185375280510864830070319},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-696666839033185378791825527477911003}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-125761498770952992427041193903493598325},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-1965023418296140507173236165185839415}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":62737375600338331655452662124767968469},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":62737375600338331633043853725323606079}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":6227021177534116498631271025417268231},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":3113510588767058243344423760738263157}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":187168927125066074195454522343461},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":374337854250131431363978689609809}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-3115826131191124096115804604747961997},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-3115826131191124100797264170547682017}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":204687064347629217362473520247868997049},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":409374128695258434687284337523659119839}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":30845444711186903},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-419240301255908051}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3188778186973788067},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3698745237520697775}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-3239372384527534023},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5707662324550532725}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":79180969179684039},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":192212169951575859}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-25590143840397},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-2026252221946001}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2373733496324751255},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1523755458043274083}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1648388998547065233},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-661010515378515955}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":31057387876437263},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":20048130375937743}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1600278892105481},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3312796004578701}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-72321371701705145},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-112060208169149809}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2099103795196645979},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-431316035122911933}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":32085146627561905},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-116471040116689453}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":53004136920336783},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-99030139343479257}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":72127606573666591},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-226286198284498665}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":78270852324902597},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-27447318714502365}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":20444774470980995},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6899414521972929}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2685482324065171},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-131771725044302531}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":95004874235103427},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-19359400908420241}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":13828690361394897},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-29590942984255741}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1898397935065017},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-577563806443113}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":43113180224299119},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":2239156907377331}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":175244449669384699},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":7505550261665431}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":170141183460469231731687303715884105728,"numerator":8729402376022065597},{"denominator":170141183460469231731687303715884105728,"numerator":45569859123567346759},{"denominator":340282366920938463463374607431768211456,"numerator":84117099980055365591},{"denominator":170141183460469231731687303715884105728,"numerator":4262899493474362701},{"denominator":170141183460469231731687303715884105728,"numerator":1651831379472919319},{"denominator":340282366920938463463374607431768211456,"numerator":29371729438946111681},{"denominator":85070591730234615865843651857942052864,"numerator":9379006363022365161},{"denominator":42535295865117307932921825928971026432,"numerator":473435831645819055},{"denominator":340282366920938463463374607431768211456,"numerator":1001519977398272531},{"denominator":21267647932558653966460912964485513216,"numerator":184165106174133405},{"denominator":170141183460469231731687303715884105728,"numerator":21589824296173612485},{"denominator":10633823966279326983230456482242756608,"numerator":553433051213915723},{"denominator":340282366920938463463374607431768211456,"numerator":39878222981346235553},{"denominator":170141183460469231731687303715884105728,"numerator":19296447680166202597},{"denominator":340282366920938463463374607431768211456,"numerator":14036807221293320377},{"denominator":340282366920938463463374607431768211456,"numerator":3497642568151363721},{"denominator":170141183460469231731687303715884105728,"numerator":7977865865257939133},{"denominator":170141183460469231731687303715884105728,"numerator":11161293580254985097},{"denominator":340282366920938463463374607431768211456,"numerator":5949501935297545639},{"denominator":170141183460469231731687303715884105728,"numerator":357461301887329189},{"denominator":340282366920938463463374607431768211456,"numerator":4662142132594947791},{"denominator":340282366920938463463374607431768211456,"numerator":18747482036335577495},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":81},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":145298112679418122891529417642660757},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-33095514711054738080461486789409319}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-465486338683844060596296286706965193481},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-117150864778307386326307089137920519843}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-32524158406984280659025630320571534363},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-69890902116954540734504024109610648647}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":2489281047124142505474705313050388869},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":18324663465579576533107397555031782157}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":593052643724647288845979277700614605},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":246212542817806388108220235642535815}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":29025536474995628103552894616029758071},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":26882195104508647859009960567359866365}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-53718296638656960504139586639384367093},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-58003306293781100346570768006118809647}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":13244612579070351260766855580835148709},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":12195242114932907993236503557670306761}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":6604179132553674535551727128719149},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1775321264719175394287620158112987}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-12209576778188053380288839390795024027},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-3315351723950018232745180466750460953}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":470752735101884307655029819653565346059},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":467656849476360617554786224328441868375}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-66123821782946898823779159441048501},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-170550689665227153776574652410145135}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-391391444049057595097022463726502089215},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-408132868029815538892535388554441142959}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":97554078626514511376790450671954137613},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":187752657636806918979295590027503238301}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":8315794602998221407409304135828575957},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":912371360943580775821313850878243615}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-310241927575107314483222913486818307},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-708670863658434648710868883492164207}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-121824881561367487738936972170249739939},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-63132656475976064913425810177777968481}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":125976064242187574811629555186612886681},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":15195210719891208475071760267140620763}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":6328862882920642697410342671370629093},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":2771079677745915875932074547224680749}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10195720949217404371302447077579823},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8698666624610115359680570678341919}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-5546134856808733298056161520331247761},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6333596371347838213314750183525020067}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":411141210151164484704340160121570380365},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":394083220559728754296910807864484487251}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":5032571118503576009709706170591455},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":40260568948028571647300027197934457}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-463367486346594747639446432656715349689},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-463367486346594747733353260373262485875}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-36575952160237615404771006578624787669},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-9143988040059403872927040860435407003}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":20980876574587512626941309079418373623},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":20980876574587512608674252903562698187}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":330903602948427984657570527682742625},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":330903602948427981039318472565743699}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":7627340687276315258845324790358257649},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":30509362749105261004935722752438869169}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-15242444073990999878493006616762672495},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-60969776295963999591527094441347652473}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":13949930480447018749746152722277371303},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":3487482620111754685392774960976281793}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-297552289562883308944897501357325},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-297552289562885507620499240350909}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-13968372307209747983792783988982047725},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13968372307209747990146456207464596407}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":465536526960313937865641462570624497999},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":232768263480156968910522508460944583087}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-326847420732233666739671904357562837},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-81711855183058426093510090910192067}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-419606042670424427636479716858524214321},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-419606042670424427721018327343017911815}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":100012891400755881721495401646369634909},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":25003222850188970420143639120416943511}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":9015222281947039917759006811118488337},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":9015222281947039887884186686444525559}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1536198373959219045386468195017864547},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-384049593489804763234116291860188511}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-129157652843465978953712311729143782571},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-129157652843465978987623864386250040689}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":128849893592750656842411623445631990573},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":128849893592750656795033678526276492733}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3435488540372682744456601824182824311},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":6870977080745365476227284101303701381}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":874666122685169332162862125493945},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":109333265335645969794665608552091}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-6876226184871381102363547739685631337},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6876226184871381112316094538152578011}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":422860541741311721494792634351144746861},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":422860541741311721454949769518389684371}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":87647730449169441},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-46069408321263633}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2744284064286098395},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2896262058346075543}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1228399597988642401},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-610494450370817897}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":144102457881905745},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":20718568887800837}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-136087506192137},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-4009727308416729}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2129177364095056243},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1335990862576948481}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-339185445785932029},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2294748351220826679}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":116006651744670257},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":74092771334655409}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1608462183033137},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-48434001458991}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-68419687091231641},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-105926897318467513}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1862903643095922139},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-48824729179735425}},{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":124310985899563},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-126005867148589373}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":155232709780206971},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":8914705800022737}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-15574815584682609},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-161780209587908509}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":112576043352747523},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":1051315386998581}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":4795338413992355},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-438157069157775}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":1570890769748877},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-18909035240535707}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":26782094952336709},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-68721094303243945}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":14690267555400901},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-5795569277574245}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1714901042974817},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2283294292406815}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":26566550729117543},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-4790750070725689}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":117304634069058775},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-9961386562484337}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":170141183460469231731687303715884105728,"numerator":8993543656286879669},{"denominator":170141183460469231731687303715884105728,"numerator":46305337340717037781},{"denominator":340282366920938463463374607431768211456,"numerator":85723578659622211155},{"denominator":42535295865117307932921825928971026432,"numerator":1134037488199641915},{"denominator":10633823966279326983230456482242756608,"numerator":112821895132914423},{"denominator":340282366920938463463374607431768211456,"numerator":30048983158235107545},{"denominator":85070591730234615865843651857942052864,"numerator":9577132675777482991},{"denominator":340282366920938463463374607431768211456,"numerator":4066569498981114641},{"denominator":340282366920938463463374607431768211456,"numerator":1096983681731292511},{"denominator":85070591730234615865843651857942052864,"numerator":789520626031914101},{"denominator":170141183460469231731687303715884105728,"numerator":21982753068265879647},{"denominator":85070591730234615865843651857942052864,"numerator":4686556348242433999},{"denominator":42535295865117307932921825928971026432,"numerator":5264816235670831643},{"denominator":85070591730234615865843651857942052864,"numerator":10193659942674658741},{"denominator":340282366920938463463374607431768211456,"numerator":14885327302208601951},{"denominator":170141183460469231731687303715884105728,"numerator":1880951276415098919},{"denominator":85070591730234615865843651857942052864,"numerator":4223206001439018903},{"denominator":85070591730234615865843651857942052864,"numerator":5901715079474584155},{"denominator":340282366920938463463374607431768211456,"numerator":6322473936697998473},{"denominator":21267647932558653966460912964485513216,"numerator":49056479435052987},{"denominator":85070591730234615865843651857942052864,"numerator":1239549843449547219},{"denominator":170141183460469231731687303715884105728,"numerator":9921428663109016591},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":16,"numerator":21},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":145243904585019617724418682290583901},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-64707776981657647032096503872813367}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-926024813366360409392977322944573780067},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-932288978325796950720260733191727690495}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-34425982982220037295882727939864295695},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-18433435329348440174837151452103138877}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":5294553758247713038027364659579107741},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":19557941241582505736183617650898985201}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":677987474079314059330924815376588251},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":567102715625295945280258166282295375}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":61487120003725560004101143303410489377},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":57153373448006954877993377489439958841}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-7138199051804326909482757450607405485},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-15359387750012971569117530004704634129}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":14078722294217473266291486862890059119},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":13010787446890608462968042862936349677}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3496402653530247691142176613331939},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-7587747634854411697252846420889323}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-13026970908679018999104355900794081403},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-3524382540256449052027380620821701855}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":58538835382367451124964364447094100799},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":930384810542754185182927313958282684833}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-288328736299772265874965102535281885},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-365398664852636419261475722016208519}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-404730020938126301752323070697879805243},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-52666872255645499793918456859164084363}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":100406434412087407118708603055552332313},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":193585739465576350035106546764627654201}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":9152489238496864165741625031746442335},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":8077173429292943462361740256688248069}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1374655438642783537124823481510318645},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1561437832878655671486803763985283019}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-125329425228664356556095184332113187501},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-129650160651550715265555277846894040189}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":129339794611251093872194692671924764287},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":15630662741604382483176144161604501413}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3488967495193288626824831872307499009},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":6143586309439398623693201030125223285}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10504251914880540989639347131845331},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2188803087577674732240904401019875}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-3074068509079576471908635866811706355},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6983289460390105427960644293325269993}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":106153973741214048530510362532100774505},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":407680599109747572527866880323240538313}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":40173096794623360004031908217820891},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":40173096794623322567635025050770397}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-921812180001163912811291153805429652003},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-921812180001163913001912667558525698809}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-38479659715866225140481453977196525279},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-76959319431732450458035395596066763469}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":11132356575253930895440331119945108415},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":5566178287626965442868839159962147469}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":753801552980418054399745024108402139},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":753801552980418046513808314688145061}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":64483023561503968605655155235043101239},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":64483023561503968543478260187362413109}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-8054241003353030177991239526379376053},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-64433928026824241503005800774101291173}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":14795943933508474396796773723763761175},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":14795943933508474388038313356740106445}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-44149285792776312205447996716255},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-353194286342212899185780964673133}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-3704127719590316058993901460848265197},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-14816510878361264242770460609185187947}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":926122541540509951128085155426501581217},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":115765317692563743879684905792157168247}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-351282880152595592095047824733001425},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-351282880152595631831199868116989611}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-432711968673268950654844466678902713617},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-216355984336634475371960469117284961857}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":205640016581519555162634974250060261161},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":205640016581519555076359851885627710903}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":9892497782874974984932274592901601815},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":4946248891437487476658423222052680611}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1687249356702553494765871168776577997},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-421812339175638375716910342701175429}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-132456455285631666978610094506016498149},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-132456455285631667014418586176177883543}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":132127761526457664559215446692448614671},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":66063880763228832254617811438382464397}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1888294998212364994824900531455999649},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":944147499106182495731295182747064775}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":253812637366699821534565419378545},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1015250549466797562319777065441567}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-1889770351021469296271958309552924015},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-3779540702042938597823069003029128621}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":109061884780472074252760576230449579861},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":436247539121888296968986705641769705793}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":115984560112772001},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-318958259240398307}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2296326724219655653},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1025619153231776113}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-407950964874495067},"lo":{"denominator":2658455991569831745807614120560689152,"numerator":-31635793870418751}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":256346526536158755},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":17031447254898789}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":74780406220439},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-15752517613208905}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1878348187508259021},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1121008530885475819}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-262536670571537731},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1945814672041894369}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":26659017109645105},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":16573270076250083}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":837968628840833},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1461604037889977}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-62784484121604509},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-98743898225576789}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1583716500378359503},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2788642017418112025}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3800649112832501},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-133749098021887805}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":394083624335879683},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":97090643227065397}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-115162609456984921},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-101571879369504711}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":70931253996206123},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":9432327990278041}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":2242383048289647},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-7235134773966133}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":2898000470405101},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-27761212361236111}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-29774741532815921},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-188933418017586599}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":667677487896721},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1721166529191383}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1576277736758277},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2270540052810019}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":1540035118108461},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-22278983159549981}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":67320187939823317},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-82925231016555447}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":85070591730234615865843651857942052864,"numerator":4625181757976735023},{"denominator":170141183460469231731687303715884105728,"numerator":47020024652780071931},{"denominator":340282366920938463463374607431768211456,"numerator":87327454942879046525},{"denominator":340282366920938463463374607431768211456,"numerator":9642605325772329255},{"denominator":170141183460469231731687303715884105728,"numerator":1967527352850206933},{"denominator":340282366920938463463374607431768211456,"numerator":30709777695528952463},{"denominator":340282366920938463463374607431768211456,"numerator":39090108286655269651},{"denominator":42535295865117307932921825928971026432,"numerator":544882336180629665},{"denominator":2658455991569831745807614120560689152,"numerator":9363058795537037},{"denominator":340282366920938463463374607431768211456,"numerator":3379447675844077439},{"denominator":340282366920938463463374607431768211456,"numerator":44700491786102241359},{"denominator":340282366920938463463374607431768211456,"numerator":19799301148124633939},{"denominator":340282366920938463463374607431768211456,"numerator":44389739287279197905},{"denominator":340282366920938463463374607431768211456,"numerator":42991998728205758167},{"denominator":340282366920938463463374607431768211456,"numerator":15755647476382470255},{"denominator":85070591730234615865843651857942052864,"numerator":1009574500358480051},{"denominator":340282366920938463463374607431768211456,"numerator":17843997221373593025},{"denominator":340282366920938463463374607431768211456,"numerator":24910332569599457599},{"denominator":85070591730234615865843651857942052864,"numerator":1676243954710059127},{"denominator":340282366920938463463374607431768211456,"numerator":859985833411252157},{"denominator":85070591730234615865843651857942052864,"numerator":1315463187967767939},{"denominator":340282366920938463463374607431768211456,"numerator":20952676930536117443},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":87},"tube":[{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":9023945538335794237560672460210003},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-2000639555773699642710903487866477}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-115135043585522008047235711664554095405},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-231840816062436635841366097676328894717}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-72661154156010491233258531182692439193},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-77568655800657886996093348729240545085}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":22464907981175584754294948604040063907},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":10407992098038863407358198790697981245}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":771360929869392572880615979393242899},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":81204321237488431220913212123588549}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":64959387214848049683750007307958109941},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":15145218549090476955971234598383222719}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-60532115142821830994916380659810193749},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-16227181668560879046368209133297975125}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":932895987662000712789156585766331671},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":3460360250052171555863458079660186373}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3690343320239095336019213231127249},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8086919118027156322027350285145847}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-13859604178771755372289194939987635185},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-14947285463151681487325083230908505031}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":116462585716906712431215237698703219403},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":231356091897248865566333034826220354629}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-78154450393419095064473820996217619},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-24373813514051804876450878356119727}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-104489809319011564275991802939990412537},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-217213645609913981214546130273282018163}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":206414301350732984868595096023947029499},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":99657973703576924930160890633910288657}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5017958815985951321333976676609166309},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":8901811687499832915130434590244851935}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1516473520840638508778346986136341095},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1713722052026443874859556875928320061}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-64368839564422436154343509211195459769},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-132937416275055938758939949290896294313}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":66303012177072818086865089836738887933},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":64216272865186718432033700188347994217}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":7665269711616750964369814006257878617},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":847840292997734774970875344552164995}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5406222358156030438872266424555613},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8782229744622215476679204709667225}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-6787887064970339963238273600725223397},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-7671278263980751354491012791306047241}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":437990934118301817542175652731095094453},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":421179387032757266334146893361530943745}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":39136437715170132571077431715137941},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":19568218857585047081731036480376141}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-916905211568861749518628058855476165417},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-458452605784430874856015398335584660327}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-80754228898511755530334303356407202605},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-5047139306156984731907158259100994147}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":11784930421677163901702018649651389385},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":11784930421677163891408630569409521329}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":854642902979171109472598523879884059},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":854642902979171100900372884289579369}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":33986926728594428544851190848294075077},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":33986926728594428513122635871477753005}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-67925590731532596610523018825242755847},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-16981397682883149172778765973313339059}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":15654333240725112132263998127989921139},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":15654333240725112122894437860086508397}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-416022784333065164402234980090585},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-416022784333067781413618987397345}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-3919288037210659332573083728541539441},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-15677152148842637337549659702419346569}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":921156128309907898488069447984644086591},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":921156128309907898396112787809642743511}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-375989536997574576814690856992913291},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-46998692124696827335743420223400941}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-445708335944854961932054571462131092331},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-445708335944854962025727580569853827897}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":13196949507260675645380657042349025609},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":52787798029042702558829073676506624501}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5408367093460009253857474204456141877},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":1352091773365002309289633484358669069}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":-28851822020274667808903959102928379},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-461629152324394687112034516474983419}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-8478571708465105658715113684071917711},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-33914286833860422644294792572385232237}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":135307743002120655014799414432291139397},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":33826935750530163740544353867553664971}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":2068512612211288853508843355663678601},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":2068512612211288849950596049932377433}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1171280796706875357381291888234601},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":585640398353436736366849032523703}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-8280633466581617089220894304488694565},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2070158366645404275100437462744014371}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":14047956148934589469616015948742162123},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":449534596765906862983411853338899144963}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":8868813169245073},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-133219628372934947}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3667540911934144101},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":313963132195815179}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-109736509867935815},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3168947954055858475}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":109469326514509495},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":105954302043171307}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":52818773185407},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-15060933259088093}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":101378135676827345},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":894106098682498303}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-744330127783206949},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-799426323191543657}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":48001210956427271},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":57462564201092775}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":445486231191319},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1369208593002499}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-27973145588935917},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-90656947532157811}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1284703055418461845},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2442148518668061419}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-5031839289840513},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-136417706918539323}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":225904924051247321},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":167433365951929401}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-182171556498314409},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-230481887772599291}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":40261212042135969},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":15350741337144853}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":16417279543553469},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-7375888899849317}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":129099552537461873},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":202179818901103}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-75610863162367501},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-14278396997488205}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":13355926481896129},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":15673377116805947}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1462460032264213},"lo":{"denominator":2658455991569831745807614120560689152,"numerator":-17518609282943}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":23599159612483},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-8338294884270459}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":5927695069265221},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-60363551385726635}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":170141183460469231731687303715884105728,"numerator":9499818772825148649},{"denominator":340282366920938463463374607431768211456,"numerator":95495524716271135925},{"denominator":340282366920938463463374607431768211456,"numerator":88944586457048165895},{"denominator":170141183460469231731687303715884105728,"numerator":5118447952374472107},{"denominator":85070591730234615865843651857942052864,"numerator":1069619178904809371},{"denominator":340282366920938463463374607431768211456,"numerator":31364582940742952463},{"denominator":340282366920938463463374607431768211456,"numerator":39868761274705360011},{"denominator":340282366920938463463374607431768211456,"numerator":4665510205095825487},{"denominator":170141183460469231731687303715884105728,"numerator":653122755474134121},{"denominator":340282366920938463463374607431768211456,"numerator":3611307065949451413},{"denominator":42535295865117307932921825928971026432,"numerator":5674950919484483969},{"denominator":340282366920938463463374607431768211456,"numerator":20869935318582797713},{"denominator":340282366920938463463374607431768211456,"numerator":46694316312786085161},{"denominator":340282366920938463463374607431768211456,"numerator":45247712876255513783},{"denominator":42535295865117307932921825928971026432,"numerator":2081139915701435421},{"denominator":85070591730234615865843651857942052864,"numerator":1081811439358639329},{"denominator":340282366920938463463374607431768211456,"numerator":18810595650131227145},{"denominator":170141183460469231731687303715884105728,"numerator":13117288868319758933},{"denominator":340282366920938463463374607431768211456,"numerator":7097619447057213051},{"denominator":170141183460469231731687303715884105728,"numerator":470235687950676569},{"denominator":170141183460469231731687303715884105728,"numerator":2786863792157764029},{"denominator":42535295865117307932921825928971026432,"numerator":2759763696112595551},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":32,"numerator":45},"tube":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":71284692719290310408831099870487737},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-64278715067171060058431946384128121}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-916168416298948376313231465099304213897},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-922439264856965639300655023631664003305}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-38235146343989137885589734169398329317},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-81360560125520020869013862295737322319}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":23772711763334991434562450496475254893},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":5524289437270656285560864269527427453}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":873641353041567113802649446809263055},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":23140188113759074136581359378642125}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":68461935128088461905551305351715900859},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":64040922276327913725470143813653886075}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-31996014013492854240303417475245128353},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-68411028025371037913837645356914518327}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":1973270604653575768328763650256122037},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":3671479847162670492604250615731356461}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1941656344028448038108323054519589},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8598523735383512474457983068186201}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-14706191860591789512530203104852522221},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-15809382038286536746984228291234652335}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":926753651397836708930669683922007903401},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":920442552824569130904824401165967937117}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-10539004956839103585108227809598447},"lo":{"denominator":1329227995784915872903807060280344576,"numerator":-1620172505837817601783163316880457}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-215539433232138841579146331540036520995},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-223704944277095179061905348434673251351}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":26489065874514411324374932061233060341},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":204943070979897806685399895574154374527}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10966273274676135952410275577884705799},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":2443297348724267043909949629559601413}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-833237001805159129555890741871685755},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1874227534532670615652676135052180821}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-132048689648914722339092518946233996981},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-136126346016084168734268272345035753107}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":67887083783252745119822863180695379665},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":131722605299785683872523388911915030339}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":8391280668243937404978583918828229259},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":7460057695583406917058336500212633021}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":11121084324045979817807806229597813},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-4389400100295175374818331593394181}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-3732935710255778052357266282915926995},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-4198985628127383454223768545303509569}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":225632918596854718128552154461685455707},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":434578839336130392603640305032811432329}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":9248986474217255185894258143759667},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":18497972948434490698685689103005903}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-456012325601768944491123800989231659887},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-912024651203537889178445664441100214233}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-21132216032498419915703446902617405635},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-84528864129993679846038198616904741453}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":24894720455450248370482244033902480527},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":12447360227725124174334133918391370255}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":964801943786237597620367183475938001},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":964801943786237588323886981406971349}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":35742807984976393027498187614319318239},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":4467850998122049124390980024506020351}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-17859825634864501402882151447921671203},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-71439302539458005693646642585564644303}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":16523808274791689281909829847618139029},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":8261904137395844635950268048746632287}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-60808724130848693257108055001999},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-243234896523396195822814731993061}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-16549002754779538289551124249603903791},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-16549002754779538297292949908096872317}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":458091742519924877012393421277898529277},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":458091742519924876965765616097573095563}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-200433873654495360319875787716568851},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-200433873654495382340217489261519655}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-229297706765029819078903560853579085657},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-229297706765029819128069087124104997555}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":216559559253366285498450702635934005121},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":216559559253366285403109657216132806111}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":11788047238472090020410893514834847387},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":11788047238472089985187361555299971697}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1007004987615118698732056849474861453},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2014009975230237406744609570394044095}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-138759138085608679763806240060464605135},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-138759138085608679803505707655027029807}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":138389397437176708575606229221008486569},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":138389397437176708520299440362754841107}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":9033948285154709425583143182888272315},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":9033948285154709410544850586001769161}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":335895290864586153206089371776639},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1343581163458342555938998480403841}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-9041236151110418383358543578091880951},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2260309037777604598794889099914100471}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":462721380656885012877438877093935780145},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":462721380656885012830860215067676063535}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":83577924162292481},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-27558852943615351}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2825514161884368327},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":254994788788627981}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-191491481643930781},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-148927592580321445}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":183334677734082521},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":75506281025735603}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":268605784066631},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-14356743245791197}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1370194354710979989},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":10355507514044959}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-443618306842211575},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-79425556694889967}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":85045351804936287},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":47939226688799791}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1915650561441223},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-80785143512653}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-48268575466159231},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-81993345318234495}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-975380380041050167},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1049211923310226971}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-9838435763288019},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-136854052543128191}},{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":3854997310400589},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":108926462573678073}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-228880764299371239},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-124651222173445973}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":174134561467927059},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":38941176107519041}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":3759919681710459},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-3859980390231341}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":79900443445783263},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":11582276291816711}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-110679124285218395},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-129796671600808091}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":31079265848193909},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":25300429329748037}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1381174707626307},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1106754851080903}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-317372543836263},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-42795436767031023}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-12847603369503983},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-153365068844815279}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":19479289491247759545},{"denominator":170141183460469231731687303715884105728,"numerator":48470634469582445523},{"denominator":170141183460469231731687303715884105728,"numerator":45258265251698476643},{"denominator":340282366920938463463374607431768211456,"numerator":10853073900205696549},{"denominator":42535295865117307932921825928971026432,"numerator":580099140453440137},{"denominator":85070591730234615865843651857942052864,"numerator":8004156620341276031},{"denominator":85070591730234615865843651857942052864,"numerator":10161355774200241449},{"denominator":340282366920938463463374607431768211456,"numerator":4986093812504368979},{"denominator":340282366920938463463374607431768211456,"numerator":1420543994935062005},{"denominator":170141183460469231731687303715884105728,"numerator":1927025222160223315},{"denominator":170141183460469231731687303715884105728,"numerator":23033141723517865913},{"denominator":340282366920938463463374607431768211456,"numerator":21956833893155030717},{"denominator":170141183460469231731687303715884105728,"numerator":24513866452616976137},{"denominator":170141183460469231731687303715884105728,"numerator":23767830323851696589},{"denominator":85070591730234615865843651857942052864,"numerator":4390909968785248339},{"denominator":340282366920938463463374607431768211456,"numerator":4628868115968508335},{"denominator":170141183460469231731687303715884105728,"numerator":9896498953209531247},{"denominator":85070591730234615865843651857942052864,"numerator":6894734329917155959},{"denominator":170141183460469231731687303715884105728,"numerator":3750358623629965843},{"denominator":85070591730234615865843651857942052864,"numerator":256661334324614325},{"denominator":170141183460469231731687303715884105728,"numerator":2947093326550062581},{"denominator":10633823966279326983230456482242756608,"numerator":725596008762256333},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":93},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":139649587373976083749744330328736013},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-16409685646779567206314138913690731}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-911280070152066423536938514076417685693},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-458765113640919504087964969713016598689}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-40133948155715493986526402174598804617},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-2660350693194958235808368506945946481}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":3137503700811570531526673396773607485},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":5849960522973630932665533944860508643}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":985299000644880775243052627925284609},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":840125558794092248195630446216361503}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":8998625770983579450662755939891355485},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":33763862689112218592063925983966720037}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-33739837390512913180597703101654476301},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-8992354285761691106808941277952966187}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":16656919300183703974515632677357969037},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":15542934789674157472714304858275984375}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":8149467433715367460957262988109465},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2280567879532532012711452711484887}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-3891360974457222858144611306784003431},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-16682526407966350409717339898414198571}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":921790223009014634883192009840610836369},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":457724638008973635465983196739983297071}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-90529651578987413042617228915186915},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-27478126510034059334502725961293079}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-444088920623491919134623013823184144229},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-460283073837122347108938588013630369697}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":217307828521421592542912476401785367129},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":26308390175559534858475700950825782741}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":11943663229615371483585346471724244477},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":10691519848842757028842814453105113943}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-114043089742996875800639525094085851},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2042961169984237282406440013302544459}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-16907709580774722534993049721488712609},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-139216383538636882874918607305296270357}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":138843809257857411938114703955265359519},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":134914846751483237520406605394206442641}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":286135032331222662815092784616968021},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":8176020383761380976437874521169873899}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5715476674158098140828201085103543},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-1093007222858110049362239948258455}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-8182513251903921454012573079670532349},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-4581857699340438903047891564414449477}},{"hi":{"denominator":1329227995784915872903807060280344576,"numerator":1814219911349101418221168132276754291},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":447878407817077629641055498814124343953}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":8397831276039658776698521684856013},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":16795662552079297429562225077449345}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-907180624512399553215333583822291197225},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-226795156128099888353589341970320188173}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-44137928571701427457888818128768576009},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-22068964285850713775495304944369825041}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":26237713959671752355914210927738522615},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":26237713959671752332826695389942882315}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1084750411458848980270974226306986617},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":542375205729424485105706763234551861}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":9376613856253379113924176386489917483},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":9376613856253379105671052100220066709}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-74969800390990482343684602479486565375},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-74969800390990482427349257799555219353}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":17403078795886089754581953725997836499},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":8701539397943044871951780173360229989}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-282464931336365719015693336867887},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-282464931336367262895712938066893}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-4357692084853036890644583134806884697},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-8715384169706073785413571397121517291}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":911213980956641555402402781380922270771},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":455606990478320777653944170344846752883}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-26613650763699898129572530729096545},"lo":{"denominator":1329227995784915872903807060280344576,"numerator":-1663353172731243813738756683130943}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-58921711065468338841755889248254237843},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-235686844261873355418549061633843460869}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":110932784943044799183699730635899477549},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":55466392471522399566856147694099445087}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":3201617248036810582553619264562197763},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":12806468992147242293121852862930579465}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1094859618577045502630071699868094749},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1094859618577045507584580509307282139}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-35440499791094440112083607013471100851},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-141761999164377760490029345615959018545}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":8835778096844580892195274718490918453},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":8835778096844580888568050594873358249}},{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":76821672484211317853635050726535367},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":2458293519494762167349771326539352995}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":383235583861357866930177519183645},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":95808895965339326662484994333627}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-9841182890221951436420559593093829343},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-1230147861277743931112468043525315477}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":475807741055070270843323998102498375691},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":237903870527535135397217834093528470841}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":187038634445884817},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-11193988790892363}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2066793046034720129},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-80999673680225383}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":415992138538282159},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1674117904742495727}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":37345978263912253},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":23354281134874403}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":453984828368973},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13501211049334101}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1123103667486434387},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":219427237751385301}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-166262544529017593},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-976226991200932245}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":74045296901693049},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":19130114911059601}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2038823016488267},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-153588091650655}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-20091646138880809},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-72861160776066997}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-670303009293525521},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1752208625242821285}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-12051420469679125},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-67336813305614521}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":519033596467723437},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":125826973952872391}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-32450882375438927},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-520002376983946765}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":181472069944490891},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":88867595350252033}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":13657396429999607},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8022744755026033}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":183786865606013915},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":72925997805357329}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-67820324499447285},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-281618250038335519}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":68643914626805613},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":8058733269933953}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1320020612158765},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2172412105737399}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-18469568683728989},"lo":{"denominator":2658455991569831745807614120560689152,"numerator":-392961190203653}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-43283054554680593},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-179464374110795753}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":42535295865117307932921825928971026432,"numerator":2492595448842772671},{"denominator":340282366920938463463374607431768211456,"numerator":98397495832797192285},{"denominator":340282366920938463463374607431768211456,"numerator":92056736738330685129},{"denominator":170141183460469231731687303715884105728,"numerator":5746210046752435023},{"denominator":340282366920938463463374607431768211456,"numerator":5022575759565905423},{"denominator":340282366920938463463374607431768211456,"numerator":32670372549087571203},{"denominator":170141183460469231731687303715884105728,"numerator":20713672718349184831},{"denominator":42535295865117307932921825928971026432,"numerator":665163019512362667},{"denominator":664613997892457936451903530140172288,"numerator":3010999811249511},{"denominator":340282366920938463463374607431768211456,"numerator":4108066193258595207},{"denominator":85070591730234615865843651857942052864,"numerator":11679066884409933655},{"denominator":340282366920938463463374607431768211456,"numerator":23060669506537213385},{"denominator":340282366920938463463374607431768211456,"numerator":51391814816545520169},{"denominator":85070591730234615865843651857942052864,"numerator":12464309397177592425},{"denominator":85070591730234615865843651857942052864,"numerator":4625002465090496591},{"denominator":340282366920938463463374607431768211456,"numerator":4943668738846674569},{"denominator":340282366920938463463374607431768211456,"numerator":20792028347136979277},{"denominator":340282366920938463463374607431768211456,"numerator":28944804188420761157},{"denominator":340282366920938463463374607431768211456,"numerator":7914896102646022597},{"denominator":340282366920938463463374607431768211456,"numerator":1118814258724750191},{"denominator":170141183460469231731687303715884105728,"numerator":3111838822861588969},{"denominator":10633823966279326983230456482242756608,"numerator":761752321810708107},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":2,"numerator":3},"tube":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":30830631818126581208671482807636635},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-31029055860994435691980314486479143}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-453215241004805318244285372703202691795},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-912646225558418695032876211244846668255}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-84046146009267836960715916085631113637},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-11109165902065782997711828641874118389}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":26445286250441932725263233727403940093},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":6180608841779459743372762290038894707}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1106805078369010713331110117469523197},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":949023817721485018878639721952992749}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":75535035537719290592071295483258854031},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":35517840231211587183915861457704508143}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-17747397407949431385738320047729820901},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-75486718708400526228706533999570040127}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":2192163651227464772448336074503639721},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":8205598529894287474412148343326681801}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":4264056119897470481287776664752121},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-9657851057945956540833663936677991}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-16436067023670427377844500529530905863},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-8782712167380768247455367765618814795}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":458409072328962830586718680932677157969},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":910471548477166589686932170968804997653}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-96783735025656211302850925500906903},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-232267311833137432160424958576353899}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-228494820519878533899153992315611245993},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-473047365942782771393299353191556029711}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":222600689755152199857812843396077111131},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":215888322530945628241475969618469743825}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":1621013920636949933855941693556492461},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":11656929002180588931225119978391613525}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":-31111446028181313820971952919524883},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2219906840069937213761289908827640897}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-138376028475087457895073521422770267971},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-142207124580299676582400705600690384055}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":35453674789031932530836997996904781001},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":138008808357293261675516267715656225723}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":1245085621980849731804154206523339931},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":8930977541744477361223918889867524067}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5871412196952039285434297627556375},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8677193789523652178657215600978753}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-2234543443005649463464310434779318573},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-4984398781450401574435128964920042665}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":238757094200960797910542043483103055403},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":230538867675940474027084336750640626055}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":14378835902709521230350879111446159},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":14378835902709500679396898493409953}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-902382788789323824504264890530151139057},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-225595697197330956176533791970523743039}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-5749265403233296562159257439063674869},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-91988246451732745183656788784015230625}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":27597287089157037703111920455394504297},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":3449660886144629709838028912254284221}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":607480068712304390652376627212860469},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":151870017178076096305307202178432957}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":78550544241354667962577600046242621785},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":78550544241354667895277850886847553117}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-39256013046644213247808272417262853533},"lo":{"denominator":2658455991569831745807614120560689152,"numerator":-613375203853815832662825626878721627}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":18290856284512228270682710182259257961},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":9145428142256114129652819893849116129}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-651751372732501834596902432837697},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-325875686366252589267881034966121}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-9160577698818734822804129745054809385},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-18321155397637469654386334703631472077}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":56641041822651226478283367181880360743},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":906256669162419623556778230365070479285}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-450743825726645054332839601149269157},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-450743825726645102812015262241301385}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-121010964028783444329327282253239708209},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-484043856115133777425139591104944496725}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":227069868300785822325420032920852721655},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":227069868300785822220746735882911246475}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":13871951156735692673144181823682962105},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":1733993894591961579267392291255301183}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1186807118929630682914139799335177805},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2373614237859261376392465212222616611}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-36166364791856027223093300334953944303},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-72332729583712054468047746988603671475}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":144256783025045780215953558345530276663},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":144256783025045780155146077858484411199}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":2667992665519678123029341031638132589},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":1333996332759839059425040654100945159}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1740115482315245770950834217342899},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":435028870578810833262187524897731}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-10680708282909039756351001069211849347},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-10680708282909039769506350035743379579}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":244396853205271942636169314325909223755},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":488793706410543885221111640504316887075}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":198343984310727257},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-34991145691946425}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":692119087584408051},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-741669366119018141}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":233333641010040759},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-523186881863225271}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":117316879355210829},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":20122340704953753}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":312497047868271},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-1566043079183505}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":218765028239430763},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":224311751674376471}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":40395192547570743},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-704492631814697109}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":7850328405333175},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":28787315246039601}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2099977806105593},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2314594980851489}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-32066574005097281},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-62962337581976645}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-93840566989108061},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-699516276230130089}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-3166417868532803},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-64650453743146379}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":528201914424196523},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":135768022615099369}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-276654981258591011},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-525695536819432489}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":183436952598626853},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":47549317667026825}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":6050219734832835},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-1024026565108841}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":200489255025535013},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":93774572253377351}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-19041437811806727},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-293830967068174715}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":36302450127041163},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":37023895544480123}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":624250434461791},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1045839781391801}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-12587791617127431},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-6965554431950563}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-8564031994863251},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-198275746874771683}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":20381799697078779727},{"denominator":340282366920938463463374607431768211456,"numerator":99872184905327999427},{"denominator":340282366920938463463374607431768211456,"numerator":93564480715614909571},{"denominator":170141183460469231731687303715884105728,"numerator":6077623654677493363},{"denominator":170141183460469231731687303715884105728,"numerator":2712129326043329039},{"denominator":340282366920938463463374607431768211456,"numerator":33324500399055861043},{"denominator":340282366920938463463374607431768211456,"numerator":42219926194520411297},{"denominator":340282366920938463463374607431768211456,"numerator":5671527541282199951},{"denominator":340282366920938463463374607431768211456,"numerator":1669762143425068731},{"denominator":340282366920938463463374607431768211456,"numerator":4373589724972486971},{"denominator":340282366920938463463374607431768211456,"numerator":47365987130255732333},{"denominator":85070591730234615865843651857942052864,"numerator":6045317553134983835},{"denominator":340282366920938463463374607431768211456,"numerator":53786898111395833051},{"denominator":170141183460469231731687303715884105728,"numerator":26106064120595158425},{"denominator":170141183460469231731687303715884105728,"numerator":9729176294093994859},{"denominator":340282366920938463463374607431768211456,"numerator":5271946480780862301},{"denominator":340282366920938463463374607431768211456,"numerator":21807788977309704037},{"denominator":170141183460469231731687303715884105728,"numerator":15166495255618036141},{"denominator":21267647932558653966460912964485513216,"numerator":521295559032355215},{"denominator":340282366920938463463374607431768211456,"numerator":1217280951843022395},{"denominator":170141183460469231731687303715884105728,"numerator":3281200028577545147},{"denominator":340282366920938463463374607431768211456,"numerator":25548612328292847379},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":99},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":104181953224215954697082182240120507},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-51950585853941170198713257700364209}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-901638239515539851837339923028186345579},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-907796445067606186922914861998182715211}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-87797622654261448567530276904288476451},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-92579967545675512050003868237751976567}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":3475866312887206926193524188336394215},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":6515839141489440775519965505380955941}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1238630790759248276140955706537842939},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":533826295768291190331843186618329929}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":79082823829611034145329992403654362771},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":74560698296739921589817130379436413155}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-74517151135842202669108001606030351475},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-79043643687324999414874008141569234917}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":18426046516641357822038705676836112139},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":17289415715802171068555210621260581343}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":8901522535439188818966011791662133},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2551230473022375351421371558722357}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-8658383374658965546650045431998133833},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-9228391325130047893041252708642861667}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":455923333929134840473289344341846694329},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":905519798841988425504819617855005465347}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-103049098659610529392598316429479519},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-244661663968812321168950401494650081}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-234890744006990352614689372736943926755},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-485703493111640760276062428396325090295}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":113895892927182639607979442490440527481},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":221207101445170078162031891176008165885}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":7019780845022839717312419589036245515},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":12669458692380749277399298583578894229}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2165795592568062088357686059117815773},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1202516019214175628691128633139148733}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-70695648351596081223572134385408450847},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-145098321315048142459045859402468663241}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":144686745306371131514334461266745303147},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":70502097232708989480919646206331597841}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10804609165027502712902738706698442117},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":9725236846084775997898679128428046903}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":6028726314916310277579767804959119},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2144365281298571603393543120184779}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-4866576825514213743169992766748055229},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-5406723021481833493572861965225021875}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":245243782797040418693372869602664211189},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":474176649439624652284178993385135304321}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":22326553313875533414774060398531095},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":1395409582117218219438855611191993}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-897640326680005747080780992313280525153},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-448820163340002873642743444395067508043}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-47829739926852505080257415258109176185},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-47829739926852505176216375084330027945}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":14485955831888983139155514754199045347},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":28971911663777966252536216794428912117}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1355902113979630985585075546006503837},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1355902113979630973879575489385621643}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":82093534296556003864927316920672793599},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":20523383574139000949094022787886531813}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-41030565303161844446917780523258201763},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-41030565303161844490305868582521527751}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":1199115977848854248207624395573057327},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":19185855645581667959216577773858249339}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-747227729499683343703504834512571},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-747227729499686958183925196686929}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-9609436497538444790021072357560502139},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-4804718248769222397342902522663283413}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":450660137463226887167595281977335456009},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":901320274926453774238227334468329619083}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-237774238748386520620383280128230623},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-118887119374193272996198980661790395}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-124151702366996538212773192972218405131},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-496606809467986152963757207114745524127}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":232173281381858834883972876998616154567},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":14510830086366177173408795809385846105}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":14984368515047004223788398570942325373},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":14984368515047004182828143145724725423}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2565645041575889034859939114701361735},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2565645041575889046106448954897145661}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-147469397892838526842917281745170331433},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-147469397892838526888696206163619447823}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":36760608506584528405065255692260141621},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":36760608506584528389160475885321439959}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":1443815589296256128802516927086900639},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":5775262357185024506414911538286719633}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":982903292798300579713260439018453},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":982903292798299255826836465349555}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-11559989682486476302740726563860008649},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11559989682486476316589893693742367491}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":62709934628021986200001031942803470537},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":501679477024175889546416717059718326407}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":203687178055831693},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-105394735363591473}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":194411905059225851},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1207578855068132369}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1341116014167104057},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-506368541324725807}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":88106768565491969},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1650243251521073}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1550116407919141},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2862290334290967}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":639537908628619577},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":36064107327476851}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":287347999669366887},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-7020210488477859}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":51203728286277065},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":2442715464238955}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1042628396230743},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-525515384086243}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-3019722128511693},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-13146020177368001}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-114769647685657359},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-132737310018062881}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-6262922483412583},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-121373172488828313}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":260490466378129821},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":279818443418339655}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-282151885675709605},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-516233418247894939}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":45080017403626361},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":12153723633707205}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10572596747016977},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8259834660188341}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":52125693474861777},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":108561368507183861}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-162000940690299655},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-295237365692772021}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":18422861844267159},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":20045166055255059}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1151205031575275},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1976740258929723}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-30102610316503763},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-29330410384154529}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-43707207548237797},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-104172503520040367}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":85070591730234615865843651857942052864,"numerator":5199333807150004505},{"denominator":340282366920938463463374607431768211456,"numerator":101360335000774727579},{"denominator":340282366920938463463374607431768211456,"numerator":95035217548474936827},{"denominator":170141183460469231731687303715884105728,"numerator":6420851364725161115},{"denominator":42535295865117307932921825928971026432,"numerator":730781298679737449},{"denominator":170141183460469231731687303715884105728,"numerator":16986937991956380905},{"denominator":21267647932558653966460912964485513216,"numerator":2688735457737334441},{"denominator":340282366920938463463374607431768211456,"numerator":6036875275369151233},{"denominator":340282366920938463463374607431768211456,"numerator":1805146551016683949},{"denominator":10633823966279326983230456482242756608,"numerator":145328735497667983},{"denominator":170141183460469231731687303715884105728,"numerator":24004025163470611811},{"denominator":340282366920938463463374607431768211456,"numerator":25317591017434348593},{"denominator":340282366920938463463374607431768211456,"numerator":56211636368266991807},{"denominator":10633823966279326983230456482242756608,"numerator":1706219726810475493},{"denominator":42535295865117307932921825928971026432,"numerator":2554822821542047009},{"denominator":340282366920938463463374607431768211456,"numerator":5613838704394289303},{"denominator":340282366920938463463374607431768211456,"numerator":22839491506528426571},{"denominator":85070591730234615865843651857942052864,"numerator":7935735350344041785},{"denominator":340282366920938463463374607431768211456,"numerator":8778355612427603663},{"denominator":170141183460469231731687303715884105728,"numerator":661161225664208199},{"denominator":340282366920938463463374607431768211456,"numerator":6910304459715276773},{"denominator":340282366920938463463374607431768211456,"numerator":26735303945382916373},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":32,"numerator":51},"tube":[{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":5411318507533743140940541893604757},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-46448232600481313075006461320196473}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-448457346101619523060611831677809549239},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-56436897192291661117639777900446901935}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-45757656642163850087760970265516277839},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-6015290309898634272861482704491982649}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":29183437534036257147112712385291660605},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":1713815509427320275277288877750193205}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":21581975151825789858077967183038791},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1196483884947693017056398230615210931}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":82624864326249289550935797636609040281},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":19524460502424927483384519695356756537}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-78058699146305085934649138935559342345},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-82591968616138491544323195726199734003}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":9660923395458269493652469498098236857},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":18176301783800638178416828520195843701}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":9268734087333758775998213874195879},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-10763106609669113057111638639135463}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-9103124612131440976579224569466414577},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-4838827739502189719414137612919367439}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":906885018580236694581203547214176621983},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":900601524402065985294506826372291376587}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-437204334464692263816487687492364727},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-513923767982177640724407993339813201}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-482465131195265403815934364431852851149},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-498252380393949138829682008043889412465}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":232881973436407559718607065242001285293},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":113212039420636147916047793966004884661}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":15157881763213543923840789823057308955},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":6864534989119076800975032848796862785}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-587162718903131195587327194765076205},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1299142249039945308569507388068778581}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-144307190571850796631361563720086618781},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-147889876527583919241477937718354947535}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":73730003760150699807887771176018118053},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":71950434596119800107538068557432478907}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5844137181795667842717105658786269433},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":1319881003572163737063458872381664143}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":6187784308393787687289918182984049},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8444178470523106774182723252286387}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-5283847260431152776143534054363220551},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11697832141329647592926395514557267995}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":503360655206671029189015369666605796509},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":487175156544307535891344559241948868743}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":3531776917723189299119213027274207},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":7063553835446357270591516937827995}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-446480971656238759460159874360445748623},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-446480971656238759563930090673209433253}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-99283414412354043239856011339357615067},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-6205213400772127714655742049063767887}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":1897505479064776719244939543631272883},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":7590021916259106870182362838381723943}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":754022789766531617953804700634795591},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1508045579533063223317395423238905959}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":85637115091672923478569426008392490405},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":21409278772918230852194971203928455783}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-85612476688868197908131745123688405705},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-42806238344434098998225648922804717773}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":10043398393901830157524569041162792571},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":5021699196950915075546185355344395557}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-212897138541351890544107544550781},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-212897138541352865522649711622521}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-5030658591276280423810690514273189769},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-5030658591276280426286685503398408697}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":896413186655235335463600404622926147463},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":896413186655235335365444063415794988049}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-62517475756193365929560568060070941},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-500139806049546980475153775629469275}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-509063629514010292225369359817933085745},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-509063629514010292342921821435656694453}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":237176808745326205587468315292642961187},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":118588404372663102736608877596970577905}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":4035880598405642708879539854490510761},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":16143522393622570792559513753177126931}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1382871066809149401263560753372189545},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2765742133618298814483904271770617695}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-150173840428227912858163952435551367837},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-37543460107056978226507382555119768519}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":74864792297550728128157191557223801225},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":149729584595101456189843627690944323019}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12468968387721466128113916086748061033},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":6234484193860733054813672101796588179}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1105335510125908776395759820973799},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1105335510125907340706902452677445}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-12479148844745034494475350859075806929},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-194986700699141164203698051974407291}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":128616354627613070726140508916042608753},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":514465418510452282848579244163678108629}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":51748714947177867},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-2460619423555403}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":275273957432402185},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-393334314314289751}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1652680828755703201},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-67065651451605283}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":62305495566626617},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-23402440909089527}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":238708381325613},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-5201373867580673}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":435396567299249917},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-4090832543847329}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":457035518300230705},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-232141093497340009}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":10139620535356665},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":10925565809649419}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2073839745801137},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-239243733607869}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-16386433653509443},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-21411818221939049}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":119862431263679929},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-767685583935196977}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-10718715257191857},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-112732966210108297}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":503623910716162087},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":138760185224808681}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-277487290385740991},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-124223803810363267}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":173742263816361029},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":95810053316243703}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":9226492919882399},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8379721902620791}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":211522439889477573},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":117146313771622303}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-164890815904245303},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-290260211584112147}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":73094214329751297},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":41410942801589281}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1087410348537375},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-932005001889479}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-16584075087023749},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-60151547624266241}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-6227148640677359},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-213606552756452373}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":85070591730234615865843651857942052864,"numerator":5296194892111369559},{"denominator":170141183460469231731687303715884105728,"numerator":51422955352709452017},{"denominator":42535295865117307932921825928971026432,"numerator":12057257185340960165},{"denominator":340282366920938463463374607431768211456,"numerator":13551936704048877105},{"denominator":170141183460469231731687303715884105728,"numerator":3144475390811229743},{"denominator":340282366920938463463374607431768211456,"numerator":34611618991988151413},{"denominator":340282366920938463463374607431768211456,"numerator":43815188055061729563},{"denominator":340282366920938463463374607431768211456,"numerator":6417381872308112835},{"denominator":340282366920938463463374607431768211456,"numerator":1947963189526811435},{"denominator":42535295865117307932921825928971026432,"numerator":617346422106906691},{"denominator":340282366920938463463374607431768211456,"numerator":48634396595966141253},{"denominator":340282366920938463463374607431768211456,"numerator":26468327490097992653},{"denominator":170141183460469231731687303715884105728,"numerator":29331589519364265995},{"denominator":340282366920938463463374607431768211456,"numerator":57015576086923046649},{"denominator":340282366920938463463374607431768211456,"numerator":21440356727142399393},{"denominator":340282366920938463463374607431768211456,"numerator":5969588275101867707},{"denominator":85070591730234615865843651857942052864,"numerator":5971400207351231371},{"denominator":340282366920938463463374607431768211456,"numerator":33172693013911706293},{"denominator":340282366920938463463374607431768211456,"numerator":9227444305813361329},{"denominator":340282366920938463463374607431768211456,"numerator":1434213147192138187},{"denominator":340282366920938463463374607431768211456,"numerator":7267170534918020475},{"denominator":85070591730234615865843651857942052864,"numerator":6983602415748338969},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":105},"tube":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":35147122874477641734760743146902449},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-22832366750779923581533913037470535}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-446126829981667722758165151038682722399},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-224559711301020056314959405222861332545}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-23798153561015222211721459084888816049},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-6241329396281381373948485994197680649}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":1910831932379120506889469383669727285},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":7198494603325381511531407100181950807}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1535120362735625571116438048297825931},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":667994487614482453759961924807507497}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":86166901168912696729562565847916949879},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":81640937977405260137133149274280118565}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-40803852530708312621765723948474812441},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-86141960510487261746572577193594155769}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":10111715393131181066840381088354173889},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":4767642379709842151624583704523635835}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":9628865230252532670383892589947573},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-5665991385623227453462643150321027}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-19103222970644795653129199849482463687},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-10129861607482867461129323153422307019}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":28185740714560269417265533271680410147},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":111963677933897518897429007437721781675}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-231031516036947268412661842710404917},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-269123282930968553699393840119683423}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-495041439477855766981923201461397245775},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-510695139379159625673618903537137737713}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":237872280653612915009596088898960251115},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":231540059240552825859534582044861318903}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":4080716537642963617335501433363152375},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":7417823277772121519941079084709521621}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1269825445621653840833749480266863505},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2799592394569121213591898303186818703}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-147123571253369793839184007315200325355},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-75290918824028561938258374707938565291}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":75067345364568752043253571894109785133},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":73349424974124646193328438301423042919}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":6305903525496853599179987071791133613},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":5716302227372599051663236356840492771}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12697871427385759475009496620656297},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8276734237374980089330618064634307}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-11441980556777803787717943530728938411},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-788879488366533058621610728938524077}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":516133848178965218328734734259591084827},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":500073435784754853015048048237618769299}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3987152672491623510982992223358377},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3987152672491580154751452295120763}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-888355866573481970733070353509758295669},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-888355866573481970943462432026506321761}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-6428394619457609645259811406978798491},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-51427156955660877260715382630040468597}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":31760345072223161234009611213386402783},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":7940086268055790301339143111798380795}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1671857124902669268767759535420870203},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":208982140612833656906287768448999125}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":44588369480435019094466394759891768609},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":89176738960870038117914925882558539827}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-89161640038862899786954253240497545735},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-89161640038862899876813649582224274217}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":20992406083272305640120303064876169203},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":10496203041636152813232673291007665155}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-964990941313634050685211469147459},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-241247735328409562867827060151849}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-21031158388127850836690746372913309921},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-2628894798515981355899164301941242975}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":891543449376788599012852008265309239115},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":891543449376788598913509097296985381245}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-16388403083806211693634266955166233},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-131107224670449707389845390297049239}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-32588473420621128390253173452290153031},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-260707787364969027183272803951595977175}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":242081612867916138125847777332775378633},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":242081612867916138006719347300343505251}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":17349144158608190613784753817344539845},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":17349144158608190568783907596661583237}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2973816656350476771087524589414315523},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2973816656350476783783266086772255165}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-152778951135749282391458154793118870641},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-152778951135749282441440634712315263171}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":152318555997253546509418492029653753357},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":152318555997253546440055607862362331751}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":13427380981388835377340782764028530183},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":13427380981388835357934319585278151583}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2475308406888441832972394586990983},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":154706775430527420224585687916587}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-3359563405587703094828452844080528369},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-1679781702793851549325766449406945161}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":131788013778263655075361135960112377489},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":527152055113054620243043861930798342313}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":25872312587185901},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-58870134498451877}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-119880957528826471},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-461188707318349867}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1874904068528206287},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":271659637910015565}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":10077634853879809},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-20054355052804627}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2282943596165709},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-4698916790160747}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":64300887028494297},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-275058356656449877}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":590242368565773187},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-55009641527151999}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":31084265427120033},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3226034314136409}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2055291709746257},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1757763322303165}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-4542551716466231},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-16966568104397577}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":81414265603452639},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-508173043504195361}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-3792960436671539},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-51692776537163697}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":478307641079804041},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":133122506720845473}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-264263507270275213},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-469875080180690731}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":164455616336883445},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":91397372309067229}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":8011489872244803},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8510539146349149}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":52557430140247685},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":60504251162484581}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-162097507935474963},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-280108339552380779}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":35552171209790885},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":20606789122253331}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":525077398935317},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-877661005193915}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-34816473380847841},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-60360181172224921}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-106967742154237253},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-214604042623034621}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":21267647932558653966460912964485513216,"numerator":1346574465772884329},{"denominator":340282366920938463463374607431768211456,"numerator":104333602322501726547},{"denominator":340282366920938463463374607431768211456,"numerator":97835269158900985307},{"denominator":85070591730234615865843651857942052864,"numerator":3571577439583968889},{"denominator":340282366920938463463374607431768211456,"numerator":6752888305326194999},{"denominator":170141183460469231731687303715884105728,"numerator":17621400433113642581},{"denominator":340282366920938463463374607431768211456,"numerator":44607072165816901647},{"denominator":170141183460469231731687303715884105728,"numerator":3406774562936963817},{"denominator":340282366920938463463374607431768211456,"numerator":2098486520869705257},{"denominator":340282366920938463463374607431768211456,"numerator":5238860004920385593},{"denominator":42535295865117307932921825928971026432,"numerator":6156817553900365747},{"denominator":340282366920938463463374607431768211456,"numerator":27633642693210946591},{"denominator":340282366920938463463374607431768211456,"numerator":61141385019455696379},{"denominator":340282366920938463463374607431768211456,"numerator":59461409229760728931},{"denominator":340282366920938463463374607431768211456,"numerator":22463893988327570195},{"denominator":85070591730234615865843651857942052864,"numerator":1584902433542418211},{"denominator":340282366920938463463374607431768211456,"numerator":24946629350480185475},{"denominator":170141183460469231731687303715884105728,"numerator":17311218333918628947},{"denominator":340282366920938463463374607431768211456,"numerator":9688286207287651745},{"denominator":340282366920938463463374607431768211456,"numerator":1553286773386033563},{"denominator":340282366920938463463374607431768211456,"numerator":7633388255571035365},{"denominator":21267647932558653966460912964485513216,"numerator":1821657675286949071},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":16,"numerator":27},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":55090183044378134027682304188107833},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-3106994215416768654075371053840813}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-443831681729655491098609653746931857601},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-893550674407273801009042500907705356157}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-98823331478605187387145475743921745051},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-103424160816093745914250829499257189653}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":1998442777612246937012341218681392499},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":30180643578729813757233005759704824687}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1700718342177559071013854816399333543},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1486637494794785906906677468551830055}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":89704416462925736193238917582259577433},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":42592596358544638771919996020880855463}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-85159504738037180797217170681648777081},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-89689224246347351906362912903021807767}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":21129525884176233454332345543466783877},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":4992734499829454710208751846424605079}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":1247640771575504869629202181980475},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11911074732447541772543312418971561}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-5001600123755542191700788283758910057},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-10584369597925849025599620078291786575}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":897031143312387046810944646217903007867},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":222712894185217483334375558116789414845}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-486680390715119801269538901290847741},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-562206011414821930158801407950022367}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-63438933850241640537511658527662929347},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-261516528961352401776427090994288344455}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":242763897276497182280286227358477437529},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":236556021130751652494654591375767873891}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":8767119953782554725017780266437233395},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":15988998225406733163951063866652616329}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1369364263936831101288758764450760257},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1504432292660014101036777554153425361}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-149840445954392863264938903686782978555},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-76587195346371679598594694487721807909}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":76355569144021474114222331386992291729},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":18674787606430161300972105721339380433}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":13575281089969713041577480832405341483},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":12346044754138327561632884333833685171}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":13025022086888375233079027452605443},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-4037295151628773450760611551440621}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-12356140120831232653171117508829028861},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13586227359969251066213448812273553985}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":528807693326532717857860491486098679823},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":512871832419776678958659105327962127879}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-258303366932093309287419872961043},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8265707741827029902956836450232037}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-441914925105061553180855604006810445115},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-441914925105061553287492930568034408201}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-53183422037996805718970156002224081237},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-106366844075993611637779739987579874195}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":16585622736770190177463753683566221009},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":16585622736770190162380753022857563789}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":923899910913357404062101156931610667},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1847799821826714793635932812702688801}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":23177019344021873193576666396991964799},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":92708077376087492702067873583923899509}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-92704409064983244290003927175257629071},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-92704409064983244381403413427173413115}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":21901417712814340548195628594755226633},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":21901417712814340533717673758085164719}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1087510863901526076346272202599637},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-271877715975382648498217788464095}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-10971585479055316228454088266149214717},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-21943170958110632468034188512710432981}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":886718760565520042312836071783804393591},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":443359380282760021106152724243975709663}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-548331135412102366605961084513451001},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-137082783853025606080831232626639551}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-533664070961840557394326763960574924647},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-533664070961840557521818759449706866623}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":246889009271096836293551596813266262381},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":123444504635548418084742873430706915929}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":2325112339552593520186782443600348751},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":1162556169776296757150417757439728347}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-797440169860802364453235864875397819},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-49840010616300147988704373418876785}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-77642513788761439676509035452848906551},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-155285027577522879405148023303380395433}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":77404901027482244322456727848637102965},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":154809802054964488572617420492486325917}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":14425790635621137791484654855527036643},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":14425790635621137771134026211683089219}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":345032218274298769617384680078037},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2760257746194386794493690120786081}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-14437319692444896474654055667874091987},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-1804664961555612061337091219759348067}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":539740062920719765374171397172144386331},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":269870031460359882656663025800876668699}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":204170868390368779},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-44714207500981765}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-423947891204976129},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-508500683421871703}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2021882091919687213},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":527465693765469825}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":10884367259647803},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-26754795640193509}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1329084396557555},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8448745357114589}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":53564709622117309},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-393629612263316605}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":344856612888836145},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":21298028055318901}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":355503630410703},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1742007440371669}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1013279113620211},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-405506848496099}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2526597791324339},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-25995113065576505}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":124752235580986413},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-35855387948886701}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-3569143411448401},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-93740519178309711}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":223504728869865961},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":124078830918211535}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-244584602323805797},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-437177680849507977}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":153166934569215737},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":21180001282552889}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":6932753859077913},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-4319639493415919}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":51303149119282371},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":7547087625297869}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-154808034685938069},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-265831836077072715}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":67987859561688953},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":622134473342981}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1022738535152019},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-825558280176511}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-35204837726520481},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-59422251690506163}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-109878699994994749},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-26482975859337395}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":170141183460469231731687303715884105728,"numerator":10939218581156032029},{"denominator":10633823966279326983230456482242756608,"numerator":3307259348124459617},{"denominator":170141183460469231731687303715884105728,"numerator":49586252896244373583},{"denominator":340282366920938463463374607431768211456,"numerator":15045361497808815907},{"denominator":42535295865117307932921825928971026432,"numerator":904822661688143927},{"denominator":340282366920938463463374607431768211456,"numerator":35869016486268204231},{"denominator":170141183460469231731687303715884105728,"numerator":22698741284589846839},{"denominator":340282366920938463463374607431768211456,"numerator":7225859294721516791},{"denominator":340282366920938463463374607431768211456,"numerator":2256999006665015961},{"denominator":340282366920938463463374607431768211456,"numerator":5551271732568875689},{"denominator":170141183460469231731687303715884105728,"numerator":24936192812484483751},{"denominator":170141183460469231731687303715884105728,"numerator":14406798117556561473},{"denominator":340282366920938463463374607431768211456,"numerator":63646571846614316561},{"denominator":340282366920938463463374607431768211456,"numerator":61936628436663364171},{"denominator":340282366920938463463374607431768211456,"numerator":23509564250164066137},{"denominator":170141183460469231731687303715884105728,"numerator":3362141101615153303},{"denominator":340282366920938463463374607431768211456,"numerator":26022746601605109375},{"denominator":340282366920938463463374607431768211456,"numerator":36092505701698372683},{"denominator":340282366920938463463374607431768211456,"numerator":10161228695288104627},{"denominator":170141183460469231731687303715884105728,"numerator":839942883056083293},{"denominator":340282366920938463463374607431768211456,"numerator":8009228338118353433},{"denominator":85070591730234615865843651857942052864,"numerator":7592920057938918065},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":111},"tube":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":20366901791535457067820481104774645},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-58699116315521381284302290332600343}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-883151552032473112724030743011697235573},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-111116765468088147176536021936838739411}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-102401678269209115557735633608843781189},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-26732008672583875805487280109497618075}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":4173415460875151226144589582106863175},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":15789784835290577902467166978669837269}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":939251218376179135240300494702709167},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":824448267348574126779023238193958673}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":93233111445321824005519377964868796123},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":44363015453521030954090548814538519255}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-44354823507795984366890835552613407711},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-93229577248301279265507490258910862997}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":5509716856287123116761017429338539803},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":5219033150210404549933594275104885787}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10324828000666558800942360067065471},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12499845459556336241971443378803293}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-20914499781755019825483577360226903047},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-22081085845483329937555265288067716235}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":892155419086111835847753712732643580745},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":27688616312277483359335520945572606875}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-255484304588914403971559863871999083},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-585720685061265631371063820761390311}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":-8123069717650236556780236424009634507},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-267633794966422142867545784968925876687}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":247558164844097181892780219983599044917},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":120736553546392455454134069490045152891}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":2348957758142907241713898564731145151},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":17188864391215405306014209472193712845}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-736449324453648490845491546786639221},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3225990883173422040437548010800887717}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-76228980955816113275905791283030073307},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-155667854152802784948277302637624131329}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":155189825276111538538929085610330863555},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":151999526077380436206847443423807688711}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":14578719415184769797722400017374005425},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":13299454488744842642402310404042694983}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":834852334674088075233647801567247},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-7837285522292887736298392003395279}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-13310247453171379131534444818439441019},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-3647577286241427902332027049560727509}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":541382890511826309915475877156227923563},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":65696356397482220729374482499343503389}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-22802990588725291593803040512300137},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-22802990588725336238422431802932297}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-439695589719918462932406249632432589599},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-879391179439836926081017419516393250333}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-109816065840678089347663291279509175297},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-109816065840678089549997526885059691833}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":4323922933308447125911155809079024115},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":34591383466467576975560016888143350253}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":254541546841064495806429073315406853},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2036332374728515950947706938533604927}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":96227020499290264318804227293991236921},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":96227020499290264245350092591120382179}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-96236783426443842264898937035636163323},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-96236783426443842357840720273449371511}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":22812574903198401726529465871740735775},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":11406287451599200855597617868453084155}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1219134796758947875042079102664485},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-609567398379476363051800714431791}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-11428703120972916443590722295726405473},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-11428703120972916449478221081253332435}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":881946468127987335453215923839401114545},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":881946468127987335351458222486196181617}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-142941693779417944543434210989960673},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-35735423444854489892249272219948663}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-136452675338323934346828352414467608985},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-545810701353295737519857994677860183931}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":251600456812798794857331854381259604145},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":251600456812798794728269152848942998513}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":2487298500020770141810982155854404121},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":19898388000166161085268423457172325223}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-3413447502396886284444908487153967897},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-853361875599221574676974947032935693}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-157692494420394477365099223317091131139},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-157692494420394477419407614846622289817}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":157203902505823713634724866180762549041},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":157203902505823713559454084336289832509}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":1933022004884745530528012501776763725},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":15464176039077964222904364343389987563}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1532996421019991305825882585905673},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3065992842039978980393686415909003}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-15476312305420611199078397182456121795},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-3869078076355152803972820480225784465}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":34514391439213049812446428396070643131},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":552230263027408796935825361070918722517}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":25168438434598519},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-8832238374038449}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-324120532002970507},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1073850218097534215}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2096723623423029497},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":709789861855833245}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3206606093689763},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-31888577588318847}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1510579251825643},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-7586097958919283}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-8038501289456873},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-243528295429513833}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":379268232360425641},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":193367701034179449}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":3878944596115167},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-4597723697640247}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1988780441161259},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-375487966094913}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3220815219985937},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-18956309759158917}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":319798453552940011},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-103524614112076747}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":979448940190577},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-84318624615095407}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":411718399821563693},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":225473826867851587}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-55205587790819007},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-200353507925513815}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":17566259980854983},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":38313899295010275}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1518198733723761},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-4396834404436309}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":197130964311708273},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":117142755798999885}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-144210827843317927},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-248501379796201737}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":64012392594349443},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":37508140861013211}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1000941288271015},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-773719660559887}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-8643064659629663},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-57520214817983083}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":-1701741010272547},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-205999620085696751}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":22203971465158845105},{"denominator":340282366920938463463374607431768211456,"numerator":107352730439669471859},{"denominator":340282366920938463463374607431768211456,"numerator":100473650921991660141},{"denominator":340282366920938463463374607431768211456,"numerator":15829519608562412723},{"denominator":340282366920938463463374607431768211456,"numerator":7746559195763539663},{"denominator":170141183460469231731687303715884105728,"numerator":18245788778647685205},{"denominator":340282366920938463463374607431768211456,"numerator":46188307237063268177},{"denominator":340282366920938463463374607431768211456,"numerator":7654759454527413151},{"denominator":85070591730234615865843651857942052864,"numerator":605946348752582273},{"denominator":170141183460469231731687303715884105728,"numerator":2938205111518677267},{"denominator":170141183460469231731687303715884105728,"numerator":25253644957996744039},{"denominator":340282366920938463463374607431768211456,"numerator":30008476719002024965},{"denominator":170141183460469231731687303715884105728,"numerator":33089585111759008971},{"denominator":170141183460469231731687303715884105728,"numerator":32220704216907213507},{"denominator":340282366920938463463374607431768211456,"numerator":24577765754203044215},{"denominator":170141183460469231731687303715884105728,"numerator":3562031209308501803},{"denominator":42535295865117307932921825928971026432,"numerator":3389275207563653143},{"denominator":42535295865117307932921825928971026432,"numerator":4697905705782489545},{"denominator":170141183460469231731687303715884105728,"numerator":5323307854772696501},{"denominator":10633823966279326983230456482242756608,"numerator":56698589033539243},{"denominator":42535295865117307932921825928971026432,"numerator":1049371048891721977},{"denominator":340282366920938463463374607431768211456,"numerator":31610202535391656917},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":32,"numerator":57},"tube":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":6746927020226980623782492886968009},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-36366327081578278713358560733535365}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-439362754595528510313334360430722785903},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-442198499606120780284621660705459213765}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-26480567674588082838294156942850352581},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-55184002237382566100406733951422838135}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":4351078425639918886862483610098272671},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":32989314147809383572523909930815759873}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":258616285779766433575640360562526297},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1823229770225446274194911449278158009}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":96748905870594398970528228420715317087},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":92259096432253392005572278357722269161}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-92253893641553318981116655166337750463},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-12094880984481571508748671632064160123}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":11475099966256400731194506272552248277},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":21784886355070067097198635870747099453}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10659391321762730486701938557542035},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-6548844210660958212057079001307935}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-5456561418232365815918825381342865057},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-11497749262370577598002024697808948367}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":110915532694083307356346910879149137225},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":440634625840601146735691568369164655633}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-267422393356133248668772178487684243},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-608714024879656811993752925123737187}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-66517227282571061638066250767156432305},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-273700172636644568001248791085731432477}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":252256566933309762739363068995799396527},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":61573153493823849970985955483869879625}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":5023682275205259326901282743281205985},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":18434917562598493759606856446467606225}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1580375801797396688618618475595660043},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-215677647629934636437143739704423527}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-154976400322834572833563680672107137481},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-39515668217429409507026895202247659533}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":9848209489469322285851598159367496583},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":38625740797725992476459684227110001619}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":488190491689316541481268534342365685},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":14292867846905916487104407424316881635}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":13696283860947617385710558945505375},"lo":{"denominator":332306998946228968225951765070086144,"numerator":-7387147474184433812915264806893}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-7152162198976422336138937685934062815},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-977142333929585168502479758306533353}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":553860283767183447046013327738490937717},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":269085574746667455893735954782223287817}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-39794264269816404506911790269338595},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-19897132134908224906297526643064029}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-109380834844914626774438736923498794729},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-218761669689829253603679054825755740749}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-113197426933787809937736354047219772713},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-14149678366723476267812129010806322363}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":18009693930985039892144039990729586161},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":36019387861970079750944453623298364281}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":69934634270362908074454550203676011},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2237908296651613041817628323228556875}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":49864837767834300857680116157941550907},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":49864837767834300820346240864186428343}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-99754971476450704391413509698659687245},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-99754971476450704485902621674414237525}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":23724631062714623992518310467020043919},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":11862315531357311988146867898096153709}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-679875812883059501603994825456065},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1359751625766124204830473405631667}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-23772607837703907972716607558055942921},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-11886303918851953992583441685721105001}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":54827098147932929527147086115862705399},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":27413549073966464760353641246077536907}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-297330741424535801945973904225485309},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-594661482849071666411102658371126963}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-557857196427250042129588292488628821335},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-557857196427250042267242073157019314141}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":32027193516626696555653681718249804113},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":256217548133013572311110326243891493621}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":21241154425039470881797520308970356175},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":21241154425039470830400436976884166931}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-3644731987320051960897092411539652017},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1822365993660025987995323754759742019}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-160001897355495574977227681103983652857},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-80000948677747787516873090977767229571}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":159501556425000303527596026964113955679},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":159501556425000303449308071794408830061}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":16542468138812597771985149223123501249},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":8271234069406298874835320155162243639}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1696459007502967629527112096269763},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":424114751875741417816988159559027}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-4138787010974525018644546124933814077},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-4138787010974525023045430899465761437}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":564623614677229083182237904821916101685},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":564623614677229083116419396878278225483}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":197358443558593769},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-30615667749322161}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-400423512163799343},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-274401523867705817}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2109478785139453251},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":827673367403886155}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-5916231032355733},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-71174547949274033}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3368358954654533},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-849847243906237}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-112197238973965805},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-557142864553876973}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":800734843684559253},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":136337542398285531}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":9295050984858831},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13909699548601885}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":486628937523713},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1399512317597013}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":8134230599951089},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12879160041039921}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":374477107901040349},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":10274331491292047}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5738619311778029},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-75319414414455019}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":374055394816742727},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":199763435548994611}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":-3039404191648419},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-45262086736135741}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":127116309018246483},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":67661064101837943}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5392928445450553},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-4468071432375291}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":93347543228534473},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":13842704287902451}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-16395756499562877},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-114547810089605363}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":59427296834573879},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":34511940796236155}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":490266497472215},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-724149017486275}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-33068098808744631},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-54863400935144189}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-13082212985893189},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-197617491277399975}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":170141183460469231731687303715884105728,"numerator":11269427287927218383},{"denominator":5316911983139663491615228241121378304,"numerator":1701655927722019979},{"denominator":340282366920938463463374607431768211456,"numerator":101739436310747619547},{"denominator":340282366920938463463374607431768211456,"numerator":16639184020621944869},{"denominator":340282366920938463463374607431768211456,"numerator":8277375073191585523},{"denominator":340282366920938463463374607431768211456,"numerator":37111402480965166979},{"denominator":85070591730234615865843651857942052864,"numerator":11745131527108320261},{"denominator":340282366920938463463374607431768211456,"numerator":8100684960147137891},{"denominator":340282366920938463463374607431768211456,"numerator":2599138227843513835},{"denominator":340282366920938463463374607431768211456,"numerator":6214631211372638035},{"denominator":42535295865117307932921825928971026432,"numerator":6395562568092824553},{"denominator":21267647932558653966460912964485513216,"numerator":1951190525506060103},{"denominator":42535295865117307932921825928971026432,"numerator":8592468044320171543},{"denominator":340282366920938463463374607431768211456,"numerator":66975776338241676085},{"denominator":340282366920938463463374607431768211456,"numerator":25668814043584890351},{"denominator":170141183460469231731687303715884105728,"numerator":3769806506667407721},{"denominator":340282366920938463463374607431768211456,"numerator":28221273699698478473},{"denominator":340282366920938463463374607431768211456,"numerator":39095012800761208953},{"denominator":170141183460469231731687303715884105728,"numerator":5572398389190169061},{"denominator":85070591730234615865843651857942052864,"numerator":489261185985768791},{"denominator":85070591730234615865843651857942052864,"numerator":2197717974500173735},{"denominator":85070591730234615865843651857942052864,"numerator":8215693519530952717},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":117},"tube":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":1701718474907671126575357320091675},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-11489391068582840690792394564970649}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-437196030143965752451810379237992648439},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-109993329640422746609813242206763478639}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-109380121126819073992635924446022085607},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-113739568265409227542909590581869726953}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":36237628697506245391122489596470616267},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":17204233664842751353582093171441090595}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2272454260363002322297323419669509705},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2010096609658017465242193751849253779}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":100247936214225114050410520769906312155},"lo":{"denominator":1329227995784915872903807060280344576,"numerator":374141609712967677258285765165917645}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-47894108974072560954101517341728355847},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-6267117045695770342197628500389248277}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":23862278235582334148205992399490436581},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":1418496324975011687248238630351027715}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10984354491706591862677900715606791},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13703919636583093735166424636471801}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-11370185570177291382383769582394138653},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-23910722156267083988906591232410358147}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":441272526043495718414014786571425343283},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":876559212496950423079893082307378221913}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-558231467090034625039054058108857979},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-631114836920544785784475983947310997}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-544297103744718736466226312126528497937},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-559433079830488745677097285240924622409}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":32107589949058678070363392487092856423},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":125507991585306584595543577021870215455}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":10721489189123453862048408797906518449},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":616461463970189941418706301308635277}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1691733518391045875635587428270495719},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3683271692930037083008508963647500471}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-157396170252389531716348784545947922581},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-5011231622888718381370411564323648519}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":159856436557079987361157800983514095673},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":19613647062516071503241431113616124637}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":4176334057413965748449618484484911083},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":7663134675617987735291398183163165319}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":7020736301913371023130166104559173},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-7255753230818255382616529732983267}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-15338342151718047449959403822139626621},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-16718043688743684941149335226281322803}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":141560213602569243793064555135361369393},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":550673530651534554909555043107635388005}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-14851527777442549027943354779025929},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-14851527777442560525864153571367245}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-870802721653904527588946771932014754079},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-217700680413476131952809489458036266083}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-7281672002565785917055213097101282379},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-29126688010263143720002756766420878353}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":18726961353620433846168357483150822841},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":18726961353620433828663229517701721263}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1226487555087700177282646727199626029},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2452975110175400336892315103846029373}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":12901545501893372884322853476429191671},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":3225386375473343218709419838705281683}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-103255386741491602471105882415112753343},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-51627693370745801283574290444074575263}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":24636350821921274994418335979638267865},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":12318175410960637488634259434334368015}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-754572452238100066677577898894563},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1509144904476205703288354818106643}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-24687529838157674908122323908980856813},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-12343764919078837460637414595997322173}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":872586717740407863847313418459199433385},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":872586717740407863742938595744365108725}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-154236699513491657248424059144056465},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-308473399026983346981680398229458441}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-569805424364839871262738960211461816921},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-142451356091209967851390048971065265319}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":260742000293102156692067714902841687261},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":260742000293102156552831835759965654255}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":22628684298136201007431627964514586789},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":22628684298136200953810190007728625143}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-3883450919980826966945490208835181709},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-485431364997603372862830945610550199}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-162213897064532814766182796084354773629},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-10138368566533300926558980407992374689}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":40425893935522036305114479844626223053},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":80851787871044072569554753581185053915}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":17660551843673389503629763255472114741},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":8830275921836694740147054633747530143}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1870682051942514170939360984820567},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3741364103885024122936351985832715}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-17673696581963257738208433031893315097},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-4418424145490814439155910768053205563}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":288460604215468107026180693383457230399},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":288460604215468106992005837339555870917}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":191663120549283319},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-29172713862339541}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-222663322007654325},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1093551436191788089}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":518374412487806273},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":55506715190643771}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-7724112728695317},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-4753007358994135}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3694085712236237},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-3048667647718403}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-186017713249699553},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-303267562875280305}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":818263003031835819},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":326671971882421505}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4057241963642423},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-8830233484995443}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":946924548547373},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1312014598641867}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":3054920220729703},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-3817898468752765}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":51890286648658367},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":154812846686799173}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10422793944167635},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-66780500051997431}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":167735048256788359},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":86188748485810877}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-166797645793700329},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-322898279894716655}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":113486561178601147},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":7271187857386567}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1208728130023493},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-9041271326341677}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":174478610528154043},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":6397044428126893}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-116634390840794923},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-208450734739534593}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":54443989779365691},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":31096120657756255}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":240015486258747},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-337362924197015}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-30919400838184393},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-51619962437102097}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-24503638112543571},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-187204709265772331}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":22885423680378871201},{"denominator":340282366920938463463374607431768211456,"numerator":110497368157888675687},{"denominator":340282366920938463463374607431768211456,"numerator":102971113652581035295},{"denominator":170141183460469231731687303715884105728,"numerator":8737414009652921907},{"denominator":85070591730234615865843651857942052864,"numerator":2207898366193193705},{"denominator":340282366920938463463374607431768211456,"numerator":37730437780181829227},{"denominator":170141183460469231731687303715884105728,"numerator":23887776860471745717},{"denominator":170141183460469231731687303715884105728,"numerator":4282024850508974631},{"denominator":340282366920938463463374607431768211456,"numerator":2783363667662290451},{"denominator":170141183460469231731687303715884105728,"numerator":3283162451298340797},{"denominator":85070591730234615865843651857942052864,"numerator":12962423871892823745},{"denominator":340282366920938463463374607431768211456,"numerator":32446230632943262977},{"denominator":340282366920938463463374607431768211456,"numerator":71329071536628644695},{"denominator":340282366920938463463374607431768211456,"numerator":69539889254387508339},{"denominator":340282366920938463463374607431768211456,"numerator":26783060449233226517},{"denominator":85070591730234615865843651857942052864,"numerator":1992910146525348029},{"denominator":340282366920938463463374607431768211456,"numerator":29344382271922548819},{"denominator":340282366920938463463374607431768211456,"numerator":40628297936118022355},{"denominator":85070591730234615865843651857942052864,"numerator":2914038264856930627},{"denominator":340282366920938463463374607431768211456,"numerator":2108316428170992685},{"denominator":340282366920938463463374607431768211456,"numerator":9197254739360294725},{"denominator":170141183460469231731687303715884105728,"numerator":17065130482746780229},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":8,"numerator":15},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":374514258093873156171793037193491},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-29086210507063336805570565977320459}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-870157582090474645699214247275623761725},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-875589911722521722049771994217069902643}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-56385314978091758901561805408860833903},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-117038599732226439149251040913679461323}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":37672996016138017037246279343317172319},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":17917826811309043359566569705035734163}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2489520662660068934628075459506525441},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1104975683547558971308233642986432653}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":103726552821139713176487046777703204405},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":99285578059505144803381974256333567433}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-99308802416091351839187329609817957689},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-51885246509842438680724564149605998847}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":24773868498892745778123555219438165949},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":23608049125361499331645977838162405853}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":1412422672160997008314278241890767},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-14317769951963527882792614644280871}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-2956952306954505518379534096881597799},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-12412756138157341201919809203030566065}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":219456205470381407277587769937422893719},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":871912306735538062350374062989831945513}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-72632140197367522763062352962814507},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-652857748449198374870639576020389147}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-556356030942737413837168868091661890449},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-285683842893931848380681554931153971877}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":261372361978031979319275405051935616033},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":255644791039122638199091983909772896069}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":1427243221308444306080838386958852243},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":10531980706081088855928386298804265437}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-3613800707293740598715139530607878883},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-980778376889213555133666535225588667}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-39929450636867584044692624801153210545},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-10159921914232670260208894749956105837}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":162045910027519249066820159545892718321},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":79609425234582432523681142011065129263}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":8914160628318244497371449521624084215},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":16399595570165498722440389095663716533}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":3598413453133693301351157087774705},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6911016820254141059717357419376575}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-8206111511568038909733699129931330655},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-2230184153844537546321907307445669467}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":578525714188392144918156520559126459157},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":563078936953766520694004160669403615569}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-20450282424927325689364942069373633},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-10225141212463668682780801647529481}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-866665241922460908507536727003289253971},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-866665241922460908733008434274375924691}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-3741882243524144626807549566694187991},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-119740231792772628267322708435193526093}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":2430855508847284326808492781003047285},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":38893688141556549192205698415026018037}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2681973574022805749498085926206960047},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2681973574022805730669060706816229925}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":26667904531772006847483907489678657971},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":106671618127088027312839592254542667415}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-106734643564122838304369454361677490871},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-26683660891030709600493459025982242311}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":25546510986532689496939415248852388033},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":25546510986532689478828576332939454015}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-416746378537662644270239220106271},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1666985514150656533696589783612585}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-12800468903100919443896417428741018375},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-25600937806201838901675216723761638387}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":434006108117381010776204742857470306445},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":868012216234762021446632498128388305501}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-638560544112527517134941597443137755},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-159640136028131896147598240122135905}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-36353586344883482910927657905536459675},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-290828690759067863361445767192611282961}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":265175645642581321765509181575160557591},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":132587822821290660810547426182171558425}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":6015102792551448877625404535188124609},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":24060411170205795454607933860560080179}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-4129423397184813572102468455801997867},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2064711698592406794478808421141780363}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-164329263261268088718311140505767292973},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-82164631630634044389673650574930780825}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":81905439440136632401306376630122975583},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":163810878880273264718159634838198217707}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":9409133856524734758330705567050453989},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":18818267713049469492277497381940732327}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4111584748990734391682592724287409},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":4111584748990729852414980742297265}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-9415891217888275671828625913019635037},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-9415891217888275681452861366180102493}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":589124259387240404839078531504444279579},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":589124259387240404768166109805099707791}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":23077448734591431},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-30079553929833011}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-928122246727494415},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1067069028790502743}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1999359420565866703},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":450752055419741395}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-2812223396665577},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-39353190277401689}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3995381410922033},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5469839028027075}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-119874100045400001},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-318315591220859627}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":815025491914656105},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":44832055453288559}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-247587566641915},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-20515052863604897}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1832298809082889},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-308902760653289}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":15504266782321247},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-801972511653147}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":221245886877383755},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":60081923847037789}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":7439125422092179},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-29397954946031389}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":37138599374626691},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":36098425645466311}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-138673557188772435},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-284251886119968751}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":100041119785590159},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":48508536425423925}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4380769228446677},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-4551285793805749}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":161052724664082103},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":46312946654153631}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-50657386546654315},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-5852577220778575}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":49249490338772505},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":3429604808107203}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":469385249866981},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-626141449724325}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-28320802296258509},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-47957181292729755}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-44839159372131517},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-175318243131522251}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":85070591730234615865843651857942052864,"numerator":5811260937637022107},{"denominator":340282366920938463463374607431768211456,"numerator":112132845730116579823},{"denominator":340282366920938463463374607431768211456,"numerator":104191633495626563233},{"denominator":42535295865117307932921825928971026432,"numerator":2292123592977578735},{"denominator":170141183460469231731687303715884105728,"numerator":4704889999737945253},{"denominator":21267647932558653966460912964485513216,"numerator":2396848585056907663},{"denominator":340282366920938463463374607431768211456,"numerator":48574006346981565369},{"denominator":340282366920938463463374607431768211456,"numerator":9045285725307985517},{"denominator":340282366920938463463374607431768211456,"numerator":2976773861525745727},{"denominator":85070591730234615865843651857942052864,"numerator":1732958713681333475},{"denominator":170141183460469231731687303715884105728,"numerator":26283082933607730881},{"denominator":85070591730234615865843651857942052864,"numerator":8422722150288644841},{"denominator":170141183460469231731687303715884105728,"numerator":36974073201056015709},{"denominator":85070591730234615865843651857942052864,"numerator":18033593860235780553},{"denominator":340282366920938463463374607431768211456,"numerator":27921075848416126011},{"denominator":340282366920938463463374607431768211456,"numerator":8420832522832752341},{"denominator":340282366920938463463374607431768211456,"numerator":30483866906369246917},{"denominator":85070591730234615865843651857942052864,"numerator":10545893840509515961},{"denominator":21267647932558653966460912964485513216,"numerator":761315659383945649},{"denominator":340282366920938463463374607431768211456,"numerator":2268538279291403765},{"denominator":42535295865117307932921825928971026432,"numerator":1201802157957778979},{"denominator":340282366920938463463374607431768211456,"numerator":35413390887478656285},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":123},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-12965235850823277671828611787002749},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-146115181178186772326411864706260977}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-866028013959627156744848202249638457339},"lo":{"denominator":2658455991569831745807614120560689152,"numerator":-6807290974461300452575982099193433543}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-58044787969252512501241502914181686295},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-120261336963980521706487040881911571775}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":39113433999313757193947194560057011603},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":37269532563677213264368599288328239789}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":340071120001301680002441428081723977},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":605810615048433053580656039299534621}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":53590658061794087183501495789279058687},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":51385684668215647534445075256006042535}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-25703008814544152069189257031637195295},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-107245550091326550220245568813165247255}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":25683749164536955899033829852848951707},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":12259986614148655215202853146378619613}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":1450533576279255742941415108437363},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-14938377617969915520340602704263121}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-24570740264686835717160410330425188915},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-1608664749962201726673721494809913271}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":873170253568543981308039671391837616041},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":867334895287182806700777144264479045039}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-603256571298506053184828917195938529},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-673883604455937329774534537163946567}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-568316451278382340966591207969869910067},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-72900772767869705491008591023345715381}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":66448336806790920573195918912668015765},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":260180739522650875915059408861106802659}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":24272897847888398468154584406342186501},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":701437309491227816215094838444169477}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-3851591601208795420652413955955483647},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4170184788929110883583174285729208713}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-161941943797076297315986957109685464481},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-164661476471641471817945344657355300409}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":20517588553143285388067855347875182975},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":80716391610874176015919568146759797719}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":9495443511146667824634439448423004213},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":17512736823826728794852467953231259875}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":14753212169584075309398996935879701},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6530107275541450436908285391877545}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-17525842194036060493494070481555034631},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-4751096518327008235159423446478645933}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":590716098484273851190802346911652956097},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":287694221434727127147184133204468955927}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-107136983657568004985698560251847417},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-26784245914392013108128932481836559}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":-13478746036691877482583385326420057037},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-53914984146767509944630839211834234495}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-122894410805546776594527978669907463213},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-122894410805546776806391768037134340951}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":20168710549773223700087790326780637341},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":10084355274886611840417811080713692283}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2925336935982788496932636782780153499},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2925336935982788476898546105737287915}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":27526044057340375091355403273090984839},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":55052088114680750143554572811973041237}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-110189552031318778301891672346540744117},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-55094776015659389200534716018880679629}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":13226950704750165888519636127407048825},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":13226950704750165878965338905518678893}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1832824777092238236322844676071251},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1832824777092244598637968495254153}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-6627902417230972983907212699189774901},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-6627902417230972987567374542514101115}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":863516032173653005688523577701352480473},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":215879008043413251395318917729297648583}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-659447180183151527859665711725733581},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-659447180183151597837868471291511963}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-593415183187791313295854838650101345731},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-148353795796947828362298529296326000949}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":269520422941423292942191833920692108259},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":33690052867677911599066970169750463343}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":25535719118866659845644850311091446585},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":12767859559433329893714855808343850759}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-4382451238577623712765379708710953449},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4382451238577623730554281342426906059}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-83174434416632764748911285954664539009},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-166348868833265529561167551461622535591}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":165824484541569738678097586069450621097},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":20728060567696217323811795796881095833}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":20015413623924091227034128629556731959},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":20015413623924091201573986548097320041}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4503752947900227203538041052360525},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":1125938236975055581320954372020011}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-5007296674418836193741895039797012849},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-5007296674418836198767872113894377049}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":601234100488596408166322303952937105091},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":300617050244298204046407161443804544849}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":22052152261233247},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-32805675842506689}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-924359150613283345},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-255564214941545775}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":946666458114092017},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":220175505522583853}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-27403709806905173},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-79372160410967895}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4252565872190299},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2451811205422799}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-68927190931712851},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-649521851354805603}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":795395270722252057},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":185626466372070493}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":-57500759840647},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-22569854647239011}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1764060099383807},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-146287084294727}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":4509954800888885},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":219598337128439}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":915586869834194937},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":150373925924173663}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":18945526141578651},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-51418036458159645}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":129888517198851689},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":7308124525654343}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-13919079681612785},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-246774868232193905}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":21742371788286043},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":39116939707859505}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2007461168037831},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-569904842236787}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":18369623833891979},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":82086964465799393}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-85795350258966459},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-83131431341739835}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":22025102289228189},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":23661382461028387}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":57273858969249},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-72401143107361}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-12716613175357683},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-44026511249055237}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-10028819780039733},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-81232504359251259}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":85070591730234615865843651857942052864,"numerator":5904699284467890769},{"denominator":85070591730234615865843651857942052864,"numerator":28454576491193127337},{"denominator":340282366920938463463374607431768211456,"numerator":105425579236544514557},{"denominator":340282366920938463463374607431768211456,"numerator":19226183940051221413},{"denominator":340282366920938463463374607431768211456,"numerator":10012467244379914843},{"denominator":85070591730234615865843651857942052864,"numerator":9742331797598737835},{"denominator":170141183460469231731687303715884105728,"numerator":24688404338310626017},{"denominator":170141183460469231731687303715884105728,"numerator":4772426159439825565},{"denominator":170141183460469231731687303715884105728,"numerator":1589845191761360319},{"denominator":42535295865117307932921825928971026432,"numerator":913940421923000387},{"denominator":5316911983139663491615228241121378304,"numerator":833070841923250301},{"denominator":170141183460469231731687303715884105728,"numerator":17476959799241510021},{"denominator":340282366920938463463374607431768211456,"numerator":76598215746607712087},{"denominator":5316911983139663491615228241121378304,"numerator":1168130080718039921},{"denominator":340282366920938463463374607431768211456,"numerator":29083643073479230199},{"denominator":340282366920938463463374607431768211456,"numerator":8887884116952044177},{"denominator":170141183460469231731687303715884105728,"numerator":15820027381522030283},{"denominator":170141183460469231731687303715884105728,"numerator":21880688045494335305},{"denominator":170141183460469231731687303715884105728,"numerator":6359938314835495981},{"denominator":5316911983139663491615228241121378304,"numerator":38095151746336365},{"denominator":5316911983139663491615228241121378304,"numerator":156916523527274351},{"denominator":340282366920938463463374607431768211456,"numerator":36712873307424915369},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":32,"numerator":63},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-26637228193872553345627578452051423},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-90657009902430957992893681818589905}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-862008870370576538749358034190977798501},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-867182616539336949842302923416867189329}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-119333105281202365210510262786822150843},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-61702185198452496841911747030858771989}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":40557684156610169680912824222613585575},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":38708799695439480249016017525402593249}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":185376939906274020541720811274316005},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":82825363547665531173691221835937457}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":55304496024537973308037691274422124111},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":53117066067878018139573363210975509465}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-106294506150986323690478814846281647169},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-27673970070587867457346301950304207159}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":26590711814642241665580272932141796371},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":6357622168074573697852930227728596895}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":1487369036863282634552418220822057},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-7782390612740784576151634950970621}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-25484500573281584738394416681672143207},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-26648872902484126232378596240747823079}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":868587684474716702735087619467134842987},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":431416501037584945454153142072107898785}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-312385675017769152376284942879611425},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-21691869011005120092604435684994489}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-72522543190053458345678820208385444239},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-594950705497508264859550207683058307239}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":67531408398328445201257657984086211501},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":66156411745347206539053274708557307415}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":25753377440801381136915975279680772595},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":23872303806806285934351484569655197071}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-1024165241282871725111647040534878481},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1106071321416188404251347224935274449}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-164069350362869036435979964561397934659},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-5208389979589361226852866306439633195}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":83070933663708555495719672427688805243},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":163551880163923948465573000147509034559}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":20192827245762784440963888960842923727},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":4666384719020330846716974518320587333}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":7560231193320526870683087225425891},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1528248350285939578272945441113659}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-18679029472714703605406330707875972591},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-20206559103333180987915539690485691869}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":602813359612721572620886776124746936537},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":146900812062768957640577064436867413495}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-67782751176516788770781710229022649},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-135565502353033625761847954479534327}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-107341416057951938177033147265388701211},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-858731328463615505648422500150751901139}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-125966174992272589778881602697130812517},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-31491543748068147498290904386775276735}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":41783895875746498519512999443978589861},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":41783895875746498479179026672633004959}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3183490212690429957984222239144495613},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3183490212690429936694862062912812995}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":56753488824102915013577959689385045355},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":14188372206025728743452855508429077529}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-14202139038004437331471608541975329311},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-113617112304035498752539075426698858787}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":3419665723665853266962516593050790085},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":27357325789326826115556012197179260099}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1003044033453319229902582957944169},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2006088066906645247509185030613251}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-13709168268562970378467500896098926911},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-6854584134281485193090773464004400747}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":859103798290991299352690130269428740269},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":859103798290991299243895827266052828169}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-679558096878198428470121989662023939},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-679558096878198501009960307709658187}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-605081054690958235456284864211548565703},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-302540527345479117807489831349591080779}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":273778368760536255586882226623762788989},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":273778368760536255431918733895925007067}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":27053945954665905677384211451596524427},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":27053945954665905616796752160966423021}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-4642319421021306117526030060469531257},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4642319421021306136285878429593856553}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-168273684105711859530742930812337698453},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-42068421026427964899107785698442929921}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":83872752829085812059455520541837857205},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":167745505658171624028110968674000544531}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":5312936602547916566683805231332969287},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":21251746410191666240169974441163283761}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4917957871562862551033425914158631},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":1229489467890714328586156182837069}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-10632824373440542361796162137655635373},"lo":{"denominator":2658455991569831745807614120560689152,"numerator":-166137880835008474566988327224757623}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":613252175937702004864854628159285946167},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":613252175937702004788716622526269629671}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":168230485144368819},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-4608289484500071}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-55513061183204125},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1929561354547640877}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":882732666446664197},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":832121445572338007}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-30454433795324967},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-9814756374826573}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2235698887192535},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4402564548031697}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-295694918937922777},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-162143682667514339}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":190930938715570411},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":184524978143565243}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-3161486717147835},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-11974915661321997}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":846830517376777},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-558020316602873}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":19903997316447897},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1682181509969697}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":926446726051545891},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":338150125073036397}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":11303670228855173},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-44798122931324425}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":28032040691113311},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":45234007306991527}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-21328127917683759},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-105660555855652313}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":37295255827110419},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":15082565578729529}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3744754221223701},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2275478656027877}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":66289695378936707},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":70983130533405893}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-70388597637716887},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-72904544508338267}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":38939407858436101},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":19855724821824749}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":447270094288109},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1069921729095053}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-22334081199336425},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-9988998002032439}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-69891829588603981},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-149050295829666305}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":85070591730234615865843651857942052864,"numerator":6001898466625139955},{"denominator":170141183460469231731687303715884105728,"numerator":57778992413006479143},{"denominator":340282366920938463463374607431768211456,"numerator":106674335481324652017},{"denominator":170141183460469231731687303715884105728,"numerator":10071477288535574321},{"denominator":340282366920938463463374607431768211456,"numerator":10640243106954632925},{"denominator":340282366920938463463374607431768211456,"numerator":39590097749802667949},{"denominator":340282366920938463463374607431768211456,"numerator":50185766646160536569},{"denominator":10633823966279326983230456482242756608,"numerator":314476463895917379},{"denominator":170141183460469231731687303715884105728,"numerator":1696223579361691403},{"denominator":340282366920938463463374607431768211456,"numerator":7705776214761620331},{"denominator":170141183460469231731687303715884105728,"numerator":27051501600599350651},{"denominator":170141183460469231731687303715884105728,"numerator":18118108213664649869},{"denominator":340282366920938463463374607431768211456,"numerator":79280505088359336209},{"denominator":340282366920938463463374607431768211456,"numerator":77418742063898606165},{"denominator":85070591730234615865843651857942052864,"numerator":7567879238766667453},{"denominator":340282366920938463463374607431768211456,"numerator":9373500850139495043},{"denominator":170141183460469231731687303715884105728,"numerator":16406653930302388427},{"denominator":340282366920938463463374607431768211456,"numerator":45362325959148105115},{"denominator":340282366920938463463374607431768211456,"numerator":13273081400565991017},{"denominator":340282366920938463463374607431768211456,"numerator":2617362169632569541},{"denominator":340282366920938463463374607431768211456,"numerator":10482279849324455833},{"denominator":340282366920938463463374607431768211456,"numerator":38029423583387627085},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":129},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-42757368252866199544169447529633639},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-110906628282562748597518366469310007}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-214526313631107257880132932505462252147},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-863143578773152506624489171785627974019}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-122497719779634090665913995759029823159},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-126464630038760949952053822668782968145}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":42004525416894760151196542868722434005},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":1254755852703367060644152424169451395}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3226330486139554934146011033189606369},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2891893208187592203871049758351113025}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":114006546734105157816809489186195262129},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":27417644876653051251507832357062286307}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-109753001237704662391502847566998152133},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-3566203411682681921730971661356275513}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":27493561961017459044549319807151155479},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":26338383570442873170528606233799907425}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":1522939267232851602332021943719275},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-16195913057987153726313048352859233}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-6598918912601507780840490504631390655},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-13777507917792319623015423800918838451}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":432041398250458696349545678508166706039},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":26825473538383547581044173939548354737}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-645550009133477179036756994752008339},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-356790304138645594997422279918008921}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-73993726815737172605887104241114462935},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-303301750572418352667338439470874435217}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":274371275866504819463682220663706416249},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":134490719641540450470093077262072633091}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":13638332267186553317388845517749148529},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":3167785092420742933882214207393825869}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-4348812715198230477118306393265985363},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4685197948992162833589037348692410665}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-166100882507297005854269117410553668497},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-168580745766982242289803660199284508153}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":21006314458202716039053565610305870431},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":41394286937502101599792087129694929101}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":21433894789448462481542324515167258951},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":19857804605532494392688615418531409545}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":15495645121841845105579347952938581},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1414934399161368135063220784377319}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-9935785515760194644811057601662549603},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-21447727693069944143076762562931365547}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":614818960233643542602052275808413752485},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":299862335814017807684782830603814104941}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-83615919058975316373241749452909029},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-83615919058975340883914154043442271}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-26717021349168752187126293477193644803},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-26717021349168752194491138760368003509}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-128952738336946503093778986046031161419},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-128952738336946503310517005660621932169}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":43231924563762820056830258358238254485},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":21615962281881410007305029818279052337}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3456849496735582961417107972695217325},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":864212374183895734705294563905108565}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":116877156879746583956914451013776203547},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":29219289219936645969040000743697025387}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-117014508456617778505415660577428623491},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-117014508456617778607784418551236271275}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":28255602401561626378437339381542094189},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":28255602401561626357218935352030967301}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2186068953000917938986401171977427},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2186068953000925172440288374477097}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-14159961728529747281225382968049576551},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-3539990432132436822337026251179427575}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":427390410451037548652775461332958747825},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":427390410451037548597570711623712988463}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-349425928868601013106463533331007205},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-349425928868601050677021117550313069}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-308328661369795191841911863847963146171},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-154164330684897595961985265080084632675}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":277951609178113506346241296648158074703},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":34743951147264188273237856253812469847}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":14307193171548507958527552965326101555},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":28614386343097015854042910107694245713}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-4908796533750382515107613472417833137},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4908796533750382534876743514637898601}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-170104771245987463744475741225920318861},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-21263096405748432976567690729198436241}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":169575143526483157460106523429494414597},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":84787571763241578683031079357549288449}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":703968233410507037243712822630761263},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":22526983469136225164098819609641859959}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5354201926510212285799421574119227},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":5354201926510206670427393357746859}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-22540867930871966743716135820714448927},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-5635216982717991691399965656999830571}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":625180034747596930072638658744970449203},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":156295008686899232498459047643612526573}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":78554294425911561},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-19430434315312765}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-830265120193582141},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1790982938455780241}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":810146787162148817},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":191022249883577189}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-7999761376313289},"lo":{"denominator":2658455991569831745807614120560689152,"numerator":-595815814561563}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4597857282066977},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1943513913831765}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-18950471166932757},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-78930288176459831}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":360036711394711309},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":89117466712281787}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-8299297889922983},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-385702795980403}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":25141368500593},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-33131589059805}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":21121393218211833},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":1421723311962451}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":911114464976484641},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":359343094420448365}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":12513357392800831},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-38480663894208731}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":95235726134851665},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":66139330177299335}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-61338957702940239},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-88983615770665673}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":62957555035793925},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":21889477919528309}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3440389181452275},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2211629217971499}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":117635104966276077},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":7507206309862635}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-55850628467799827},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-62943870925249043}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":33927812088643881},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":8110235634459209}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":864779688879429},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-985226893279315}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-4805873360899993},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-17843583611425443}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-59642698161691785},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-67138010521774479}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":24412687675849308915},{"denominator":340282366920938463463374607431768211456,"numerator":117357165621658640245},{"denominator":340282366920938463463374607431768211456,"numerator":107940907519900390935},{"denominator":340282366920938463463374607431768211456,"numerator":21087966671460761451},{"denominator":170141183460469231731687303715884105728,"numerator":5646861207991263139},{"denominator":340282366920938463463374607431768211456,"numerator":40213106636123673731},{"denominator":85070591730234615865843651857942052864,"numerator":12750644302233419039},{"denominator":170141183460469231731687303715884105728,"numerator":5300504587114576019},{"denominator":170141183460469231731687303715884105728,"numerator":1807696157192136989},{"denominator":170141183460469231731687303715884105728,"numerator":4057502393341476367},{"denominator":340282366920938463463374607431768211456,"numerator":54928864023967741223},{"denominator":340282366920938463463374607431768211456,"numerator":37538803894879400667},{"denominator":85070591730234615865843651857942052864,"numerator":20499125062789979295},{"denominator":340282366920938463463374607431768211456,"numerator":80110909171909962409},{"denominator":170141183460469231731687303715884105728,"numerator":15742781936460422945},{"denominator":85070591730234615865843651857942052864,"numerator":2469605392020840899},{"denominator":170141183460469231731687303715884105728,"numerator":17002051788294949017},{"denominator":340282366920938463463374607431768211456,"numerator":46987163800506569719},{"denominator":42535295865117307932921825928971026432,"numerator":1730142710857673437},{"denominator":340282366920938463463374607431768211456,"numerator":2806761010817106811},{"denominator":340282366920938463463374607431768211456,"numerator":10933631566752811221},{"denominator":85070591730234615865843651857942052864,"numerator":9840979355954810717},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":16,"numerator":33},"tube":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-9287006844105639237443928360077081},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-130075369597649775602870486932476003}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-213582017504337829125666992579047908353},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-13425321553157645381912425405191580961}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-125580264193352688503806604992548837339},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-129439372182551701254556579839345333561}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":43452774552643199216362227913738900233},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":41598464911646865063936448512618654867}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3501881902913979775462220709959655509},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3148113358221146621276266413349468765}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":117371140653822934442672050935924245073},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":113077626203137262781506265282153189077}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-113184497518508361555302539559158791993},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-117510645373779732520005825126573961389}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":28391119768897722836668755597002555829},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":3405307473949590809984602280218983189}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12458186973260739542713104041379487},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-16830592908127128853061230483734095}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-27303054856206765779562594473617459587},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-28455871665398515553286665460398146385}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":859659241623496317106091610979010237333},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":213526202074611534893019201520554630563}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-665548366526940110082901755048398299},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-366083665439606155532476969422793095}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-603627070270648003947420427969792185019},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-38635432154609394939754049261770796019}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":139266208547564886268517624495394066599},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":273250141167803642420239120863270964657}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":7210512630741163224819538980752149807},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":26855267669299378140965484831959152825}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-2303916934435728267232534269018815099},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4952689390369952365074681563333385231}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-168037498641217365866674888503957992669},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-42599838321540575626838827347182948739}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":169867869870738907249265710523702257825},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":41877421853082703695328999278257775887}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":11356901628820903004434588263821998695},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":21089295649363872932536729520551731629}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":15878923224032441292023585133881007},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2585248987981468270583433031295577}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-21103211121709388041432454565893696457},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-22727587373426354863031149461046183793}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":626734466903944461505977385708437281591},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":611754143608119509597909870817248417729}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-101136841743756298201599906378977219},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-50568420871878161563034253533392095}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-212821030505574827269752394505018755183},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-851284122022299309318320811039343745227}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-32962907328316194088806660683074676689},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-131851629313264776574458241350475910911}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":44680357382727225647993342034562824733},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":44680357382727225603829086075962623719}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3745821291506721017100949347938099373},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3745821291506720993145964104946538077}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":60106018648922070975034531043542269803},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":120212037297844141868092626168843341177}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-120379101927243413410641256477342592385},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-120379101927243413514627220382866725817}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":14573782385133385579282580928132229069},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":29147564770266771136232678740981590195}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2371923910326711211374865959836363},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2371923910326718911644035437672399}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-3651898762628266610745399426543144591},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-7303797525256533225764181178612720679}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":850552088015071963217285296904833957465},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":106319011001883995388148786685757628635}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-179323597210584132140617156701555657},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-717294388842336606345757716978393665}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-314073203572213265947293714026248122339},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-628146407144426532064196147503091834627}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":35255293973120052226777785019906554659},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":17627646986560026103027476248646092647}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":15108147418640177793758347809900561865},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":7554073709320088880506457433999157091}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-5181635252573675454254977769338665917},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5181635252573675475073023619394622793}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":-2685051231635886090088218053044633539},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-171843278824696709836124147091754593445}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":85657341068566694021666503616627922667},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":5353583816785418373312375472353313909}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":23840804330854740393275919796509111537},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":23840804330854740364410705728126476717}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2906199023597087474350263271245603},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":2906199023597084466783486678353631}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-11927252606192968666717828398106149251},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-23854505212385937356244798757300528221}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":318509662222532595271484202689459992277},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":637019324445065190461466056101536590099}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":36020985639996077},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-40551851433740785}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-94557528914584769},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1634722647275655585}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1463104210837890129},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":683930628116288525}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-32330130233211471},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-72984657729126005}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4651180538408337},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3398995288176499}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-150449937647357141},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-604011897725472135}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":333786715538211167},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":335134755819970441}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-9626144156634401},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-24808158181662437}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1517719052552201},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-503549494375823}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":21758921818476059},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":231192319066423}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":880092999512277341},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":91620732719092529}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":13400320635711255},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-2027844418843351}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":79301693879706663},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":22029722035574453}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-19836695225553217},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-73386986705660947}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":26043527681270751},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":3594721040439037}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1549726523459263},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8516112728836715}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":103000366200898029},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":24766873438062405}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-42343654160815039},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-106887301769855527}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":7281313470818705},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":12802827187345413}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":208252158840955},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-904203410449681}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-4046622839448293},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-31476409620876749}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-49727910848970821},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-59774834884054931}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":42535295865117307932921825928971026432,"numerator":3104018837961368053},{"denominator":170141183460469231731687303715884105728,"numerator":59608242650827436765},{"denominator":340282366920938463463374607431768211456,"numerator":109226212517727801275},{"denominator":340282366920938463463374607431768211456,"numerator":22061800715552143239},{"denominator":340282366920938463463374607431768211456,"numerator":11973467533582488229},{"denominator":340282366920938463463374607431768211456,"numerator":40836661947905220287},{"denominator":340282366920938463463374607431768211456,"numerator":51826762615133840769},{"denominator":340282366920938463463374607431768211456,"numerator":11158650550628919953},{"denominator":170141183460469231731687303715884105728,"numerator":1924436087859133047},{"denominator":85070591730234615865843651857942052864,"numerator":2134896066812171933},{"denominator":340282366920938463463374607431768211456,"numerator":55790696675068510579},{"denominator":340282366920938463463374607431768211456,"numerator":38862021469099627455},{"denominator":85070591730234615865843651857942052864,"numerator":21186771938363415691},{"denominator":340282366920938463463374607431768211456,"numerator":82837779798977369729},{"denominator":340282366920938463463374607431768211456,"numerator":32726578856301855005},{"denominator":340282366920938463463374607431768211456,"numerator":10403215142140100817},{"denominator":5316911983139663491615228241121378304,"numerator":550193164668541201},{"denominator":170141183460469231731687303715884105728,"numerator":24318112117585189939},{"denominator":340282366920938463463374607431768211456,"numerator":14424445820843352705},{"denominator":340282366920938463463374607431768211456,"numerator":3006698170569985221},{"denominator":170141183460469231731687303715884105728,"numerator":5698463010706286535},{"denominator":170141183460469231731687303715884105728,"numerator":20358131879616063853},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":135},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-110014034974353172648677910013688771},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-73629450444473518185965122853115247}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-850684830136789803422375939075569926545},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-855418000177467877646087607382357161321}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-16072239133095215445796957689188474021},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-132326165786609518840408904639718229121}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":22450643246576409185808734281758026561},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":21523219952470854543026840311280096559}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3793090238584947183349863032513953433},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3419489414307875800540213036074125957}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":30175030567851841305443370586004202727},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":58226191473669915196657030289157830501}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-29146539184530903637939247147000012559},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-30217418480766313522085926570815631807}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":29282220721545657770561935379175586365},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":28141533699341178422403046215790092343}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":6361679831908876502734154387975455},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-17467522400249315029600209728682823}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-28205441401317722694771617616883086499},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-14675130979367720685781549305010248487}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":855324322359349926615082815656851486185},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":212472326946650408379940971986633709097}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-342364851188532375912880502524994245},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-374934282400538809745445333790358847}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-615214427188060579210034590099251201657},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-314821691351679311973962981933489426475}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":70652820155377273964034427215493636973},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":277433867906625107333654532138222198257}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":30448786998407880028142566713044478543},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":28410564048062475390254059129430524781}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-609186874714925003087145678958372895},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5226510358029224928801643640152227377}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-84940124855038285692230387475711164351},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-86062732534592747492305217748689487367}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":171595228219184184435306286357996511749},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":169350689671738598802812810954885111297}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":24032228558194395383579919378477402899},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":22359734014796428473045363835435326793}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":4067594571677713603258204549891091},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4645530336158069881802493371837331}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-22373653759525207514742576356345242453},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-24045795472992799804478168801014051641}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":319280771893717562987481442351099523537},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":623693200409837130440377668760364306699}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-120410275552007539804405887813562297},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-240820551104015130313099948837209797}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-105969198613496280797987939702871351083},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-847753588907970246626977888385361403137}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-67330338554280216223226271195218944943},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-67330338554280216334109577707676366369}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":46128082903010610928630999326641085257},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":46128082903010610882463382412774163085}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4050801874119058737160714092399517031},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":2025400937059529355896454670250798721}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":15438640558286930442626790949464665767},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":123509124466295443457813067196601378173}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-30927106168230415295771368718355984363},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-123708424672921661288707195050926429497}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":15016031143010813761708722538924607541},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":15016031143010813749964973059223154991}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-640666904794169929222456738896117},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-640666904794171976440256944044613}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-30102971403325432736245058390422359025},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-30102971403325432754218324033996346281}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":52901392389593548045429606757156040897},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":846422278233496768613017693603770227479}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-734859119231511088956772438976700403},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-734859119231511169424964045162886903}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-319775406427756117311676736961601678773},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-319775406427756117399262620217551663225}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":286052878007735598213567394608420614061},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":286052878007735598042268830059045228473}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":31858888817462742527551168346088699307},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":31858888817462742459525981587823106725}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-341285801965716367462840077110600779},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5460572831451461901313472082178110567}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-43372609136518028237115305655641677623},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-43372609136518028255346893638672626217}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":21620685338908014332713705781288668377},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":86482741355632057280515107351901020099}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":6298213046808771305709815112613286367},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":25192852187235085192777337934815112263}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":6292367201233507179276675778541133},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":6292367201233500742441695810167753}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-6301546194468267714261420276635946457},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-12603092388936535440402415836572174435}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":648771784944017489788705512779784913953},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":648771784944017489704466302556004477751}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":65548293106696371},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-21147507407562405}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-83932175994220985},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1473049993508439467}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":651744465107660253},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":149198020414474713}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-15738865539069511},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-34441421335472203}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1165415553009861},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2965667269635305}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-289361105156426295},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-142301522265264401}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":305492266824982791},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":76619221994392021}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-10378417752449927},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-24468663790019667}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":89316765098603},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-960528211323985}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":10957190313375339},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":8523387442857123}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":418799587125634861},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":179971285052816405}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":7022759383506841},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-6775965903538451}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":129638914778241821},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":24257856717399669}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-20397439663629783},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-118516444411794849}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":21108625575019141},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":7696877927534417}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1402499305394721},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-4072013078757129}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":44589422218800393},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":9875693955257251}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-14957905243754153},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-89418983347623443}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":24687152749353199},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":601042612829993}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":802901709258317},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-415253916608091}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-13261546877390713},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-27470855455026183}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-40129597204033117},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-52710802054084047}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":25265448286090783825},{"denominator":170141183460469231731687303715884105728,"numerator":60568194544208980721},{"denominator":170141183460469231731687303715884105728,"numerator":55264979044089355299},{"denominator":340282366920938463463374607431768211456,"numerator":23065105901137058393},{"denominator":340282366920938463463374607431768211456,"numerator":12680088711208122419},{"denominator":170141183460469231731687303715884105728,"numerator":20730353853802829163},{"denominator":340282366920938463463374607431768211456,"numerator":52658606265915047273},{"denominator":340282366920938463463374607431768211456,"numerator":11736704356682667679},{"denominator":340282366920938463463374607431768211456,"numerator":4093240802183846175},{"denominator":170141183460469231731687303715884105728,"numerator":4489968662597523425},{"denominator":340282366920938463463374607431768211456,"numerator":56689178953290394979},{"denominator":340282366920938463463374607431768211456,"numerator":40206498352519002665},{"denominator":340282366920938463463374607431768211456,"numerator":87533192726919563375},{"denominator":85070591730234615865843651857942052864,"numerator":21400055693078402565},{"denominator":170141183460469231731687303715884105728,"numerator":16997666596260772179},{"denominator":340282366920938463463374607431768211456,"numerator":10948540911820097201},{"denominator":10633823966279326983230456482242756608,"numerator":1138698060367300353},{"denominator":5316911983139663491615228241121378304,"numerator":786093190419118685},{"denominator":170141183460469231731687303715884105728,"numerator":7511713011173489973},{"denominator":5316911983139663491615228241121378304,"numerator":50275012268952335},{"denominator":340282366920938463463374607431768211456,"numerator":11872470629011463785},{"denominator":340282366920938463463374607431768211456,"numerator":42086959108438150611},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":32,"numerator":69},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-149222287906481984931140176342656151},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-332404763056642821734179106561379597}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-423586035630495505837213648446937362467},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-212935254137833391153021689324960721747}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-32872039290342379735033615456922222311},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-135122878680322093091056268674763808807}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":46348954538519514170281938288140156185},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":44494957698750304652000991141384758383}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2050175079292825182829620452225301421},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3706429195164617729533377549554613597}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":61995510652161008289613816366408450435},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":119792150186013266900188736306288139483}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-7497207429544209874655788811953125283},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-62096574709033956077989486826576313773}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":30165716232242048063411481564056744049},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":14517218415023647961050850202596439019}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":3244895340660140557740428558844359},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-9052639926938686830804794875463039}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-29101653044238560947925256396589976199},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-7559255903028570082076161088779631483}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":425541532780146642314124417233118987397},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":845773290108080070518613461051221057061}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-351532452039019406528680106931613641},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-383330148206662699530150351314340617}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-313357146915857936484835846006925661861},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-641035426958822462218829050201277277729}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":286610162439336868974528938421243519241},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":281534817267807478612207473240345338747}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":2006005542200217129001445196759802005},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":30007428855288897906248352445865132889}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-1286387674860277698746268829137819139},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2753198115383378693842048822700957305}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-171630273734721360230981997606434250359},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-10860020289654678473601348330727122261}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":86616982694096734803395089828866861193},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":85550714221285578325176109405350192941}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":12694405211956875090745730177282382239},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":23668803653848183718068399414186305237}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":2083750936555051945547280940795499},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2042594995527149842798833600590861}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-11841282189181501388450780369114611001},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-12700986359296174171121259559518365725}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":325150973269467540938986177015164346497},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":635543477545746313637409800531779328049}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-141496559035698562092655410057734165},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-141496559035698587887089690491099725}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-52772292253875127390470848921015622197},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-844356676062002038494505051129049212541}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-137377997797471366873302610981999792041},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-2146531215585490110900787775271675917}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":47574028182389887062240033706099464493},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":23787014091194943507004158183975776411}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2186088343362226842345259799605849149},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":136630521460139176807962724578449043}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":126766099146468487974792751533125644329},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":31691524786617121972590612953779752695}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-63500086057396126394758813835333707799},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-127000172114792252896795497465444971381}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":3863495097095736509705187234028675021},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":30907960776765892052956947406662683795}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-172323054613271182403364304262195},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-689292218453086904594307235485255}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-15491059073903185153030833213876585953},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-3872764768475796290618395550696751663}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":105299471288682427797463346903938403049},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":842395770309459422264010039606444195363}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-751527075012707137239510838141161857},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-751527075012707220437219290632615481}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-650873122346102598916696382587830146527},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-40679570146631412443594108819892847697}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":289985535755273317657710231032338954861},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":144992767877636658740410716168248774741}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":8385337833700909543102299665899478289},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":16770675667401819050896095213179065955}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-359083225615165805279130822131195055},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1436332902460663226876667958518249393}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-87523775079029039595786674586095391929},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-175047550158058079266984447018484491101}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":43632244612651539973248826586337410477},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":21816122306325769973615280240762758525}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":26582735377863326910852273657719524997},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":26582735377863326879561181787224655595}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":212307377798106805532376061506525},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":6793836089539410895678795861855313}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-26595495604016820162969642232790832985},"lo":{"denominator":2658455991569831745807614120560689152,"numerator":-207777309406381407716438311860543451}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":660439242602680489460310265953052506575},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":660439242602680489373295675083662790265}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":118392569257604677},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-44093012938246493}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-581452105464708205},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-655520821962817825}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":286647942691973793},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":126642903229375175}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-7450804395269489},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-32109994221750743}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2317717381297891},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-161533560038113}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-271704488764144905},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-264625134692797813}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":69015668786941497},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":274391927368835813}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-5341353879958473},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-5937357184939817}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1339391284587285},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-459139684784157}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":21661205537241989},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":9209386569135817}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":786976453967677349},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":42990051672792163}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":14429520841458347},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-22457226086565413}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":103669496478086327},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":6916685469562605}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-450658441114825},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-46684259359443651}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":4180192029977887},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1863934420838309}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":320081639050685},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-3872738908802255}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":76153043485589691},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":30116375903759083}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-18760313667495821},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-18366004953110027}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":20599383442591525},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":6729443438250615}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":770868063952755},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-761310778982381}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-10494616735483643},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-1479150104398749}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-7744198709986567},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-45948527903889339}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":170141183460469231731687303715884105728,"numerator":12856595744667719987},{"denominator":340282366920938463463374607431768211456,"numerator":123120939427169164971},{"denominator":340282366920938463463374607431768211456,"numerator":111853893238768536087},{"denominator":170141183460469231731687303715884105728,"numerator":12049325141821372035},{"denominator":340282366920938463463374607431768211456,"numerator":13414246220489061665},{"denominator":340282366920938463463374607431768211456,"numerator":42086376968692591413},{"denominator":340282366920938463463374607431768211456,"numerator":53500068185925429809},{"denominator":340282366920938463463374607431768211456,"numerator":12335741872293437025},{"denominator":170141183460469231731687303715884105728,"numerator":2174416432354897575},{"denominator":85070591730234615865843651857942052864,"numerator":2359130769856591903},{"denominator":340282366920938463463374607431768211456,"numerator":57626839792238844491},{"denominator":170141183460469231731687303715884105728,"numerator":20786598046180492879},{"denominator":340282366920938463463374607431768211456,"numerator":90356302859723446451},{"denominator":170141183460469231731687303715884105728,"numerator":44199758861162859169},{"denominator":340282366920938463463374607431768211456,"numerator":35292715317710398229},{"denominator":170141183460469231731687303715884105728,"numerator":5757568137260966675},{"denominator":340282366920938463463374607431768211456,"numerator":37682530589355938317},{"denominator":170141183460469231731687303715884105728,"numerator":26004590178275657355},{"denominator":340282366920938463463374607431768211456,"numerator":15638610965245264245},{"denominator":340282366920938463463374607431768211456,"numerator":3439912529631709175},{"denominator":42535295865117307932921825928971026432,"numerator":1545080618776489525},{"denominator":340282366920938463463374607431768211456,"numerator":43476835304210941949},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":141},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-192040792731213566464383379230366163},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-373932986733108580919477445774617079}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-105474167538473551191270332463865170975},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-424096808265106336485534234796761995507}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-134308789705325221854978328348905673317},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-34456915934419331942430116641301145863}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":5974338810683656017747754347001987023},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":22971451030257603371258432619594582173}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2212022719158170838015520676043345083},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":2004665183493013635661002769661446039}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":127241541697591191778060346235206572513},"lo":{"denominator":1329227995784915872903807060280344576,"numerator":480837544689827796354197189032892341}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-61644747655274050138005399087643476095},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-31869697233570927336689390739408387313}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":31040474209923514398900112938253927569},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":29920016516699195622266594005242879633}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":13227565126603378968314252100706393},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-9371157858155925449651854015226491}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-29990522733275185754282235961761033323},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-31115009433777655573910458049351034787}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":846940187468114149653044011623414894841},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":26305034222560635637229405585414242047}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-360266281827639498916976013973066541},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-782526000576148537453128031031941917}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-79766145609181014664980013846967790421},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-652345644694089290354973740051329409593}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":290531423877429206407482235001768685791},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":285555261799991863779467340376628927043}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":8445784055160068410983609684714955007},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":31645083550443016772369486104483110185}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-5423740087459063601285029847105624101},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5792067527383046382489141514722252179}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-173288790520095479280383673143641958421},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-175305250779861815961159165733866223579}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":174785527227838888290590218126613361405},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":86381627771377903184428440372910210279}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":13391576945554931252411138577319068811},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":6254037999478916372859752777624714707}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":17077720727039715905655640181437617},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1744966742504533874197959187047937}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-25029571442742184883863729273185105087},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-13397852397025522307841622703874328469}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":82744689546987930935131725984631795767},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":647306703673807938840401023942663017313}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-164451317890332676759951886264184471},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-328902635780665406024048662639488771}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-841096640138211809757825137278691301389},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-105137080017276476251104239375831806619}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-140001980593135384948708005703915736085},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-70000990296567692587843015431982488185}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":49017158823057777161624758271335136407},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":24508579411528888555633368084727186621}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":588789969556787620243302727083837697},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":1177579939113575233396587213454956365}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":16247601260542664228692738922005792587},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":129980810084341313743876615253562831535}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-130252195951734536557661861418243420055},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-65126097975867268333309367494361844509}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":31774143037469048054847362032488911647},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":31774143037469048028922536251494302649}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2954147112895644496307322472743179},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2954147112895653730502914902549637}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-15925748756503993329331885002127911749},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-7962874378251996669623744434074101539}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":838476653216945993250340383232493647105},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":419238326608472996566359418684777012897}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-767286930273887452157716213426262239},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-767286930273887538131526615390547813}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-662115988343169417938619726571963141907},"lo":{"denominator":332306998946228968225951765070086144,"numerator":-646597644866376384887836132544044053}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":146921366194890106963440637279908718681},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":293842732389780213744325272643418294989}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":8815708464522368394969385063322440405},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":8815708464522368376652338510625592665}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-6035619534282718542899104406993723199},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6035619534282718567116330469733621189}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-176515996549962298197171374817814833465},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-88257998274981149137552369197737928787}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":88003334753164539189646097453110038727},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":176006669506329078271772801419623613259}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":28010028830937670399999183538940130383},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":28010028830937670367445422260724982585}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":7316435022887161387000337297589345},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":1829108755721788509346893716172093}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-28021992979687935402694670048649050853},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-28021992979687935428430501923072859533}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":336011802237877598625826186769504344385},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":672023604475755197161822227118577404507}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":53128748458666041},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-22830062569272541}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-490921602086321113},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1152783647268969117}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":995801100108708847},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":209100796410623975}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-27573403029453115},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-29613150688674803}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2287578801503069},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2249148255035945}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-249499447991223825},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-15188554104318283}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":61616169672470263},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":120110425460114361}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-10626918347478705},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-22742439825911933}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":626949498443885},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-881972148588217}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":21093324224854813},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":4739803135634441}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":730628094072811653},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":160251840896956697}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":29156248711969501},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-9227965693559455}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":80661027232164987},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-7950023667719951}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10658834546199591},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-35622399602854133}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":25724877369231343},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1547526948739551}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2358164391077405},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-3664898037346089}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":16012481471982021},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":21454945674641969}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-2221281237750533},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-29538717559947347}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":8442854407359337},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":4137732575930359}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":369578045078013},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-87521384426597}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-7909984637511675},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-20105967654161797}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-22405176218807113},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-79143973594993773}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":85070591730234615865843651857942052864,"numerator":6544028408506905333},{"denominator":170141183460469231731687303715884105728,"numerator":62586728920695125889},{"denominator":340282366920938463463374607431768211456,"numerator":113200212826380889693},{"denominator":42535295865117307932921825928971026432,"numerator":3145398075220804167},{"denominator":42535295865117307932921825928971026432,"numerator":1772078041062052127},{"denominator":85070591730234615865843651857942052864,"numerator":10678595229892068491},{"denominator":340282366920938463463374607431768211456,"numerator":54352082532010367789},{"denominator":85070591730234615865843651857942052864,"numerator":3239088782439521971},{"denominator":340282366920938463463374607431768211456,"numerator":4616029860642165235},{"denominator":340282366920938463463374607431768211456,"numerator":9909797007043498363},{"denominator":340282366920938463463374607431768211456,"numerator":58605710725330361525},{"denominator":340282366920938463463374607431768211456,"numerator":42963099110932598581},{"denominator":21267647932558653966460912964485513216,"numerator":5826120690694940107},{"denominator":340282366920938463463374607431768211456,"numerator":91237049141323617257},{"denominator":340282366920938463463374607431768211456,"numerator":36619683139760340257},{"denominator":340282366920938463463374607431768211456,"numerator":12103769051137064203},{"denominator":85070591730234615865843651857942052864,"numerator":9736346074680967249},{"denominator":42535295865117307932921825928971026432,"numerator":6716825073526723227},{"denominator":340282366920938463463374607431768211456,"numerator":16270506650988179741},{"denominator":85070591730234615865843651857942052864,"numerator":918521679408416521},{"denominator":170141183460469231731687303715884105728,"numerator":6430908972851789639},{"denominator":340282366920938463463374607431768211456,"numerator":44886703811527548801},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":4,"numerator":9},"tube":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-59645037914580907683702057722333881},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-209607180967434455243917503016197653}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-840551850760377599706086088098592592999},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-844779434428849198359884936154546976441}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-137037892536714522680680366524559222135},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-70219472572141482303451404449970832821}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":12309381168831333709380616511950692067},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":47389195238730392811395632825854389377}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":595568548261483240711370312759631827},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":541072478904898203511904266166713661}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":32612388596781506580749055080327820443},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":126356826341950983620069810625650618941}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-126586361813306152167151519612983396859},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-130724464828167158390812597990800328695}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":31905379584409298099076989634037945739},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":15398568232402756801694026790753646481}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":6734095438543026752270375678770971},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-19376948586101620406158585171621565}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-30870899199333099608115981026406840883},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-31983088684065806587572832840846895557}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":421450051601610608671433115828449684887},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":418928387132801633855635834801000585755}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-368559515383129080985516802480872673},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-199364172352091918035605570635663035}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-649461613444102305202385582721718726173},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-663576702464105242345493579183809674159}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":147188742305435127550557993777709523335},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":144748770718992384428172129645029621811}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":17754539494263098444236571287548114691},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":16661357464417232451636042193858990787}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-1426946824116696389080459210045982271},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1520807607556364709441099445078147873}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-21857137067805640088794808661228515775},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-44190408174643676380626816478607861807}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":44062856438543616494847121132053785447},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":43584398854219086997495387014827285685}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":1763426920838360549873769994004330223},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":3300173931183604166633770774571583567}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":17493337941899925392306780533254265},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2860320202048934254551072464451461}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-26414268020618058127918235243726301065},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-28226543854605678478432302935348364713}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":673530174348286802879962804200569543153},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":658984694630946454539221549381892789327}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-94662601384175861652279781210704501},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-378650405536703500060915876066885611}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-418988209132778653874094223880506501065},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-418988209132778654001690967151306257313}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-142531274287817426216217040714798366459},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-142531274287817426445877602625521659065}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":25228239479518998172252458504439195341},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":6307059869879749536494611206368082763}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1266398286051215066478043654823483541},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":2532796572102430117984939167033211673}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":33287816663442383801314711679287365109},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":8321954165860595944896918726395341595}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-16682812114087356243877217542373791405},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-133462496912698850061679578675429634703}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":16314754662134991049434191569316195327},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":16314754662134991035829368633834349225}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-394021197395143536500349092199707},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3152169579161158084485232859668587}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-32709993580567266591487084633197367883},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-4088749197570908326537318101701947299}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":208667184156019577396736100548724555093},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":834668736624078309467309840912263274417}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-391067509010548365773889385985985985},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-48883438626318551271647819183930169}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-673282126904507940630145243009347275243},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-21040066465765873150702048810063329087}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":297626928021707512259604998110422023219},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":297626928021707512071302012240614394287}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":2313903682691151356449326351579003241},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":37022458923058421627208580884872924549}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-6331130692719089104348388996044072033},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-98923917073735767652936626547527083}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-177897219043339042532196433989745990567},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-177897219043339042612690582730712752683}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":177400118169360175658031328880547846641},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":22175014771170021943376409076738943213}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":7368568864476696861932129824912507135},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":29474275457906787413877486174230425195}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":7859695956469936513184050194840153},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":982461994558741083829421063580687}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-29485199981381618496008917778023613377},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-29485199981381618522772970719091081273}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":683526852770233373187017622639652761129},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":341763426385116686547165003626611211483}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":23689880494786871},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-47145030270798691}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-201300614326153197},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1002301665204719135}},{"hi":{"denominator":1329227995784915872903807060280344576,"numerator":3337464218365045},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":167080952363983137}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-3129567076673835},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-6764599936666745}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4487299097728301},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1953016676721631}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-112076617950149045},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-110268295192357649}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":435272876595156769},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":51305423246137149}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-10219232205470611},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-21544267750622009}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1173243589406915},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-851461635656345}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":5074227723878859},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":4684999212440033}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":10481293727880119},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":146034346505984597}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":29033649338042557},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-7543343908483155}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":15163506122344313},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-20409115259742193}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":5624965220114259},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-26058143998860095}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":19041132261249829},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-7217776061105489}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":34342841905119},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6899166907414023}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":52975859769216695},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":13624426478323861}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-322622450116809},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-1448263822165973}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":13577853637786555},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1852384663492821}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":712205612489457},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-324600355250493}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-2770937626609821},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-16825134350706167}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-7269269836858493},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-33640518170627853}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":26654946099487060715},{"denominator":85070591730234615865843651857942052864,"numerator":31824223263130887469},{"denominator":340282366920938463463374607431768211456,"numerator":114570166487774903679},{"denominator":42535295865117307932921825928971026432,"numerator":3282434193440861581},{"denominator":170141183460469231731687303715884105728,"numerator":7483963992363265221},{"denominator":85070591730234615865843651857942052864,"numerator":10836403393744357801},{"denominator":85070591730234615865843651857942052864,"numerator":13803973394103586911},{"denominator":170141183460469231731687303715884105728,"numerator":6799580208854635201},{"denominator":340282366920938463463374607431768211456,"numerator":4895228867448503835},{"denominator":340282366920938463463374607431768211456,"numerator":10400266633973787569},{"denominator":340282366920938463463374607431768211456,"numerator":59627913588531293765},{"denominator":340282366920938463463374607431768211456,"numerator":44377232998907950933},{"denominator":340282366920938463463374607431768211456,"numerator":96119627886465068047},{"denominator":85070591730234615865843651857942052864,"numerator":23528546215116181463},{"denominator":170141183460469231731687303715884105728,"numerator":18988595458017192997},{"denominator":340282366920938463463374607431768211456,"numerator":12715228997104159819},{"denominator":21267647932558653966460912964485513216,"numerator":2514212415864870915},{"denominator":42535295865117307932921825928971026432,"numerator":6935877152923569163},{"denominator":340282366920938463463374607431768211456,"numerator":16919653828222654805},{"denominator":170141183460469231731687303715884105728,"numerator":1960296818840801053},{"denominator":340282366920938463463374607431768211456,"numerator":13376384840984990685},{"denominator":42535295865117307932921825928971026432,"numerator":5789679555610174965},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":147},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-288941063918528660822688408039802735},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-117087695148220358905534842145698435}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-209362624677218190319241086689281825837},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-420750883481846963267298600306024471207}},{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":-1091201737034400197338675731193190403},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-8934712804232801384557850781598672565}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":50676405973564214875170746152922045571},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":48832798028557061804166290371399825699}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2561109647476633891934287219014730601},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":4664553141065526839110545766793948649}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":66806544964491861018710802563820615159},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":129577223434936601711260505023218203275}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-32460937834189535691603468219506018027},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-66964098743261040339446878040597148013}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":32759334796811255455756038567520798103},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":989521165200969530671768478293051989}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":13702507708723609194094635102651587},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-10003680921449151381733026705700623}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-15870823752794236397026385698728424991},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-16420073789891805720081377633211664793}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":209741734197118544388272685023465902963},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":834064101073192334525587173679187219937}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-752818424651405347860715933142165759},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-811450922178784264050208825497922353}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-660714283820652228987348873434193188037},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-674731329045824118500057402612869471183}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":298150815997717022961395843752305433335},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":146682028216671395248992048915714125611}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":37273037656248021526196683608979352537},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":8759869470129075376108245961583919403}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-5997402002384905678834067866917844071},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6379577321363034319484431068653379799}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-176336560023214287671097483890073016605},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-178130925290694392931836390968467929647}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":22204154295719122798398343781744145977},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":175825940077504200036726806860362189913}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":29683380849622020331056506528685661265},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":27824100828861631482599745986615656559}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":17916586742294840287949017359833209},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-549253471287155428494607574937659}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":-434940832989295743151325875818607309},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-7423502498761251492945748453987360747}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":342510957907410574759411043726650591697},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":83822418457537928084713891410186800085}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-13510228740844691978196484422896099},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-432327319707030197735643368763497143}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-834998643939738405026115438236620937909},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-104374830492467300660705830033639049841}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-144964773979819433529519828692644445353},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-144964773979819433761916920389031745357}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":51891031182734753358153545644396994971},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":12972757795683688325837581118261970881}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5438346422436498148057724475039297523},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":679793302804562264559235816717423687}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":136275631425720701981633761707188985825},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":136275631425720701893473042856145662259}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-68314608755400269878805562567383106645},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-136629217510800539870006474642953151313}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":33472977818359896000867317898969627129},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":33472977818359895972326913355375643567}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-3349649110535300621238847175879807},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3349649110535310996842094482418079}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-33556507812234210866940062330544784551},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-8389126953058552722191852584561641949}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":830975561653013247049557400644376431497},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":830975561653013246927817574257497277049}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-796075304468468372062007495016704075},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-796075304468468463736192011698560995}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-684374310839584628799549448443373582769},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-684374310839584628997749586760832503915}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":150670314562236907482418926568824844399},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":301340629124473814770705299146588854193}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":2426207667808194886455682686023228423},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":38819322684931118104534618597692780461}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-6631545860196016415607312117174753565},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1657886465049004110579124836312428423}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-179192722879738278686167550947069924503},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-179192722879738278769262093635933750123}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":89355472141407041340936144517721669105},"lo":{"denominator":2658455991569831745807614120560689152,"numerator":1396179252209485020056996371523341725}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":15487493750564706617618551743469431405},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":15487493750564706600026524895471612809}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":8423050664279456086145618669232547},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":4211525332139723862500536157264455}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-30984608900817315094620276065735391321},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-15492304450408657561220120609148739767}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":173737759877820161508392720055014285927},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":694951039511280645937982036754472287337}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":21000196249839269},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-48300711085842565}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-319187088112797771},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-861054483517187773}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":722985124342665851},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":8011178704460661}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-22340046536888355},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-48965651775062853}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4375082022028033},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1691830923911813}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-197154209774599861},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-98944683661726315}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":380272943501392285},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":85531717141382537}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-4798381140196629},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-20318626621576087}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1098592212198781},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-824878687357713}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":19391217796247289},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":2251745722433303}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":304668723294757829},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":32549091120098537}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":14275227610504717},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12262462046332393}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":43422526200991773},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-15288212904107263}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":32066719995922689},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-35715481923603285}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":13292474024509081},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-10557738596438121}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2068882981089691},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-3229353732785191}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":5374532759763193},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":6670213729783849}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":6936564674433863},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-4402644813557779}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5341562677458043},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-56912085837357}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":345521035625753},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-609649317318237}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-3412716871703715},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13858286456265647}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-7449269972308487},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-14100133241194859}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":170141183460469231731687303715884105728,"numerator":13575263592786405583},{"denominator":21267647932558653966460912964485513216,"numerator":8093416707408970963},{"denominator":85070591730234615865843651857942052864,"numerator":28991308036323421913},{"denominator":170141183460469231731687303715884105728,"numerator":13694148891527734237},{"denominator":170141183460469231731687303715884105728,"numerator":7894442757088492045},{"denominator":340282366920938463463374607431768211456,"numerator":43981047163085509083},{"denominator":340282366920938463463374607431768211456,"numerator":56093069999484155405},{"denominator":170141183460469231731687303715884105728,"numerator":7132420669813200183},{"denominator":42535295865117307932921825928971026432,"numerator":648354986025436361},{"denominator":340282366920938463463374607431768211456,"numerator":10908481886397634583},{"denominator":170141183460469231731687303715884105728,"numerator":30347720417312606771},{"denominator":170141183460469231731687303715884105728,"numerator":22908342899853628773},{"denominator":170141183460469231731687303715884105728,"numerator":49531534841362428711},{"denominator":340282366920938463463374607431768211456,"numerator":97032385894570654315},{"denominator":340282366920938463463374607431768211456,"numerator":39366227083028963551},{"denominator":170141183460469231731687303715884105728,"numerator":6675164909407075013},{"denominator":170141183460469231731687303715884105728,"numerator":20764554160128875981},{"denominator":5316911983139663491615228241121378304,"numerator":894801529353692979},{"denominator":340282366920938463463374607431768211456,"numerator":17586628373234523195},{"denominator":170141183460469231731687303715884105728,"numerator":2089960963741533473},{"denominator":85070591730234615865843651857942052864,"numerator":3476189947872190785},{"denominator":170141183460469231731687303715884105728,"numerator":23884973050648096355},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":32,"numerator":75},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-343213865214907199627946551420487713},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-521433680389342282074137088920495545}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-834491878714915717083060844736232853679},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-838363589326739706994528722276546172015}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-142215197050220960919335643670838587865},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-18171996178273201736018701488926639781}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":52110401689578793253459268782443033487},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":50272709766755685518456625058664481333}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1374351480879183991420311300924228219},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":5017613946503540710446392881993785003}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":34182582765842252767257065829715881875},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":132753592830480704457164303411707541349}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-66529823391192171574496789196930749273},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-137088148085529411169235195646126569931}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":8400315065087004167738548632054161367},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":32521536998039089338403686216605231497}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":13931735551353790348696773514908641},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-20631600893283928771414842817359913}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-8150412389939423866683663340655911609},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-33685089767853406714258963869337605353}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":417572265792960472547617736941369908423},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":830386581967494590012324759203347107663}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-767632608470349618346079745015176141},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-412257389765211570845673064868712367}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-671889884460060162195089302489174745961},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-685812308904537946545648705491876783227}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":301853934736856148215969196392339589753},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":297157260608913219166338991534975677507}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":39074106765778279071657931337830117197},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":36794498051645104133380875034652874749}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-393267497202818584051620655577142451},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6680787329985014940050513358308951831}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-177728616195563220159610403013811120117},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-179414644673321443885470710574136569065}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":178932583283734832846620849533924049313},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":44307461066940747850652552066838004227}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":1949269600305808256007777031706119975},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":14641913387454163446813912613110170933}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":9173550089745785600452365582671105},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-187598009970189452591059681078097}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-14647467063528591200559887535993356473},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-15598796335150771675005599966666230851}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":696434805131768794230247728280462963957},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":682092635841173881857005815783637556683}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-245006733791092411713399081542853931},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-245006733791092439438330877391766801}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-832165662643469184977719686286136638495},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-416082831321734592620869538493424840691}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-147301608169393991918994628357021162955},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-18412701021174249019271740943512793953}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":53319896418516840144987899975439957747},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":6664987052314605010982867136334705149}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5828916182123504047320585740472581285},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":728614522765438001754302022403108003}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":34838053181568917881726804729636522059},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":139352212726275671437482301330456274245}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-69875317427569866879278278963435958077},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-34937658713784933468178846650800695555}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":17151742532245839565514794554395470725},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":17151742532245839550555620721875926759}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-3544842560010586444528952006619933},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3544842560010597428923205867366063}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-1074686234389771275907671849592763371},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-17194979750236340425962684199618521997}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":827400411825760113514225364339293233321},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":413700205912880056695141995342069555685}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-404559665026487109232551618312241695},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-202279832513243578266943900958621231}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-695395363468768963296279302257629523541},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-695395363468768963500446061140426180795}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":152493191231466739080924706784160299285},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":304986382462933477961802377612633080315}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":40652497375534973103249015541912798585},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":40652497375534973021652063061676113243}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-3468266527272360781750895838199833105},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1734133263636180397882386595122046119}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-180404070907114694905177342462583004449},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-180404070907114694990912990429296611917}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":179940820875345582030510394896995208513},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":89970410437672790956159683134109576343}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":32511647834371586074829905575602057805},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":16255823917185793019137982350280330741}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":9005829035769346001497098995880375},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":9005829035769337095103516587259781}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-16259841311975916160394778119133792149},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-32519682623951832349693980278746605227}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":706298281422507323400786747967420565945},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":353149140711253661651125503438981457909}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":36900061070483449},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-6102586173900053}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-121685783293499385},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-728485252724257799}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":600734268079783581},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":186765875075559899}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-614055661269037},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-43746432657414591}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":528018993681463},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1448806849056251}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-10602880553725277},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-175643042375829837}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":328003028878003313},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":139015185419991709}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-8855957241329307},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-1185437641202677}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1025117832261931},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-797777084859879}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":18339344530335203},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":8484125134892711}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":273987685732682939},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":227104521996999907}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":27692923049886765},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-4925190688811047}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":7149448802396743},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-19173604772346161}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":9809282930772033},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-21684092318150045}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":2088742656160751},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-6531032079417067}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":972587658358887},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6000244764663575}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":34098065995632293},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":316255214477597}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12842796937261435},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-25528961318905093}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":1017796757616933},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-872441960436433}},{"hi":{"denominator":664613997892457936451903530140172288,"numerator":1301961604295},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-286488607328067}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1537005549222027},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11198305001256403}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-301010215807031},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-46548951346054831}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":42535295865117307932921825928971026432,"numerator":3457952673760353651},{"denominator":42535295865117307932921825928971026432,"numerator":16470892313410986491},{"denominator":340282366920938463463374607431768211456,"numerator":117382665399038482493},{"denominator":340282366920938463463374607431768211456,"numerator":28550433116632755573},{"denominator":85070591730234615865843651857942052864,"numerator":4160062075306151163},{"denominator":170141183460469231731687303715884105728,"numerator":22310819398049439687},{"denominator":170141183460469231731687303715884105728,"numerator":28492460208218213615},{"denominator":340282366920938463463374607431768211456,"numerator":14954118310010587203},{"denominator":340282366920938463463374607431768211456,"numerator":5491285679471812159},{"denominator":170141183460469231731687303715884105728,"numerator":5717503498218293407},{"denominator":340282366920938463463374607431768211456,"numerator":61810251402842877989},{"denominator":340282366920938463463374607431768211456,"numerator":47282564531391246337},{"denominator":340282366920938463463374607431768211456,"numerator":102049906939021188979},{"denominator":170141183460469231731687303715884105728,"numerator":49996528682911570019},{"denominator":340282366920938463463374607431768211456,"numerator":40787767722726604101},{"denominator":340282366920938463463374607431768211456,"numerator":14009904642003568457},{"denominator":10633823966279326983230456482242756608,"numerator":1339096600174170787},{"denominator":340282366920938463463374607431768211456,"numerator":59076328435259944649},{"denominator":85070591730234615865843651857942052864,"numerator":4568006702132448499},{"denominator":340282366920938463463374607431768211456,"numerator":4452577000426282709},{"denominator":340282366920938463463374607431768211456,"numerator":14447381370513493275},{"denominator":340282366920938463463374607431768211456,"numerator":49245198089487411709},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":153},"tube":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-100369532960064077914020332466090199},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-578543652448075059702795281524162841}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-831678299391357250100450218075155487971},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-208841892777945188965444894078194215413}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-144660882529105982608957417661704254575},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-147699797036240491814581525772082906799}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":53538597444441134208290554056874700593},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":25853984132383688823622927137476715505}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5890443005997812830828392607076656521},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":5388113468707463148212274503477109209}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":139799605275272049149499417909608238865},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":135884078775770552198359000939202792019}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-68116086871864112199257753463533898079},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-140202611414451377989471686805028711919}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":17215047398196262019582133926324619935},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":33366631487467381742678318166898215583}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":14157266194560105205214966475801187},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-21247571036578210549957430143663077}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-2090612787146942577676677662031652647},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-34516836773182377483959037773866608783}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":831436461033896457035890190165660497471},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":826827467225064357172562297151843093283}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-781571129503549158086795819425342727},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-836661805301577273646852397316072725}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-682991181377359193524608208619392292869},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-696822475999613546274020604660181936317}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":305489396840383080395379402109286148763},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":150439827466908614850648532619865507645}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":40911357170029048147291073609298804935},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":19293437204404562938780839453811430229}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-6592103523586765339177689786875676183},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6986526889679276103473910890843194449}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-89517381383694283604361519816680129991},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-180614363890885681983168150571433649637}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":180151155214015824941744307246608292741},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":178550920846013888970134560678249539967}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":2045569320320847609381309242661370873},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":15390042549231142791690530434879281481}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":9392207362398964248294144418165579},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-772507514813699753793989989254263}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-30789926326710871835729771313472358243},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-4092094008471913053079352079634929183}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":176942742639502299326354551556773880511},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":173381650682077701724288948864405669327}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-551777804683562549544788748134932377},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-551777804683562606046734482897868989}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-829479547100324411483856522465687744655},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-829479547100324411752497779280713693555}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-37385281573309125999636899276739765487},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-149541126293236504236526581062027267629}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":13685548437605672153827131120300102997},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":54742193750422688555794149706485412897}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":6237625568958803675092263516711058365},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":6237625568958803640041507231498097745}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":2224679019366830480672370441499624877},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":142379457239477150672329574971923502051}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-142825153569579438002401304424627632831},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-142825153569579438118354209274570959479}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":4389998298574442397318389100844556055},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":35119986388595539147202396918300725581}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-933962459258079359450855067645955},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1867924918516164528760280133872391}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-35209286197246858166027445950615451881},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-35209286197246858189997511504031720695}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":823946324103601060388868512637952817943},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":411973162051800530131313126591531114983}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-821286120559014846772062163626324401},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-821286120559014944357924350417970303}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-706348152713428825618630502864977599853},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-176587038178357206457213113967222201021}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":308566769327530279574415722126577259065},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":308566769327530279368368298129668263155}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":42521033667088070878872428343920266089},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":42521033667088070794368560682405975481}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-7245748100796536102134448661698430789},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-7245748100796536131531337719981802113}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-45383219866259117788251601484992419697},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-181532879465036471241424940258431903201}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":90545735006312783991768132223968402885},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":181091470012625567861672132394675485595}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":8520927804104976091211172717787592391},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":8520927804104976081720721875618546653}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":9607257478138191831185851589031817},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":600453592383636396991831111748099}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-34089855961171276802483365922079008743},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-8522463990292819208125416261294733101}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":179392688755762383996249900901866281629},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":358785377511524767941734706420724855023}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":7986487336246235},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-48559094812797779}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-179319585222525177},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-75360634933174097}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":121220061810507689},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":130110339170485337}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-17154937061221893},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-19177567904349343}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4009788092468383},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1197659086259141}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-71411423164298977},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-308225217459461735}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":278661891027456465},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":27524423406655239}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-2014312242024455},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-2187467588139529}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":59488090563261},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-770673897358965}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":8598461264698837},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":7849074305359291}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":121929720959867045},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":194058840815623117}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":13160873337632055},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-7725309265962407}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":1971396407243075},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-43234840406918045}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":43395079238200117},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-9556555976991273}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2026431665323439},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-14490008856070363}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1802485037721101},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5506977629721605}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":26210955488666357},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4465457543561797}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":17261921894606173},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-17104870471478381}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2962340627488323},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1513280505272883}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":639295491634993},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-536609907356679}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":39072018244315},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8830401826161777}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2078927257842931},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-37656264141347679}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":85070591730234615865843651857942052864,"numerator":7048686842657521119},{"denominator":340282366920938463463374607431768211456,"numerator":134108845660391540649},{"denominator":170141183460469231731687303715884105728,"numerator":59406053511749165065},{"denominator":85070591730234615865843651857942052864,"numerator":7436646821995940287},{"denominator":340282366920938463463374607431768211456,"numerator":17522774419017116547},{"denominator":340282366920938463463374607431768211456,"numerator":45268365456460813147},{"denominator":340282366920938463463374607431768211456,"numerator":57892170326271245569},{"denominator":340282366920938463463374607431768211456,"numerator":15667636698359352223},{"denominator":170141183460469231731687303715884105728,"numerator":2904498664162697455},{"denominator":340282366920938463463374607431768211456,"numerator":11980358852596115215},{"denominator":5316911983139663491615228241121378304,"numerator":983973432905208929},{"denominator":85070591730234615865843651857942052864,"numerator":12193976891356302423},{"denominator":42535295865117307932921825928971026432,"numerator":13135184187015396349},{"denominator":340282366920938463463374607431768211456,"numerator":102997236180846902259},{"denominator":340282366920938463463374607431768211456,"numerator":42242662394663786683},{"denominator":85070591730234615865843651857942052864,"numerator":3673697449451991077},{"denominator":340282366920938463463374607431768211456,"numerator":44193928952714998129},{"denominator":340282366920938463463374607431768211456,"numerator":60914882630447617809},{"denominator":340282366920938463463374607431768211456,"numerator":18976426063205330269},{"denominator":21267647932558653966460912964485513216,"numerator":296191895262564705},{"denominator":170141183460469231731687303715884105728,"numerator":7502347644309318313},{"denominator":340282366920938463463374607431768211456,"numerator":50744188323679191463},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":16,"numerator":39},"tube":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-57975293526585305990589572007687009},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-639750112487366060667360358719857789}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-829011798603820642380166559237294631481},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-832516091981207912226358245870025048655}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-147009979609578980542783497189079594389},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-9370391575483068394055925416842001531}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":27480058496822491023459071205779590535},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":13284412421986761634214200730449832647}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":787706473939491099243831795578969851},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":5776390003302123482932611692065958431}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":142819377406948689192187254997790241277},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":69483486103100445843479764228208291423}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-139359593304336421019019465472799716225},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-143270008812369548414390387814498459959}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":35244796050177745015951558699529342517},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":17099447477485502555286714085498107617}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":7190331844042469778015408874020375},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-5463258987352958404125853144401197}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-34285029619937107074665010849997471201},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-35334328425292844618469892020683782357}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":206961509895395367417106745385949458589},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":823389762023367908126410811697775079565}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-794651128706408325156271400342013643},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-423956459612543836913797150320662039}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-694020991862897418099703783992969471359},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-353882353960806435032729482220273368811}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":309059791911974782338187056509396339745},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":38066722676629999962219954408582100109}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":10695959596655404825981657575905802465},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":5051960213454557096008249973807148153}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-6896542249015363681018668669116283813},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-7296450304308942505849896542926852227}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-180256555582860567191789357605336359623},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-22716463603175230540708650497347444041}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":22661335153527821358383956809599509221},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":89895418195846291569784555889242899863}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":34305219544872623468911299451694026125},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":16156181044380179828547130297493851841}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":19227968404353946961374323174476013},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-1646179160482225789276675331445}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-16160328100463281901865520027127616901},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-17155460215589624487158099847677741605}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":719032599378531589687590302738597031297},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":704883357205171293703879973760223207925}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-154419470968625339606985593104134525},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-617677883874501416043818586768706107}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-413471056040471946692988624073194395869},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-413471056040471946829693425721485774061}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-151682886754997109678554746133603909095},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-151682886754997109919362812096338729577}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":56157080210281854041647485703327255375},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":14039270052570463494918516387858654513}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3332391924443723836504516680022858865},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":6664783848887447636129800121015755989}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":9084746419041224478529269469500432309},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":145355942704659591564473953179121659981}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-145851298861368891279909195671209440445},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-145851298861368891397690018118637384595}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":17960728149284635950522360437723003033},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":35921456298569271868223829908080720141}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-3920613558965370293574213913912801},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-245038347435336411002552354592803}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-36013444125202592144638820472591114731},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-18006722062601296084868909078126445205}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":410308049968451970304674197272213674085},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":820616099936903940480701874022187733823}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-416301035859131288496056829380495211},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-104075258964782834702308272842891327}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-44827224094219865288654836733173467383},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-358617792753758922417423409311709982029}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":312084400064422839592701603742817447845},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":312084400064422839380564752723521411053}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":11105990736320238136013111773129503759},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":44423962945280952456573271525382785285}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-7558835203096210638556659121220447613},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1889708800774052667343779898520579679}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-182580814467358134938151461941959795433},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-91290407233679067514647961541649579085}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":91082329431365615974071907883983994437},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":91082329431365615911272902994765006617}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":17845302749248129892327307839334764999},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":17845302749248129872622854446305295029}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":2556614352171117105117018425598861},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":1278307176085557292437308404281611}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-35694536928887258204562880570102642323},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-35694536928887258235725393070907970137}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":182192672985542312097410112159729030251},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":728770691942169248285066061716131602239}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":55200201603866091},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-1498224672527843}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-121384108527695139},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-246541629465153689}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":385507442197978143},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":79235802826108187}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-14691058847349801},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-33427996949062651}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3808579353445845},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-992907885048145}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-117163976034268461},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-133815674867917323}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":234108153256896625},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":41788948912892905}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-7213926624901707},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-16029002528223163}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":442107845764107},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-46565584806515}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":1998494133459121},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":3571203175323021}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":215107066348333581},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":80899427550557629}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":24894308503925201},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-3025133624968885}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5409313156306711},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-46866051124514067}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":46419030556964359},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":46675938720893}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":625146041792031},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-15542944694446035}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1691657361263253},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5041201642964059}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":9682742339176345},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8738351243961493}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":20779729730919797},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-10082028674372827}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1012221264840957},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4066788331667731}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":611076503880577},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-251800961014685}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":362072530667709},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-844840699786825}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":8714177187497161},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-29806559186549399}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":28756366411613705469},{"denominator":42535295865117307932921825928971026432,"numerator":17064869009136259009},{"denominator":170141183460469231731687303715884105728,"numerator":60125448580840737631},{"denominator":340282366920938463463374607431768211456,"numerator":30977341606895462235},{"denominator":340282366920938463463374607431768211456,"numerator":18437215875895733875},{"denominator":85070591730234615865843651857942052864,"numerator":11480486369897961347},{"denominator":340282366920938463463374607431768211456,"numerator":58815146095998416667},{"denominator":340282366920938463463374607431768211456,"numerator":16406037945730982233},{"denominator":85070591730234615865843651857942052864,"numerator":1535104669838892449},{"denominator":42535295865117307932921825928971026432,"numerator":1568134508559046797},{"denominator":85070591730234615865843651857942052864,"numerator":16047263155580507805},{"denominator":340282366920938463463374607431768211456,"numerator":50297703974114138611},{"denominator":340282366920938463463374607431768211456,"numerator":108158577764181832575},{"denominator":340282366920938463463374607431768211456,"numerator":106045262670308257109},{"denominator":170141183460469231731687303715884105728,"numerator":21865751869099747921},{"denominator":340282366920938463463374607431768211456,"numerator":15405863806928821895},{"denominator":85070591730234615865843651857942052864,"numerator":11389544663177131069},{"denominator":340282366920938463463374607431768211456,"numerator":62783574010016341507},{"denominator":170141183460469231731687303715884105728,"numerator":9850197778166977095},{"denominator":340282366920938463463374607431768211456,"numerator":5039927464021116303},{"denominator":85070591730234615865843651857942052864,"numerator":3894288185635545297},{"denominator":170141183460469231731687303715884105728,"numerator":26133966546602618051},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":159},"tube":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-66280454525027766036304520302473157},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-705111033776809290617829374590252111}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-826494158214699305224728042235667370737},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-829811256976504979144472194752276980041}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-74630905782820095140135139567205540917},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-38013739710400831865760864165216906855}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":56374122011021190832838934441686330789},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":27280434194066983040283475579119141257}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3365669806376662851101749044742169415},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":6182768452981634522023508002941487007}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":72894121185520826732544092893996268153},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":142000703335969983695356395748024358739}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-71220147468654041590061790075833862701},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-36572220315005407850725205170560886035}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":4505542611271690150957459495383897681},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":35017280332864652251596032335656979867}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":14603664134926725661043312315582023},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-22445616783012886818623412246359113}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-4388282482008283528867163520678558617},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-18068261633936083790919341909137521417}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":824376333727564556212033425989742205357},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":102509529685991199747548036833858948347}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-806897223077479918069575628617692029},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-214574075943377314368609506338605751}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-352491089265739417337135782161975052827},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-718641920350978744117860947535201792085}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":78141934430281921527624677081719665871},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":77030554320949308543699563076966130903}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":11172645215426364356973244813034679211},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":21139986433843069473099590298494321245}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-450328338102084861932064592184829205},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-7610200321265140903127183143345646813}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-45348901120703827928400577055835496921},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-45692088576256726526910820797648910793}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":182352936859049302741667603262140814235},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":180951307029689597319450413165065642907}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":17958035104658260215354989415560867805},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":33880115772764724759790988221621874995}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":9838549537224026793602858554853421},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":388067558383014547246977393016973}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-4235820226049477781404082370340913041},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-35919503336150367763739726357221092923}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":730221933246690828666315318996604234427},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":716165068553756058907597645246541067831}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-343879823160071225762453713483019477},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-687759646320142510350964097288667891}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-412277464346594147562131397408087513283},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-206138732173297073850649601935192817535}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-76863322749069656157725585275724376113},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-153726645498139312559127914152380668255}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":14390937632946767691098442754982262045},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":57563750531787070699889687984658598045}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":7110686003013645427714605353824091067},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":7110686003013645388941321635058238353}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":148280370751765720173239454885867489845},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":148280370751765720079936200316589659891}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-148827709776563893247786342234699489513},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-148827709776563893367431763916450532089}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":18353444435948405206241279591094930263},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":9176722217974202594533564344164328369}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-2048459648690431278655337898611225},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4096919297380875530872849872452565}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-36801408575055421425882053807451035173},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-36801408575055421452149817646715094317}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":817412316250846809468173055211271276165},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":102176539531355851167126918396201622239}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-843100810603190330398411871296033461},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-421550405301595217062828339663291551}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-728060602519721169696742537120708704859},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-364030301259860584959677839229026251933}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":157770954445246905018552813537152091203},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":157770954445246904909393546914469848027}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":46360299494768789530407620088670309941},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":46360299494768789439882561671124967549}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-984428440368656620278147670969969949},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-3937713761474626497259893719960247013}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-183549587679717111093415539660627873535},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-183549587679717111187330256060948576105}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":183162195970024139617556127344078577435},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":91581097985012069744080736230243484473}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":37331732786514569402582257333987326603},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":37331732786514569361685705301760912777}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5431221911501406670311437371051843},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":1357805477875350328522770185148633}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-37333107983169969358287748459729116145},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-18666553991584984695312880052938374617}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":369950187225272524235096330498794988653},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":184975093612636262090630466527569386603}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":47703841856070803},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-23532123621117391}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-17418403180085131},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-397644946857831981}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":4700009724903063},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":8522535470059259}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-1537221477463289},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-28958588184029723}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1808267332718095},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-828965630523221}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-11650011537666275},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-114826836073916641}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":194151819347128285},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":29853553732915141}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-6358798876475611},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-3646280831866291}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":205254515339659},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-719127383383521}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":14747947815647929},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":6399499748578537}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":11742891721836141},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":131010779458584781}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":23452431334900269},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4742896654939177}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1420505582818617},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-6176996050403533}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":48478156758790611},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":1909940089635911}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1029995323354799},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-8138991280734115}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":803660553251411},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1152397148228029}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":13467261797192235},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12237631202993563}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":11743414746758759},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2143843627297851}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2477135316012415},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-305412996391159}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":582300670351869},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-236663215246013}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1293083104904109},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1239495280636043}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":6251981797152265},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-22931318634253547}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":29365644290612161675},{"denominator":170141183460469231731687303715884105728,"numerator":69501910397614688029},{"denominator":85070591730234615865843651857942052864,"numerator":30426254140052294629},{"denominator":340282366920938463463374607431768211456,"numerator":32243711109453063361},{"denominator":170141183460469231731687303715884105728,"numerator":9692209554617473325},{"denominator":340282366920938463463374607431768211456,"numerator":46583400494715663435},{"denominator":170141183460469231731687303715884105728,"numerator":29877744242467436143},{"denominator":340282366920938463463374607431768211456,"numerator":17170037740540778747},{"denominator":170141183460469231731687303715884105728,"numerator":3243005507157621989},{"denominator":340282366920938463463374607431768211456,"numerator":13129707695598494875},{"denominator":85070591730234615865843651857942052864,"numerator":16364118285752265815},{"denominator":340282366920938463463374607431768211456,"numerator":51849524740020355097},{"denominator":85070591730234615865843651857942052864,"numerator":27820820797513275997},{"denominator":85070591730234615865843651857942052864,"numerator":27284711856120529923},{"denominator":340282366920938463463374607431768211456,"numerator":45255420212815291879},{"denominator":340282366920938463463374607431768211456,"numerator":16144194581230659747},{"denominator":340282366920938463463374607431768211456,"numerator":46944505753660258385},{"denominator":170141183460469231731687303715884105728,"numerator":32341720091710873817},{"denominator":340282366920938463463374607431768211456,"numerator":20444594144484071433},{"denominator":340282366920938463463374607431768211456,"numerator":5355692543080035363},{"denominator":340282366920938463463374607431768211456,"numerator":16165233749407640349},{"denominator":340282366920938463463374607431768211456,"numerator":53817679802541936407},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":32,"numerator":81},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-600226341812903698162046877487833293},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-774741762428880300820999627751625811}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-412063459151404972209719864575895507793},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-206813727847406360893734132985470770033}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-151415912074922455832650577250185922601},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-77042829437834497145846131942671265993}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":57779811839262138794383068610582338109},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":55976776695950711222484176078304509651}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":7179799484012768184622287845584227027},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":825944986178634835787162655077084407}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":9294057375440992188417658172896574975},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":9061489646107916948819840269623945449}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-72736394775042575289372052296945170521},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-149257882662922557590395013168058079517}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":18413862897366454155785659382000613855},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":17910379843942211687259276562099039897}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":14828174897138021605233343925198623},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-23022791862703851989422341644181069}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-17956224572056937264640019300411604773},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-18461199477500525341433927559739502919}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":821030173078102299365883459729310634511},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":816889441666118711800532810079501026655}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-818341364249130702588162987675382161},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-433923634188587654364928273695670601}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-357938821847123343021540684489959717445},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-364728530913479135898520777144728305859}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":19750992191363092217818397306876499333},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":155823784754578828795586287118120381425}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":11657649536731864428201794118195231907},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":22089390628104559269606974254556870537}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-1879470647778650196961954491648494653},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1981852177732674823734056828458853267}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-91226784681421345091353867076658883169},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-183726020407997137737145009840714801731}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":183339738404225478911512882420757379819},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":182034094469231871034882797252835499663}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":37561060831636235786540924923347242027},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":17741388564073686759217564544651966833}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":10065521409186475470075886732385215},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":797100010621824723598228542519257}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-17743527131700015999971898013715570959},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-37561880918272294046134639255122890409}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":370670631872039649470608082646245253195},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":363686980870978510217191358314989014469}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-190514317524062806108539226682900587},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-190514317524062821142619735621032163}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-411159669049788070462237337072932993017},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-822319338099576141207904021115546471775}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-155672345157364610874597129484455159211},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-155672345157364611121191253658351845333}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":29480718437662282254389633138408572779},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":7370179609415570555208864687983420155}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":7575612351897843067764922275200875815},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":3787806175948921513515135951560590499}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":75575779956187285743646171237503243863},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":151151559912374571392661531365420745169}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-4742285396052679540248825846713803539},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-151753132673685745409511774448549888007}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":37475298133334767848916626286329802115},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":37475298133334767812988193882696000217}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-2131198200218558761940447075595375},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2131198200218565608916387489505689}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-18786087146298509434728314079373598141},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-587065223321828420264595825635276595}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":407168668150436272933945488806604489085},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":814337336300872545734111347995184962287}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-426411518531393869208082597091320773},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-426411518531393922654070118218047085}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-738826173173929932115060241081753316245},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-738826173173929932344017456623680759963}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":159470974490517902836420328224294470567},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":79735487245258951362061220566776958663}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":24164521300285316417011079274360112487},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":48329042600570632740378402805319244563}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-1024393470336348831027143578807510153},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8195147762690790682044787380347935163}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-5763779787127204288327186196796742345},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-46110238297017634330800157962856661829}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":92042963865525283890805672135383335923},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":46021481932762641912088803703720471767}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":4875808819940772451312628647089380943},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":19503235279763089784037474134513829649}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":2878530981569689205695882478854439},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":5757061963139372723966081857562459}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-39004927206407552029082301665955725987},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-19502463603203776031314046228277101667}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":46935133200378655028131897145350462603},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":750962131206058480339288233897591032249}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":41261415997473741},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-22961700085930419}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-23840652975311023},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-315171556836427095}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":114474297167506425},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6002501390213701}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-10030415762186531},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-24935959679748903}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3433869668013299},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-700245076709175}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-2225597150237649},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-97427764613978917}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":158638563701970737},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":38564893144216385}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-5511746284502161},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-6596533936533761}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":762406994977811},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-692959520344811}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":1688585814949543},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":2823710788239237}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":325321432511497797},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":12782818343055909}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":22033348407172497},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3731701124876791}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-1162940270168773},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-25531766392708393}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":49756313005957571},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":6714973528870317}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-2063043799702733},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-4189207131890919}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1543695515309927},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4209315199246081}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":264860659057083},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-15027176195600573}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":12740983694555351},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":105404775989387}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":588449843289903},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5509460512285381}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":34586467924701},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-445778616875013}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3509160221802643},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3421318138737381}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":15579618806644813},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-17010044770952217}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":30024568609791595861},{"denominator":170141183460469231731687303715884105728,"numerator":70784504016454842417},{"denominator":42535295865117307932921825928971026432,"numerator":15397448317385716223},{"denominator":85070591730234615865843651857942052864,"numerator":8386680403629027743},{"denominator":340282366920938463463374607431768211456,"numerator":20365258128667486171},{"denominator":340282366920938463463374607431768211456,"numerator":47253587344582694745},{"denominator":340282366920938463463374607431768211456,"numerator":60714636841575210203},{"denominator":85070591730234615865843651857942052864,"numerator":4490093885255654567},{"denominator":170141183460469231731687303715884105728,"numerator":3423124128578124501},{"denominator":340282366920938463463374607431768211456,"numerator":13734821708483693963},{"denominator":170141183460469231731687303715884105728,"numerator":33389142683064241339},{"denominator":340282366920938463463374607431768211456,"numerator":53433104996360701667},{"denominator":340282366920938463463374607431768211456,"numerator":114457727765651688557},{"denominator":85070591730234615865843651857942052864,"numerator":28069930976941611193},{"denominator":85070591730234615865843651857942052864,"numerator":11703890625309102775},{"denominator":340282366920938463463374607431768211456,"numerator":16910942869586648965},{"denominator":340282366920938463463374607431768211456,"numerator":48353585418322732523},{"denominator":340282366920938463463374607431768211456,"numerator":66615534553799815811},{"denominator":340282366920938463463374607431768211456,"numerator":21209697273744261529},{"denominator":42535295865117307932921825928971026432,"numerator":710865762756038913},{"denominator":85070591730234615865843651857942052864,"numerator":4192357539029742165},{"denominator":42535295865117307932921825928971026432,"numerator":6924345672777423273},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":165},"tube":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-334915577977561100545973962064948563},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-849116059605324705421540753468059851}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-821911390803518641136961136906624267523},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-103106081890671726567903096426390440131}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-153472013718692280541168245735461684011},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-78009165756581299141998745848154555301}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":1849263225367801495126839249386028875},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":57384564678455673239426446851912200099}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3823654864344806641781950270295384327},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":1762765286151301127940258711415787759}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":151568238118168172296155699807678805179},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":147915052155498780944800700128799393131}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-37113925678031565541534134184162660265},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-9510985834781410811414661844882241877}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":37593967229193045777052245682084867001},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":18304162304987503222460573660303611789}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":15056273237213092887345429993762357},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-23581896975048749199009782970748449}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-18351285172951952011553142785479024187},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-37690952637419078050863965736864660805}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":408905080674778347106765472789441837775},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":813831710362457846759952044101782937255}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-207255669158157499263648705832559163},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-438304047089420582977338898458510789}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-726710324042557999666086377758132516609},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-740213108814189699972647969184871143551}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":79851715720750644814995509637336268313},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":315112469557992835436432099726780959081}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":48602888993031095293959980443220928979},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":5763890360481344432012022695402854041}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-7834064264249906279513265002583576561},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8247696851243373106632426455322151319}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-91716078213292469722628117271446913351},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-23075808619738331990856160440151379935}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":23031617429049488348012666255057993479},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":183041002251982832010834821373931387341}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":2452472912927188740508166167676488871},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":4639968906365426024565644335218917365}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":20588932447294055504172851692507587},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2439706861214400780761192838863561}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-2320094935952723637131658510290641643},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-4904676131813436229489832114551938663}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":752392928155528255828195541858151015265},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":184628078231942284105472864362377810925}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-420296537030765210287296578577828509},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-420296537030765241062506383663461047}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-205059116154002248279607185668163048123},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-820236464616008993407129170397347690163}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-39380026203923275784260546190240148563},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-78760052407846551693305284497181589523}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":60349408527682701465133138616951022123},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":30174704263841350697672439606062777695}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":1007478526154057984787824110279638935},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":4029914104616231917768724882040190259}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":38492109709688800527968983477801715167},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":76984219419377601007948554791754275527}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-154626414941981021786699154366163868039},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-9664150933873813869387173124396707623}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":38225718425497162539839700198876510159},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":9556429606374290625569219254581306069}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-551814921189892920544666207415563},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-551814921189894726121419278405717}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-38324755858333048712675612831594538773},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-9581188964583262185351254578905953443}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":202848330084880040863116434010158955915},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":101424165042440020414493764667788724271}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-26931760886252426316964048949243241},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-861816348360077752266946898988899221}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-749535290954760868328337741908377722487},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-187383822738690217140935931471110763043}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":161143593908510177525500630883055178155},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":322287187817020354820029231339142829085}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":12582294642293628921825533367294030797},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":12582294642293628897616137070316559599}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-2129402188278457901969544319903520151},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-1064701094139228955412264710914441193}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-185256704053497832674431725337534951635},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-185256704053497832774025480209830624317}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":184937735065123787782277494725983754425},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":184937735065123787645092874348192378391}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":40714172745961091345840954090412514493},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":10178543186490272825460513550602714341}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":6090147908283763287867918182560111},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":12180295816567514506377855437169169}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-40709329448290260743804560927773003889},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-20354664724145130389295717860105610933}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":761958333210674049755704137593564155419},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":761958333210674049641673008278090823331}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":35752006439740999},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-11151089722322225}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":16720458026234731},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-244684305859319555}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":168691639663668103},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-20662365667824731}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-3942306998041089},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-1334065018584113}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3262402277037805},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-151214601564321}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-51399176140035301},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-2549524923055521}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":31865576018872675},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":19713370441155471}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-4691141947225755},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-5938489881946369}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":709179090652323},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-41674805152339}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":6149077594546541},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":1227069687495633}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":278883900120976467},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":75954553009843135}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":5164991618718127},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-186101935687373}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-14197295641378811},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-25999925945923457}},{"hi":{"denominator":664613997892457936451903530140172288,"numerator":98444939282115},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":8843616294180299}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-5651080125662289},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-17024042698754513}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":749901236570579},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-960096240944347}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1072098382749085},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-17189939838133275}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":26906800643964021},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":2084955986882463}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":120064192097593},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5978558235405009}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":525197551205257},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-210367295385307}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2118294092594273},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2120524023346535}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":9004109702527117},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-5968060045817579}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":85070591730234615865843651857942052864,"numerator":7683757905605279397},{"denominator":340282366920938463463374607431768211456,"numerator":144219511480404971691},{"denominator":170141183460469231731687303715884105728,"numerator":62339591965600816807},{"denominator":340282366920938463463374607431768211456,"numerator":34887399489262101551},{"denominator":340282366920938463463374607431768211456,"numerator":21380637928736717935},{"denominator":42535295865117307932921825928971026432,"numerator":5991690869297674473},{"denominator":340282366920938463463374607431768211456,"numerator":61693933345274559349},{"denominator":340282366920938463463374607431768211456,"numerator":18777818671367309449},{"denominator":170141183460469231731687303715884105728,"numerator":3610809512148707871},{"denominator":21267647932558653966460912964485513216,"numerator":897562987737192639},{"denominator":340282366920938463463374607431768211456,"numerator":68156344675607448079},{"denominator":85070591730234615865843651857942052864,"numerator":13762557466895905629},{"denominator":170141183460469231731687303715884105728,"numerator":58842045354953715395},{"denominator":340282366920938463463374607431768211456,"numerator":115469656925321722471},{"denominator":340282366920938463463374607431768211456,"numerator":48413106112668396283},{"denominator":85070591730234615865843651857942052864,"numerator":4426825027533066299},{"denominator":340282366920938463463374607431768211456,"numerator":49786138269463271533},{"denominator":340282366920938463463374607431768211456,"numerator":68580941744560588469},{"denominator":340282366920938463463374607431768211456,"numerator":21996400632787077263},{"denominator":170141183460469231731687303715884105728,"numerator":3017103012196493795},{"denominator":340282366920938463463374607431768211456,"numerator":17390258840114841447},{"denominator":340282366920938463463374607431768211456,"numerator":57000592487988321347},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":8,"numerator":21},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-743647065345133076998030368184859107},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-231937278214078637839823388657258991}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-819848672524696762216345839992769812543},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-822593856496784961095854930373524240085}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-155430037057060453290186681950025147681},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-157853118060102029134291155095302007429}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":30281614974929337687641694193521339533},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":14695864966760749140039605123683546605}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":508383352259085952112672387589914285},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":7513554431425895004055550958972213985}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":77188572859995189182975578135780552867},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":37698290372326537098907337643989530289}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-151387768097542688558415167215003830047},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-38760353464743313963471940953589851625}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":38342102016207087489200317774918126229},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":37378986590793398960075735428113180043}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":15290204420503093497522667464029493},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-12060063112210351679690589193507097}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-2342225983223486916962757649802398913},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-38441201341788072651929177816903263795}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":814718687247847359002955061446027571301},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":202726294444524806913078556329216223887}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-209746819588537025177720672410644923},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-13822310350100080485076825106035339}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-737483185631769769747485894147679799323},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-93864132631671424177903670161173964123}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":161371686838887866206267095672415649229},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":79629892114793953390830961920200660903}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":50606439363862546225966293353921128761},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":48075998515760420130868636944472006813}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-8153422367845582420680579287658768943},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-4285338158148832348023135258324318097}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-92166557315298959437768789231737597403},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-92705750102662051192430687302328770795}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":185094427483350530051257726529363827371},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":91986936101508619246238578856690654875}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":40950939283803846273384010082683257575},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":38790418479050883267485052267618897761}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":10524898044624096262899597556379809},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3311223689887404049758254022670003}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-19394658420262970667583506164331019693},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-10236355124835512068579975875643912461}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":763379305455572545204262116658660227925},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":749582445178334695354291135568691871001}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-461688737238195935973590628551878275},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-461688737238195967509703737169711065}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-818307228155440331304264880298703804103},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-204576807038860082899605703038734981735}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-159270210386098583726630261322000303367},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-79635105193049291989618797426986397659}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":61726971580113218791922979299017268845},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":7715871447514152339922132791885840365}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":535223972803565375597555502835171613},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":8563583564857045964694243628351730837}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":156730039758231597478823482592641524611},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":156730039758231597381473941829666023929}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-157446498985993476220775620648604132515},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-78723249492996738173131249951668103445}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":1217412649211452372695047593235881129},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":38957204774766475886988462204142612903}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-4550609765536367008354465597466759},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2275304882768191117455868532069337}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-39058188062371285760412860150522636853},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-19529094031185642895218782916737469471}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":404291118021804436770253623954413148817},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":202145559010902218350284446408767905333}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-870135050066831693200576501655176483},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-108766881258353975828487861194418525}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-760190968984003419780572463194218959963},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-760190968984003420022536436672228376911}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":325580302778179383498562151440515552777},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":325580302778179383261111185389194081677}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":52359682673374957355106141736037256917},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":52359682673374957254997168266095292547}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-8842414044241794445587798676824058921},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8842414044241794482661772501426485825}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-185998669147645187687252985794841704377},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-185998669147645187789758476060968209047}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":185719530271524401023593837568296810185},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":92859765135762200441205723243215247903}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":42454170759490259984169784816852592221},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":21227085379745129969276668306608985121}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12859647210684326830673170804111717},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":6429823605342157016760080216814007}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-42445627422682197200320729906492013371},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-42445627422682197236383077938103499973}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":772891389973955264429902756478921070985},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":193222847493488816078150499134721301115}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":7779612028304987},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-21671330024773731}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":26214577040890331},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-185278654755652009}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":118992842026360447},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-72497356992418027}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-5853252302660023},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-4542799738579647}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3103644898851091},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-544660860316775}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-33450100030252303},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-33675725171704965}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":25101285204283145},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3338994988836785}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-489405055544333},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-166395303067307}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":660586568019627},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-641808925720451}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":11140071895949245},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":1047704007944445}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":236664151304938377},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":51744571432152097}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":19378436057825933},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1233183898598389}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-8847864735446659},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-6547146395320733}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":25291719290784075},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":20576348108280027}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-6691068615371689},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-4284722559165113}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":736788418825761},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3514964627666683}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":832226672155933},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-2355314651869523}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":27833920408736613},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":7063099624926045}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-360486455398335},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6300824812679271}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":498365639962149},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-199058397038305}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4808464651838385},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1036122205692183}},{"hi":{"denominator":1329227995784915872903807060280344576,"numerator":77838745163387},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-7654798055232317}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":85070591730234615865843651857942052864,"numerator":7874720638634112271},{"denominator":170141183460469231731687303715884105728,"numerator":73480056011849672541},{"denominator":170141183460469231731687303715884105728,"numerator":63103960833238428369},{"denominator":340282366920938463463374607431768211456,"numerator":36266799508639443679},{"denominator":10633823966279326983230456482242756608,"numerator":700984314238310111},{"denominator":170141183460469231731687303715884105728,"numerator":24312071990579733281},{"denominator":340282366920938463463374607431768211456,"numerator":62694906554451889289},{"denominator":340282366920938463463374607431768211456,"numerator":19623163360226815119},{"denominator":170141183460469231731687303715884105728,"numerator":3806313718993232959},{"denominator":340282366920938463463374607431768211456,"numerator":15008878213544065311},{"denominator":170141183460469231731687303715884105728,"numerator":34796135673470472505},{"denominator":170141183460469231731687303715884105728,"numerator":28351370396011287251},{"denominator":42535295865117307932921825928971026432,"numerator":15120580752269859025},{"denominator":340282366920938463463374607431768211456,"numerator":118710479480424091487},{"denominator":340282366920938463463374607431768211456,"numerator":50049262824160337803},{"denominator":340282366920938463463374607431768211456,"numerator":18534492641568554349},{"denominator":85070591730234615865843651857942052864,"numerator":12810726940279924069},{"denominator":340282366920938463463374607431768211456,"numerator":70580810130541251905},{"denominator":42535295865117307932921825928971026432,"numerator":2850679271983296211},{"denominator":340282366920938463463374607431768211456,"numerator":6398128263968222471},{"denominator":10633823966279326983230456482242756608,"numerator":563382866324280563},{"denominator":340282366920938463463374607431768211456,"numerator":58636589211609403567},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":171},"tube":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-205424462212004634266412343836969951},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1010650100983137372155084994402396385}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-204484914375844725312807522921507179685},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-410245832703150612934447867471470635469}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-157290080307516839716879337636100175389},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-159590325389279473918507806685681108465}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":61939542638708871209109165185479468153},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":30086363479895452374685534707597379455}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":8640519147941496527239791265532801635},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":7995306993820349092014967130694194221}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":157130686527927301923801942621772872161},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":76808538992201373235287175056349410157}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-77133910584820656433578311444706116501},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-78926879446519201031290967728952663909}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":19535593850841523424196006282331037217},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":38131777394809842019375195046618545863}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":15532379306335909790109321419746933},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-24634533437471331864940976252420809}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-19115298679878324056155258333721759927},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-19586091172760327057980738054965226743}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":811757935165646937552540753097587292843},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":808111786904379196551790584727095856567}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-106036011013422280696308628079829197},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-891962269347673972698306936216853249}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-748199219151774214845386854156985055129},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-761559937181640749674895729471888473155}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":81507022279221261457478440865901443715},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":80467883029258847288066070770244423901}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":26320112187392424840134953722440346733},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":25036197850942239234687531842708801941}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-8475570895907437498204716389234449059},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8895949467971378594939323094007508951}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-11572389519757351496922965732700557917},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-93071474844959855593705092833722960375}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":92933060477172910674199531120065443719},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":184834581077432450566947742115863293435}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":21347254098693369559964392384267959941},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":10123533868395115941624770973793038839}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":21512555852188540348336078329336621},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":4207203820746971778914229024680767}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-40489785389521756689795301615264140879},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-42685225977206797229887892541329515427}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":774302812501683207315782210613749539759},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":760586724400561921011216429996459493111}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-126301123970991848723928960947044289},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-252602247941983713624192577203233165}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-816532355988805887290885571841825741375},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-816532355988805887590696003017485378635}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-80461552814646730227257521378640757505},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-40230776407323365177558410367764174683}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":1971670893363036680695947047722090395},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":63093468587617173706886834880889528729}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":9087112797045288573408682979945358529},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":2271778199261322131591894534781711415}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":159435492185502460004872505227730625275},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":79717746092751229953063757715787215263}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-160212416493928565488319108047337213135},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-80106208246964282807922408008173676225}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":39668833254567264609794139857509220275},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":39668833254567264568793358067888907099}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-4667838617846705338018416578129623},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2333919308923360689419630716450099}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-39771526276792209199712343521153642573},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-39771526276792209231077016072008713711}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":805905868657565986292752598878370397707},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":50369116791097874134400506328968105623}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-877839956154598209778396347143388103},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-877839956154598326583857868059442029}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-770796235853240134660693569833783673017},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-770796235853240134909329438609447156477}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":164411988483820218104252779354969025489},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":164411988483820217982234569662985012379}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":54419521025030317422378334666322427885},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":27209760512515158659458943986688583203}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-9169158498273738629483005477914423531},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2292289624568434667068817061727680171}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-11666794385154385615875897840825403245},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-186668710162470169959481807196233756671}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":186433254064669037714738810958173763225},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":186433254064669037569487031951217570917}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":44225774496513257864281970123787526011},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":2764110906032078613562609919570440025}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":13550754205163063569805758733271885},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":6775377102581525005170404063116687}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-11053278190541441350803415546486573265},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-2763319547635360340036686674438627271}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":391881872938922063876635377473085375597},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":195940936469461031908159190068490195453}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":3416872605534899},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-41931002718143143}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":41323254725816383},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-137144217446908491}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":80381212632837095},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-3086116062045353}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1992729914061615},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-15442346414653355}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1479790630897443},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-514017787160227}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-17553028277591925},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-109365653991395267}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":77277830544802937},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2655605656125153}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1598829740709649},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-4760520856378071}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":77083076230005},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-617764666132161}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10045467559879611},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3518743599175779}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":198607505615608231},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":1871270932706055}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":18153920591389881},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2186699556285771}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-9937855804628347},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-52223823144932035}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":50314209689631001},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":2767799866319667}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-1813898586686463},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-2138207228767311}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":366077141461433},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1610726080966633}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1972911225886563},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-10012429219100173}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":28316151703849439},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":9184224767283445}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1371966447849903},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-3248345802785021}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":472339606897671},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-377809469421755}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5234844194908821},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-9023898533451}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":21366816435527305},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4076802817115379}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":170141183460469231731687303715884105728,"numerator":16159018159418539003},{"denominator":10633823966279326983230456482242756608,"numerator":4681103757011892125},{"denominator":21267647932558653966460912964485513216,"numerator":7985608180848652979},{"denominator":85070591730234615865843651857942052864,"numerator":9421501719953854223},{"denominator":340282366920938463463374607431768211456,"numerator":23518815620884778877},{"denominator":340282366920938463463374607431768211456,"numerator":49326588585221195703},{"denominator":170141183460469231731687303715884105728,"numerator":31859451928960208941},{"denominator":340282366920938463463374607431768211456,"numerator":20497229203694488165},{"denominator":170141183460469231731687303715884105728,"numerator":4009896603894699593},{"denominator":85070591730234615865843651857942052864,"numerator":3919768228361795913},{"denominator":340282366920938463463374607431768211456,"numerator":71087915222094198193},{"denominator":21267647932558653966460912964485513216,"numerator":3649535028149011821},{"denominator":340282366920938463463374607431768211456,"numerator":124301760332063904059},{"denominator":340282366920938463463374607431768211456,"numerator":122004123786604476277},{"denominator":340282366920938463463374607431768211456,"numerator":51725298314730934421},{"denominator":340282366920938463463374607431768211456,"numerator":19393788504134259077},{"denominator":340282366920938463463374607431768211456,"numerator":52724694897907495483},{"denominator":85070591730234615865843651857942052864,"numerator":18154080885002453289},{"denominator":340282366920938463463374607431768211456,"numerator":23637543342751382735},{"denominator":340282366920938463463374607431768211456,"numerator":6779307400765359541},{"denominator":340282366920938463463374607431768211456,"numerator":18683972689250149619},{"denominator":85070591730234615865843651857942052864,"numerator":15076068881619665837},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":32,"numerator":87},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-903995384973657943095674794466989863},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1097816280000997231610737221811401179}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-408092524338264964465200850601751067505},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-204635756468829816307050733959581121943}},{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":-1242596950364071013819729069682146101},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-161230417041576029345974722747147469759}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":31652354142429920127537806439497574743},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":61551667501808038548743889808094313795}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":4583349286681642476756475555665902549},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":4248285393067065260746082387397902651}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":159828002705180276947287028645943855799},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":156385821653015077429716931939077014215}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-78547396564807962424307351564387224379},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-80305925846695719285111938064024015387}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":39780302918315128712120734285342823879},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":9716437356370823059937885709918334711}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":15785371457459986750049294337728283},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-12561017045531586583555929261832941}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-1217704607897072474588425640921644049},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-39882953549355984922662014720769626859}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":808929895645442214932649498121283189569},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":402726649813554400505613499097868762889}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-428492310462889918525662317775801273},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-898673430801410448329911722642845561}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-379430717735129990448052255053941873703},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-386078385303847184870392019386106308711}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":329263695912456184597014855130389773083},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":325171036874370849779344110729169754237}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":54703210159659037045218843629572127597},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":26049645365227251972486268712908752351}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-4400057244045071165286133595058183271},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2305777512401665870181894964542508695}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-46477333505551973785419844261211243357},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-5837583914893150643669233198305907105}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":186569966163700456199400541263269028801},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":185625037394615950291634880155779185967}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":2779348828903409736266682870785854619},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":21115118129580446866959246555587931831}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":21976026548912446129130442051050519},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":2562992311957406349064566958020499}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-42222239888207151508894995457705432561},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-44456115232957608423152337746547985107}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":98145737553585349527236399108829378011},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":771527555478985538545347641146577084995}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1101674304800224747947053791182064325},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1101674304800224814400219967380397009}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-25466012306351895332302297607496483447},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-12733006153175947670927157020893168435}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-162479383812787567040641827036012823339},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-81239691906393783649774578042813683029}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":64448278211770510203626406005149952283},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":32224139105885255062661669202003051509}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":4815317206983834783935161878666175007},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":9630634413967669518579793948491880339}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":162084016911302948713696529680024982229},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":40521004227825737153382389618498607697}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-40730820750866731236102230846484639241},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-81461641501733462537011768475942328023}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":40359701347658938711527774164970058297},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":20179850673829469334360049159589685149}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-4763229306661178708531255233932611},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4763229306661195597006476621384463}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-20231923413678807775608061510352233117},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-10115961706839403895991683571350210457}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":803365830814984308274599650213420153079},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":803365830814984308129155999130871080023}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-442499090547838870502997556942896509},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-884998181095677861268340988387327663}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-781354131697426472955357788382222714185},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-390677065848713236605392049137743902765}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":332020895253536661422963780363423556315},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":332020895253536661172231672040928639153}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":3531728273751785595566012057600256995},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":28253826190014284711080840073597816729}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-9497428883770841507204860554960501261},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-4748714441885420773891126521235628473}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-93634359393673790364446418724112331421},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-46817179696836895209343508878724707017}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":187080872778136790839400594221991482959},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":187080872778136790690005433140345443635}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":5753534162177351203081871500036104557},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":23014136648709404787831621844317434621}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":445377502082328279448406188976237},"lo":{"denominator":1329227995784915872903807060280344576,"numerator":55672187760290978846833081426017}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-23005528516113752337376538675331104797},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-11502764258056876178368505946582904443}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":198644469184136770691613123599916470393},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":794577876736547082642418643446947064571}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":24254104289569235},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-5046962233511861}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":108220607799877229},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-6094587297280991}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":12289810462146339},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-60632279418001051}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-561722425934829},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-203958612882341}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2821048702835421},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-251799336345631}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-3903796650604437},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-43535291162836189}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":28917998784816905},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-11157372396143541}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2538413938474981},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8492046840963559}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":288618866696067},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-148677149493841}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":4511030393162417},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2902656943196095}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":20584918773688709},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":5416617355792223}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":8503915442062593},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1019477879335253}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-5277903843406891},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-25836622603653501}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":3107896281909939},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":11415140875765891}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-1878594897330841},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-4242844369663683}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":732637029959187},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2955452874949529}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-2096151911907299},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-10381324902350501}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":28428983270807555},"lo":{"denominator":2658455991569831745807614120560689152,"numerator":83351116985817}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1853839391177467},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6588315695299533}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":447255143912877},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-359356867250929}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2760435479235025},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":287216568608179}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":5582793182276845},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1143387135555259}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":42535295865117307932921825928971026432,"numerator":4149283523377541785},{"denominator":340282366920938463463374607431768211456,"numerator":152729395946359468225},{"denominator":170141183460469231731687303715884105728,"numerator":64684226312232488815},{"denominator":340282366920938463463374607431768211456,"numerator":39146130569811559377},{"denominator":340282366920938463463374607431768211456,"numerator":24643602580732471495},{"denominator":340282366920938463463374607431768211456,"numerator":50041902210177741749},{"denominator":170141183460469231731687303715884105728,"numerator":32383615705896044547},{"denominator":170141183460469231731687303715884105728,"numerator":10700430553222049855},{"denominator":5316911983139663491615228241121378304,"numerator":131932056836375659},{"denominator":340282366920938463463374607431768211456,"numerator":16372245930426623427},{"denominator":170141183460469231731687303715884105728,"numerator":36322451241767786957},{"denominator":85070591730234615865843651857942052864,"numerator":15030412385982342369},{"denominator":340282366920938463463374607431768211456,"numerator":127697874131715705953},{"denominator":340282366920938463463374607431768211456,"numerator":125352606131867944959},{"denominator":170141183460469231731687303715884105728,"numerator":26721263944129786773},{"denominator":170141183460469231731687303715884105728,"numerator":10143242940143971945},{"denominator":170141183460469231731687303715884105728,"numerator":27116156930173319705},{"denominator":85070591730234615865843651857942052864,"numerator":18672175130168677043},{"denominator":340282366920938463463374607431768211456,"numerator":24493496917674922573},{"denominator":664613997892457936451903530140172288,"numerator":14020266716006851},{"denominator":170141183460469231731687303715884105728,"numerator":9678999999462038621},{"denominator":85070591730234615865843651857942052864,"numerator":15501297049106769295},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":177},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-990539652540174739855021305612627431},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1189233044817775239219122926226640683}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-203646342211733836257928955697237320003},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-816748687893458170097249356620547529099}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":-2511210158548648528106249256882669659},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-162774004968913052355950853409374170957}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":64658109957494662548360606595260361161},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":62919619546519674946723082223845741175}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":4856444167067309752076667547940411191},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":9017582181813140639946938232929375407}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":162468326889241173379960653195917517921},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":159098510551753713964590499880089281309}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-79933852573673070298864884001314244351},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-163314818613170389503623166250692477475}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":20234273874157697953705150607184367973},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":39579976088595249975613697473944119943}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":8025956899546191031743502685301697},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-6394851934165048434617395513527153}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-9920629692178681481502302234519036393},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-40572593849489558663040552569827860025}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":403118187781731927070452358999305730973},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":802931306504485175659383528995224075109}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-865142775745743265298691784819386145},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-904829678759767586031748004053033347}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-769472861434015965401520111217636688629},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-195676651406564414498313673795020819239}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":332452881897014157816530585179164721117},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":328420765308821133536462311764612474545}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":14198588917662464528314949759310366969},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":54155650508850368341768786499722993403}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-9126649022435772378060483038436664549},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-9551743780815434892285705234190998813}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-93294138737015690395003296901181179675},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-187392604358419271430084308111780029497}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":187207934582411621135072536082589904435},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":186347178451586528284421975692284727687}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":46275445932126863313513441201153246873},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":10999508306472380968236226214752608377}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":5609728618430809928993366968618967},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":6065786329601072419891511246647737}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-10996493599424418550119573506775879467},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-11564339510594646556957993354127003559}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":795971051237997876767198026035708723477},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":48900461163475301385827566489617193327}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1197148350005162852961992330170599483},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1197148350005162921280931800510607575}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-406723858022309321838662402927053028435},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-813447716044618643989049775462363653545}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-81969890005322480224866042868887195241},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-163939780010644960711908769900696803849}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":65790814848892215650332067482967656713},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":65790814848892215569025243450669098057}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5097175412101798753576049161449671579},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":5097175412101798727767554894379732263}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":82337460140958597640389298913700396657},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":164674920281917195179160986620833433807}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-165578292775248338061373286372905578041},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-165578292775248338193128960977984316901}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":41028928308738868225366747842958041125},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":41028928308738868180691271532744709165}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-2416830443985267761546636123861203},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2416830443985276646857601405237077}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-20567123683024092075290694690554533475},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-41134247366048184184765263628684779653}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":200240893001567790826127276132084548627},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":400481786003135581577919552201695986897}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-891682926655521465628150624114582929},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-222920731663880397357505322593950051}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-791867704493913469926587802110334359323},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-98983463061739183773615956311580269183}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":335173740512841440968053214176139013641},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":335173740512841440710511593791238627781}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":29311514939899031240017826439671223497},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":58623029879798062369621990481469246759}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-2456701117547349205001241812997759853},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-9826804470189396862436975568059591141}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-46950153511527803240236815585934116283},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-23475076755763901634061960993300251439}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":187664375728094256750757917332163709013},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":187664375728094256597143001371486940305}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":23930468436938146058584205834895042115},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":23930468436938146033207921027588479669}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":7480987023956052901006231592409077},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":1870246755989011326158813886478839}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-23919356353600803902648714229211451035},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-23919356353600803922701918642434053567}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":402668143272353109584150539816382650337},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":805336286544706219040797625059075396321}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":677271417648219},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-38747888037811103}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":128702155604640647},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-65043027878021171}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":24084740179574971},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-4350664750677579}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-352314073920131},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-685910257584939}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1342196686068863},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-253600582492213}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1931105342424589},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-67864316610314775}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":41580141969663219},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-15881192784555839}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1947694816030529},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-7562525593264379}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":270776271409479},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-572395692550995}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":4039763068103617},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1172975618966565}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":67513143344254833},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5664847919699297}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":3981159094811661},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1979029485760817}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-10808299641437077},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-6337108480462897}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":48751539608511403},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":11422312031821639}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-7536525081648835},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-16701535645932987}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":733552427080257},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2714432972406411}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-5875899556237147},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-2640332379100089}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":3525218561779839},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":11632959768465455}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2198258351182423},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-823332573997285}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":105811042054535},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-342401482929497}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2844546901360195},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1131000295647723}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":22885771022449279},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":148125268733187}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":170141183460469231731687303715884105728,"numerator":17064629724234363495},{"denominator":85070591730234615865843651857942052864,"numerator":38941403053096866857},{"denominator":340282366920938463463374607431768211456,"numerator":131006689075360577933},{"denominator":170141183460469231731687303715884105728,"numerator":20324138524081259973},{"denominator":340282366920938463463374607431768211456,"numerator":25806898469801378239},{"denominator":340282366920938463463374607431768211456,"numerator":50771011234293673187},{"denominator":340282366920938463463374607431768211456,"numerator":65841166038769981981},{"denominator":170141183460469231731687303715884105728,"numerator":11167465369859024527},{"denominator":340282366920938463463374607431768211456,"numerator":8884753991163690897},{"denominator":340282366920938463463374607431768211456,"numerator":17089070336338719299},{"denominator":340282366920938463463374607431768211456,"numerator":74264654495169005875},{"denominator":170141183460469231731687303715884105728,"numerator":30945991750099052453},{"denominator":170141183460469231731687303715884105728,"numerator":65577692028436741279},{"denominator":340282366920938463463374607431768211456,"numerator":128757856734677758867},{"denominator":340282366920938463463374607431768211456,"numerator":55202248693654458041},{"denominator":340282366920938463463374607431768211456,"numerator":21213913389120992401},{"denominator":340282366920938463463374607431768211456,"numerator":55766589421594491407},{"denominator":340282366920938463463374607431768211456,"numerator":76799173585975497725},{"denominator":340282366920938463463374607431768211456,"numerator":25374090606186164517},{"denominator":170141183460469231731687303715884105728,"numerator":3797994076610459951},{"denominator":170141183460469231731687303715884105728,"numerator":10025462683234533099},{"denominator":85070591730234615865843651857942052864,"numerator":15935219225602165071},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":16,"numerator":45},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1081318779179318195637214966914801819},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1284874035388383718735601010564171327}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-813140970931967447735201423733952759585},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-407554609283368836758787726213149905243}},{"hi":{"denominator":332306998946228968225951765070086144,"numerator":-158482204449904687011463527083574963},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-164221841917554074908770402558878118829}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":32999583207625129403557760764927602059},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":64275957300272760271790873367909174501}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10279288738193839130909441390338950649},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":2389640427818968223746902663765461033}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":82525488255446548172243171864533213451},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":161754354733570709976756582090206069491}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-162585662888390176347955982434553733273},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-165961864039157662312485389749378714631}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":41135044086590243952964234135422019581},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":40273552154444349192692971873038714205}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":2041861857530911729557842406852263},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-26003300891942377458447356444935603}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-5047198121706598841323847592733409877},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-20620101755350519468422100665607947821}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":803679007995847270080191607286900281385},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":800547236187217652024272038751122253883}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-436417308746935712181128762801372789},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-113813169118889745530647890550562035}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-780036535913113568237559363237457652385},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-793212493756242615415543612486085014833}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":335598332302987875109165150362818011371},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":331623402248042081845905729760827236067}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":58912614415159856645664751042068923303},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":28120217188062546531997336012825786429}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-9454762209465845550061466232414676293},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-617589309532237820093462953678104401}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-46799237684843530783338405928835877901},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-93957315609554349544372879422565884213}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":46945505056053121767744449468079581657},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":187002967506350602203230725703568094907}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":12027842530597574914092829323555833543},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":45796818094644199566695679710344678077}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":22899816222759712591027581057361583},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":7024710839293551482996005172912109}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-11445065698262720503282353718830427071},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-24044102592408554314683018714851732913}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":201680193643690414914550301162893400573},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":793228665865634351862887247513208198651}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-648397231378355504964145303996595549},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1296794462756711080234069841165515977}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-812138535536928531057680184617467823877},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-812138535536928531375676262308355524501}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-165305164038370824790706053966277357163},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-41326291009592706264058959429584703215}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":67120528244891296422347782704621914867},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":4195033015305706021121928336417978589}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10778448136146325044055917893196918887},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":1347306017018290623754161972238671511}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":167207588780539452809668493129432506645},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":83603794390269726353284813219754665539}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-42044178495295527254124189044658340279},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-168176713981182109150447502596317818977}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":41675655528297197926649841616867655429},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":10418913882074299470010969531019835149}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-609483978563261655704850085971275},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2437935914253055967016455263556473}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-41781847245570122744335692693972980381},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-41781847245570122780001552718426681699}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":399350193832759393624654268841107133843},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":199675096916379696774320574800709012655}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-448986632960668450466088126058754465},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-112246658240167128545022536310562609}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-802340006571232792803096826945996992381},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-401170003285616396536238964580996890551}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":84571297515659448467489965061744278291},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":338285190062637793605491249559738392551}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":60764602733700916890389235193049105379},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":30382301366850458388184392204777354293}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-1269607202737380697063560697341367975},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-10156857621899045620867311507778178095}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-188266339786220181367687168811157747335},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-47066584946555045370589498867251163409}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":188185772726412194430227419448887743303},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":23523221590801524284039245141824022945}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":49723016204497287649030296248916514121},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":24861508102248643798232975777194785635}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":15678670228035040548078063807086363},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":1959833778504378060215253323011719}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-49695314110202199734941634464014540839},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-24847657055101099888236289610901830911}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":816041504406480387657828583224519790587},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":204010376101620096881695648691425958713}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":4882088586050353},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-37047941179690027}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":144671714896552321},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-38772333907119917}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4408424780918741},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-38320150578640465}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":650543958624205},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-9207131471625441}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":637432335558737},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-16331446584923}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":17338125195485605},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-12879534311448267}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":14032262315999465},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-39147243726178901}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1429975807956479},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6730321462311717}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":509132273539221},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-137540656913757}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":7220521595172717},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":923545366666583}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":27344998049158673},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-19520229419814161}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":7454097333840985},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-991534709775905}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-21533647896020765},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-12347842162522239}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":2967734999400097},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":22310597691269075}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-1840330657162747},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-16328431752837311}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":91803752143149},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2498304799256371}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-7105313129939033},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-10578976703360205}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":27695955225162817},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":12176039805463539}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1216282012490379},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-3253738056185101}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":400495847335007},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-40813988218261}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5755091762121005},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1548109283778117}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":23084265487654619},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2990175333010933}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":35124601468824216719},{"denominator":21267647932558653966460912964485513216,"numerator":9931644801315125887},{"denominator":340282366920938463463374607431768211456,"numerator":132686047362482987547},{"denominator":170141183460469231731687303715884105728,"numerator":21096767911626001949},{"denominator":340282366920938463463374607431768211456,"numerator":27009774889827297157},{"denominator":170141183460469231731687303715884105728,"numerator":25757502606870474223},{"denominator":170141183460469231731687303715884105728,"numerator":33470883662331570007},{"denominator":340282366920938463463374607431768211456,"numerator":23300331573566979797},{"denominator":42535295865117307932921825928971026432,"numerator":1167958425933634281},{"denominator":170141183460469231731687303715884105728,"numerator":8915121648397965441},{"denominator":170141183460469231731687303715884105728,"numerator":37974334564440442053},{"denominator":42535295865117307932921825928971026432,"numerator":7963194548392484885},{"denominator":42535295865117307932921825928971026432,"numerator":16834577780952670033},{"denominator":340282366920938463463374607431768211456,"numerator":132221718762469794067},{"denominator":170141183460469231731687303715884105728,"numerator":28502870918592552617},{"denominator":340282366920938463463374607431768211456,"numerator":22177429382106843769},{"denominator":340282366920938463463374607431768211456,"numerator":57328387008785062461},{"denominator":42535295865117307932921825928971026432,"numerator":9868621149929741279},{"denominator":340282366920938463463374607431768211456,"numerator":26280134891219776703},{"denominator":340282366920938463463374607431768211456,"numerator":8032814514734955757},{"denominator":340282366920938463463374607431768211456,"numerator":20763368887655389047},{"denominator":340282366920938463463374607431768211456,"numerator":65512947184330656023},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":183},"tube":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-147038641879504939337248690297597067},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-692350642363636448669007700627875225}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-405926023744456266896101463956768737789},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-25425781642212756618396857044823341373}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-10234881844867222093965598188303911765},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-165574814445569622966274716062957355107}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":8415916464979043220353574734014663887},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":65620090752121089991935981603950045991}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10866083782370032084502482809328752427},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":5059856914425885692824922937735702071}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":20946918552033873708776423786361009783},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":20544081311151402251686089912755875059}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-165247851347776542887988693526639821145},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-21069033202811811827729327473784266819}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":20889468002629303001445390107442095275},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":40945594120236675089335770323726627283}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":1039834664448084646329558480273369},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-13195115184250088350945148608663535}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-20525420506605918434146743903684615769},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-41884904541575309691172501345744330099}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":801259261734227475857398604107600263455},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":199575591113666087582125902628500707385}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-880138156289261207171718386581649923},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-457890294870666541695437741897972473}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-197638876518120445619314793097537251411},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-803677490286798656970545467392979286881}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":338702726227805454558352079241422759657},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":334781630988956550282973761830215584733}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":61056936134195204571611762542662004037},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":58352595851531713236067571119223023111}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-9784034186728266462616768336899183727},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-5105868510669785018249377644397242511}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-187737269546054309809386247650235213985},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-188370714546623341324996392386224469901}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":94147118592132135819756879411869266725},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":93797195560926571907328680705117089669}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":49976603105441285398820854738140640759},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":23812931424073424181407642423033649837}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":11678608776027110731167450829883061},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":4000370273564553874066358215827627}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-47604359743538179827683465425434902625},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-24973944690086229801911546778145820759}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":204354401171311704626202342183633370719},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":200998479465605982552865746657144367355}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-350141139606159588353167354286598457},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1400564558424638425828855996678921311}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-202746228094351614199379042800756260065},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-810984912377406457121993724975917997855}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-83288267006506231639519788030615630015},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-83288267006506231774001501279864955243}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":68436903097706610052773657280620526299},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":2138653221803331561412440351524256301}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5691547993055979560005588031531055177},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":2845773996527989765875387478158759537}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":169681483918323623841613357301138799265},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":84840741959161811868503194746223516769}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-170717884212021002228183522814276671175},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-85358942106010501182192474274420273015}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":42299046898331861535079312103451137353},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":42299046898331861486478372943175724263}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-305404007311437755210460601338925},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-305404007311438982894404695607597}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-42405787896635465796475180704682365761},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-42405787896635465833673062260348936179}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":49786089240906218581137065795780106865},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":796577427854499497142691684094686141015}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-903953926972276045928500151320066763},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-451976963486138088536524143948686471}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-25399190353497549565646188630659675325},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-812774091311921586377232644933885555259}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":341357912264108038029527402586700781437},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":341357912264108037758010748728980971813}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":62931317846606588076919638418846294047},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":15732829461651646989800549657976130783}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-5243577195427616565640815718565555983},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-10487154390855233177642226917535259203}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-188667862311943304601371538424434916311},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-47166965577985826179805315564782438179}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":188647091733608493652886633720508485073},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":188647091733608493490593525882304088577}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":6451718050157576125661129897272656113},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":12903436100315152237715087128100005279}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":16400286376486221757750221110419709},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":16400286376486204777972529935949165}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-3223754894960015089475326029607735735},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-25790039159680120737300450521374919203}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":826696081637706763730243131511976188897},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":413348040818853381797789525751775317105}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":17511076312808281},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-8753886916202291}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":156060596638649247},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-18284839353671821}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-10034765078692291},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-163331143631481055}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":450643432596919},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-7698334839305387}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2403367723848573},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-542768548912801}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":11943243376496537},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-9212289372378043}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":16988283397071411},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-22235841999135211}},{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":-7796581766951},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5975848710187685}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":474162272111465},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-129675736047503}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3186962017880375},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":731300500410783}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":85840296869787235},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-28995221306665959}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":13874891565548267},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1911908159238935}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-10474830040011321},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-47704021172788139}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":22930499897169073},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":10640885841902291}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-3503443262195905},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-15826608281759267}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":361733390298801},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2292985728602323}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-2012513608474115},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-20650184415137731}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":26854445623544577},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":12385298222988477}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1288454037659229},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-3174561560825317}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":374431149418703},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-306329508902353}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2821648700912739},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":471055050587781}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":2825170134815967},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":2246307821333877}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":170141183460469231731687303715884105728,"numerator":18090914988888727509},{"denominator":340282366920938463463374607431768211456,"numerator":162151604168450318263},{"denominator":340282366920938463463374607431768211456,"numerator":134405065059972930845},{"denominator":340282366920938463463374607431768211456,"numerator":43783032561637315801},{"denominator":340282366920938463463374607431768211456,"numerator":28253340007077155415},{"denominator":340282366920938463463374607431768211456,"numerator":52273116082224630239},{"denominator":170141183460469231731687303715884105728,"numerator":34034991441792133255},{"denominator":340282366920938463463374607431768211456,"numerator":24297980637015697565},{"denominator":340282366920938463463374607431768211456,"numerator":9820975120145998637},{"denominator":5316911983139663491615228241121378304,"numerator":290570079942434619},{"denominator":340282366920938463463374607431768211456,"numerator":77693266559809557815},{"denominator":10633823966279326983230456482242756608,"numerator":2048886895888320609},{"denominator":21267647932558653966460912964485513216,"numerator":8641495449740099355},{"denominator":340282366920938463463374607431768211456,"numerator":135746037314804638029},{"denominator":166153499473114484112975882535043072,"numerator":28737456070601661},{"denominator":170141183460469231731687303715884105728,"numerator":11589213890278587427},{"denominator":170141183460469231731687303715884105728,"numerator":29459280926178398783},{"denominator":340282366920938463463374607431768211456,"numerator":81139319345401920197},{"denominator":340282366920938463463374607431768211456,"numerator":27212459225367447805},{"denominator":340282366920938463463374607431768211456,"numerator":8489548465258074743},{"denominator":340282366920938463463374607431768211456,"numerator":21495962745913296145},{"denominator":340282366920938463463374607431768211456,"numerator":67322985631494847351},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":32,"numerator":93},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1275475469038674961401336187201306379},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1488665406219035446670878196096898011}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-810718639515736974316318155483250763221},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-203074075440376342762234568605536881593}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-82567650212205388968634279443794902709},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-83416968282005623235821753737721033657}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":68642094837296328705038740014806983365},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":66951465290179626074941087957005148369}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":11473440983766614252643686780798299273},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":10701226708632959516409918755474685117}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":170040913799423161911856377637848677569},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":166892774889552373905982209395357930851}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-83926764999045265486670210322498475871},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-171085369829006311404903773782337789929}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":5299923765009783629982617288872955091},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":2599702535853428540004012782852684095}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":8481240035806607853523074077957803},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-26736587002853939788910520033041001}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-41701403487013641241939147471221999931},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-21252920536289228132952298749854274439}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":399489225211650161629348180228416670805},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":398098911422742481582409067454832928961}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-110892140775874525248492004785411239},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-920741110757529519095476441969540559}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-801032823855209101624803057760379482395},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-407052325507723006703870373708765663351}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":170884366634898585278301293018630913109},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":84474532426571687930508608537808301215}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":63226268426425540294568480928528442313},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":60491084323398180829902151218666154221}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-10114038112934377453115687540377655919},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-1317779150322632335880458215610909897}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-188211174752447657069847197784711235711},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-188762825090172900048246905850153096397}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":188746617316536856812685019969856121617},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":47030864165210696830845960810473401623}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":51870376374134028858438557201436049973},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":49484420630093205234024550682604045241}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":5952373067382898165549128395645051},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":8991737175675862343763246383169579}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-49457501656608788914939322851977752925},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-12958906548135724278740609193330594127}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":828064097546674188945451258926603708401},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":814705660724236631813597187392379042729}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-754199675309086515371121362862251191},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1508399350618173105394812301766371979}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-809986762109553560394912651970347129207},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-809986762109553560726049182753276168077}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-167755010524790166464524694507359524049},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-83877505262395083368481636168405269631}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":17434864661968741429291071963188450011},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":34869729323937482813159837548670812791}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":3002111848732691958873291319735553209},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":1501055924366345972051616850159240701}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":21512017180017340030426315736306266205},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":172096137440138720137266475337005289693}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-10825075394140029399396694677345658169},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-86600603153120235264425339697408597575}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":42898289180217257083390650461547982983},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":42898289180217257032728466225437609547}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-2430953858428549043827591900063703},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2430953858428559361557436812795139}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-43005233208501471481642122574859383043},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-43005233208501471520423534540510533083}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":794595705525988035405629569927209327909},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":198648926381497008811632836552791073867}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-227428769613985892465597052729111199},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-113714384806992963102191086759884613}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-823173010033728640855733699666656122717},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-823173010033728641139597293742305726713}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":344394563284704879499614370505078449941},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":172197281642352439610463289680026001407}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":65122121395867041944783536712117324111},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":65122121395867041823276874974758086151}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-10817255107122188762134084647799517591},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-5408627553561094405287095306459311975}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-11812948009577581237908676312351436285},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-94503584076620649963812765392015273381}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":189050376641672998123866351455541541921},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":94525188320836498978555275764803527519}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":26766168774562319582594610089528326671},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":26766168774562319554421012962129564845}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":17124822843762959005785482473659269},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":4281205710940735267839661476300409}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-53492206042738539393281838284618008029},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-13373051510684634859445936023492860379}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":104662823629118716829013901471810654969},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":209325647258237433623437608186703824151}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":3888812273814687},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-8169764114495511}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":160209785625206949},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-440828785812747}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-11483436392478821},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-83159667520893971}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2602857651269873},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6234757078475985}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":557274918297539},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-545085297079111}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":28851673785637083},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-12273540309318929}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":7691924719763137},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-47210574875354067}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-683321759615553},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1314388177514889}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":217761764607791},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-486037627966159}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1403993844193577},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":572769709904101}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":65684828367840325},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-36367500450275301}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":6320586393512093},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-916745674850503}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-20202515943954929},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-44943624477921893}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":21551263890453515},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":10081024531463605}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-6632064101741611},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-14907534615969077}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":350362854788255},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2068932054156793}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-8701552850930841},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-19915336917416595}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":6376576198623251},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":3098975857297081}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-666617458707379},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6065430865648611}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":345828814726099},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-284300522822493}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1368365442403781},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1063096149973455}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":21921830898523717},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":5671100743198617}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":37302167635244314401},{"denominator":170141183460469231731687303715884105728,"numerator":82743970042129504793},{"denominator":42535295865117307932921825928971026432,"numerator":17018451585449636557},{"denominator":340282366920938463463374607431768211456,"numerator":45417887570341214301},{"denominator":85070591730234615865843651857942052864,"numerator":7384682036587252245},{"denominator":170141183460469231731687303715884105728,"numerator":26522662949760141251},{"denominator":85070591730234615865843651857942052864,"numerator":17306082757211443405},{"denominator":85070591730234615865843651857942052864,"numerator":6332201250644991179},{"denominator":340282366920938463463374607431768211456,"numerator":10317269064334140565},{"denominator":170141183460469231731687303715884105728,"numerator":9694235382423545983},{"denominator":170141183460469231731687303715884105728,"numerator":39749042846806729203},{"denominator":340282366920938463463374607431768211456,"numerator":67470332909512953457},{"denominator":340282366920938463463374607431768211456,"numerator":141919426483557818515},{"denominator":340282366920938463463374607431768211456,"numerator":139332425333154233653},{"denominator":170141183460469231731687303715884105728,"numerator":30374596566711252623},{"denominator":10633823966279326983230456482242756608,"numerator":756822430963215571},{"denominator":340282366920938463463374607431768211456,"numerator":60537748001170540223},{"denominator":340282366920938463463374607431768211456,"numerator":83371344762284591101},{"denominator":170141183460469231731687303715884105728,"numerator":14085948823441676139},{"denominator":42535295865117307932921825928971026432,"numerator":1120862294201931815},{"denominator":85070591730234615865843651857942052864,"numerator":5562319817485470659},{"denominator":340282366920938463463374607431768211456,"numerator":69172264148757309023},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":189},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1378771085166870828596505781919402613},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1596705817744546076758139935166059205}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-101217580566336129025354969671179910909},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-811123164360375059890788610509862660759}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-41604583226179942831869175888900283223},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-168000343987646690843105426412879148713}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":34971489613741239919494247241122852145},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":17067390326377322772583122661291473791}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":6050755619812772125782909703102068875},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":2825818017263723510651379931142305227}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":172447213450036128102542984392928191637},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":169374180637022234363057878703613209799}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-170402028256592029586976422472307982687},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-173560587810881755999047423692971612011}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":42995595959034092909881397097809695941},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":42221652558253835772766925570547143459}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":17313600305414346741477438376693783},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-13519319878356335744227306102507255}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-42328411025435683494181634077731355847},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-21551089868716753258558549074109099717}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":796837741297715730539521890100216117407},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":49639662929097087382889594913868456081}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-446960382951771658608909145660327825},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-925478013462643889655034418486274085}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-405735771330924807270162266354679370527},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-824497029162569330143859565227844178959}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":344799010320321285098687633684476958489},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":340975568035639899164602205711812167121}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":65419558322123234283319762025015944929},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":31327423341330146961594567894167001713}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-10444340760851934944082397701462947905},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-10872477060884916816074732859121332957}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-94310314981527895992756205763408746683},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-189092953451930918144103678303968467261}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":94570604019934911475868250272230766641},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":94296094960900839553011042004419783163}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":53791904546908767713979532737242483117},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":51371726607299702421624883354192719165}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":24255049969519106204862553248380801},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":9995291821915882126908061277493485}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-51338907580416178439526927583527436459},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-53750614969856808360309814286467533915}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":209665707040274407513336297264816077987},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":825366443135107778433605035975246530511}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-405057151055041673250721978297328971},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1620228604220166770020852272520650585}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-809143863181275609943278952018977489817},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-809143863181275610281245168418423024867}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-168841831403322972717455912814850318243},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-168841831403322972993404883636820922737}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":17756937064356629528497480526744372407},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":71027748257426518019783588422705455307}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":790914915797785874858305044332274357},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":1581829831595571741999511237565404769}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":174451146847542765631624404660700651911},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":87225573423771382761955727038162337917}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-175626144500168442003653535016866010015},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-87813072250084221072254837766860665885}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":10868148093680907273693425919679503025},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":43472592374723629041982087166155165819}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-4798545325038255148914945926267987},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-149954541407446150502860095557931}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-43579369912952807050714186243958014241},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-21789684956476403545566087028847018015}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":792756104352460581986687011725493834313},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":396378052176230290911932937936060968197}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-457676059597644048652136308674307871},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-915352119195288236167958930251273215}},{"hi":{"denominator":20769187434139310514121985316880384,"numerator":-50875232484967028173009847495719637},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-833539809033699789877905146420199505695}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":347397784004227761393093949904604669263},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":347397784004227761107109331632984948991}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":33667980180903841142499529039540782567},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":67335960361807682159608645082330252847}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-11146714966467247831710678330735277183},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11146714966467247882310954566695094139}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-189286261961885509731734220179579275463},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-47321565490471377464029433385008788937}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":189397685176820176106167690116075417321},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":189397685176820175934863975299301818293}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":27738997760629971768088294700951685339},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":13869498880314985869463762692951728405}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":17850161482415916871045674109466923},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":17850161482415897939273021793299459}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-55430882464331471107595465071888073415},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-55430882464331471153646415808654165559}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":847863614288961533680468200522491367251},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":847863614288961533538328881149727440397}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":6959960348754383},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-30471424597185209}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":20175819388301975},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":13669555123543807}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-33030835832441971},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-166689951703557855}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":811211441900605},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2484471505505487}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":514927848026741},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-555450675177381}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":16299159573692393},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-14485239808259771}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":285075434311151},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-48552723024948979}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-443825213387047},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4622263841419565}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":398568469532477},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-455396546622577}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2478133945503059},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":110401008528923}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":3051416326625677},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-42153653109028351}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":11465147271095059},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1806183992296983}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-19201504754211547},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-42008583259165497}},{"hi":{"denominator":332306998946228968225951765070086144,"numerator":39237245701933},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":9415625191386861}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-6182321419777987},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13926558121612311}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1358128815033511},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-932309686518773}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-2272195514425739},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-9537603830951245}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":12012895986674101},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":3049368136157567}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-337467175589459},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5739550550995835}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":318286173447317},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-263460881361113}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5272175375983841},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2284850904920457}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":21144432843141189},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":3262979280864975}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":170141183460469231731687303715884105728,"numerator":19243393253509160181},{"denominator":42535295865117307932921825928971026432,"numerator":21113654962466416441},{"denominator":21267647932558653966460912964485513216,"numerator":8619228490815609019},{"denominator":340282366920938463463374607431768211456,"numerator":47099059947746710463},{"denominator":340282366920938463463374607431768211456,"numerator":30867087823362933607},{"denominator":340282366920938463463374607431768211456,"numerator":53832933512710165759},{"denominator":85070591730234615865843651857942052864,"numerator":17600912839799507703},{"denominator":340282366920938463463374607431768211456,"numerator":26393719036967406881},{"denominator":340282366920938463463374607431768211456,"numerator":10833161306057715375},{"denominator":340282366920938463463374607431768211456,"numerator":20206957376956623527},{"denominator":340282366920938463463374607431768211456,"numerator":81365079769518429367},{"denominator":340282366920938463463374607431768211456,"numerator":69425207490819632715},{"denominator":10633823966279326983230456482242756608,"numerator":4551390593309750299},{"denominator":85070591730234615865843651857942052864,"numerator":35745408822800464325},{"denominator":340282366920938463463374607431768211456,"numerator":62691334380024738981},{"denominator":85070591730234615865843651857942052864,"numerator":6324631685971468237},{"denominator":340282366920938463463374607431768211456,"numerator":62186763467425840375},{"denominator":170141183460469231731687303715884105728,"numerator":42822971624336220273},{"denominator":340282366920938463463374607431768211456,"numerator":29159249408475088447},{"denominator":85070591730234615865843651857942052864,"numerator":2366398863157669879},{"denominator":340282366920938463463374607431768211456,"numerator":23023981706147514379},{"denominator":340282366920938463463374607431768211456,"numerator":71062350449241257807},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":1,"numerator":3},"tube":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-743069028108268616776499440517547593},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-427187750058223801361358782226477897}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-808917823938044830901412432702913623789},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-101263191627187371893876102736512101563}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-20951039114860813338765974955880966329},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-169075288977923104254096746051142409243}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":17807385605440701083321459503860873913},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":34786946892054825107217272819941639145}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12750428715410737515180263613838327003},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":11926005025988548916549898022208630391}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":87396926659260567001484250094438381773},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":21474548903928695380134670152529901081}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-86446370636834127916921389835314502803},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-175977391599390401398886129140621001027}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":43566766333048012524247423663673584289},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":21412006970506919877946513132871069757}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":8847090768651017715985147202963313},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-27292540151316000715215614341871541}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-5366378083709352466996727506983403687},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-10918277514485334298164210761691377353}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":794838163500024143361055031601783282281},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":198103395939915765951700104263766748529}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-900583603259585453944713809715798193},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-29065236430409508771259478097901453}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-821874714210062203127591434182520548409},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-834857672446726580409014086824853035937}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":173898099248905327920882761984536710275},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":172008301908291007575972237079579075113}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":16908938452764926238221662876853238399},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":64842828905290079253320232893460516929}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-10774503108147445801122585743229948593},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11202023097894875411237572589902383017}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-23620952410102565618902434607701336921},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-189363108005028273504412916022710291733}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":94740035131355750024046114606920044635},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":189002632906002053280334809320356356173}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":55740386301548726398179961394698808721},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":26643499399427648038346683091603846257}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":6173150335802552204918221344095465},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":11008457488221097351161677509287639}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-26623890034420809803629173341568551065},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-55692039807810817467493260498922905563}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":849216388004799621198292263758100213791},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":417989416795816540207734003417279416483}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1735971420914096410435506609833163037},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1735971420914096489950808807256245209}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-404227931849130561486938009607113067031},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-808455863698261123318842159129367485425}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-169838347058720626615326679570419566167},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-169838347058720626894815057381656211659}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":9037669872126349269928450040936180715},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":36150679488505397030882274946177561929}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":832611826991146636791178901943170447},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":13321789231858346124177121957450625961}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":176746171239279780510697263473245953263},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":176746171239279780401380648955220915799}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-11124513806093059485983874461275063371},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-177992220897488951919004396678190724819}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":44021190093906962071761656784084642881},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":22010595046953481008385207477775114073}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-4692597400426353984501384323561173},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4692597400426376723867387644333067}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-44127407971626562303826212553990084591},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-44127407971626562345935405217387966993}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":791059386109640404504130790987723159723},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":12360302907963131317772755592977890343}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-920965473810142578085366764119361417},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-920965473810142720959540751813786585}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-105484690847484550021325733490020780117},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-421938763389938200234754448854114359563}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":87592549262716503957141891314340348063},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":350370197050866015535157856640338325951}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":34785892007856948603139341227212516467},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":69571784015713897076907663637257793911}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-11475084614269307931607268951959488231},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-1434385576783663498056421296221538919}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-94753582263137612950971039026368790651},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-47376791131568806507421008927797122933}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":189691086912266866091760726483149798027},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":189691086912266865915821591583449388063}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":28724951386162670378045693776779250649},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":3590618923270333793483618906565719251}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":290219759446504235684301081682047},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":580439518893007847201970656301095}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-28697639031783618124539202752220030417},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-28697639031783618148361310982194926369}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":429190879787934534445433148150527491737},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":429190879787934534372431628686883690883}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":6277128124295083},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-14201243379447297}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":160635949622404751},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":24535310959975797}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-40677651751273689},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-10329676239382809}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1875277178063549},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-60772140727013}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1898575904887887},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-574576809528659}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":35321834391606151},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-3247792723340793}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-2688412241706969},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-48993207658029769}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-257108981360955},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4084611947889035}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":183247569306085},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-107073771398437}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4392198923010775},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":668735885334289}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":8754472016023181},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-46576837173100549}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10380093842040597},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1820902412193345}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-9001696615779585},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-2441714475813451}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":9307340021391165},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":4335706082031419}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-2837730316755539},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12926412276343987}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":329057034759631},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-420470314999667}},{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":-72260386582561},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-18184761282569549}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":22530947688444667},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":1478050408809439}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1341431515723489},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5410457024383271}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":293547867249483},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-61296588220465}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5052100031898395},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1186021165157821}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":10152285790817995},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":7097146046153941}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":39737172727207798705},{"denominator":85070591730234615865843651857942052864,"numerator":43103754909559865301},{"denominator":170141183460469231731687303715884105728,"numerator":69840945160789448559},{"denominator":340282366920938463463374607431768211456,"numerator":48827705231885832965},{"denominator":170141183460469231731687303715884105728,"numerator":16119816830231421161},{"denominator":170141183460469231731687303715884105728,"numerator":27318699274546687431},{"denominator":340282366920938463463374607431768211456,"numerator":71609394457307547525},{"denominator":170141183460469231731687303715884105728,"numerator":13746853581391971663},{"denominator":340282366920938463463374607431768211456,"numerator":11369285606548282987},{"denominator":340282366920938463463374607431768211456,"numerator":21052734600180102957},{"denominator":42535295865117307932921825928971026432,"numerator":10412052394493811531},{"denominator":85070591730234615865843651857942052864,"numerator":17857746623930023903},{"denominator":340282366920938463463374607431768211456,"numerator":149440982874840511071},{"denominator":170141183460469231731687303715884105728,"numerator":73347455520316406829},{"denominator":21267647932558653966460912964485513216,"numerator":4042617745797637691},{"denominator":85070591730234615865843651857942052864,"numerator":6605137913551723241},{"denominator":340282366920938463463374607431768211456,"numerator":63866511113325454343},{"denominator":85070591730234615865843651857942052864,"numerator":21991053544410305101},{"denominator":170141183460469231731687303715884105728,"numerator":15087689363628514247},{"denominator":42535295865117307932921825928971026432,"numerator":1248299592125367789},{"denominator":340282366920938463463374607431768211456,"numerator":23820768201124104575},{"denominator":340282366920938463463374607431768211456,"numerator":72994915750876059829},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":195},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1597507472649845138118004665998563923},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1824718788353060686966834938882827981}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-202062452422668944721157914944144828699},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-101155400307251115610108611480648252631}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-168706464252793366637089633222248549889},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-170060135758089427440752426949242977875}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":36250687794483264336537187486737639367},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":35432005943627702862486750391919778821}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":13420310760813219829824578619129463457},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":3142390993523125542503786616307768403}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":177080500398491186856908161230233305815},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":174158996452992940931356264148221132997}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-175325126042794092540646360925105282465},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-178335310616537587170718099643689302413}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":2757008606781000777041104729034111663},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":5425191472760281638710599913860869667}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":18107821728230189683275648238048557},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-1718395437492110619459901604141879}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-43508428255268574040502567447441681971},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-44217844832110904142618753213581749117}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":396490307982649021403065332174425046951},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":790735499836923434611694140314310753569}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-226806311512984780955937629432826893},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-467335503338120610308502590376670709}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":-13003834149360269019339820316576531555},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-422594810152741470363098454575799947423}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":87690730052448307924735581990161385353},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":86755969995346788315893082949171685915}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":8734225666037729666776510196773203357},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":33526988793876388014548575947227424781}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-5552040462698055466542946946114243123},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11530421336107479919333736078273140059}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-47313536296934294136294184484784497633},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-47393828232305127102687889536131896071}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":189765276416598511998937817494218916847},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":189356841705733694149966881477752890059}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":57715004445075716317699135303047185171},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":27614719487084651025602853900888816415}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":25119551960298008039188418700541113},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":12029353215149784480792761287021667}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-55183306110877208026930127531766937885},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-28829534822709919416791750366977518813}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":859727382624437450935701011383384887745},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":846545417807241987160843088657207362297}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1855536555015245579144150762326361645},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-231942069376905707661444306723962465}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-201980571871456316427784686668178239219},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-403961143742912633031637117431704605477}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-85373008187709412716402923420994209309},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-170746016375418825715856093781330055151}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":4597494443806248963104333250234250733},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":36779955550449991654226102283096491811}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":14010001726897196545287953123281285749},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":7005000863448598238985183564523442043}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":178980927467673108051182182575823156821},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":5593153983364784623132010792627970685}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-180299012254671030168554289286915829235},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-180299012254671030314279910587383030343}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":44543339934331525074214596473726404645},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":5567917491791440627118933851425339677}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-1135041856438363601982166280506455},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2270083712876739130632060975874419}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-44648580966315144076614159505985293455},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-22324290483157572060235405874103781185}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":789506197607380973742911495060482886317},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":789506197607380973572249401231330601341}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-926660396199421512762496112941811301},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-926660396199421659753146243991586971}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-854189191235645189272576095628838313017},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-854189191235645189579217128066482286745}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":353314403953672564363963691092321887013},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":5520537561776133813484345953108438193}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":71828545369135656511851632615253356373},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":35914272684567828189200410557897187273}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-11801910725003875266123752112390833365},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11801910725003875321298403108660250291}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-189671910896395671235850240794860151355},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-189671910896395671367014168749838975889}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":5935395668163635291857859687431129541},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":94966330690618164579393557340783642009}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":59447229112184207031375558271970492573},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":59447229112184206968930703220574599881}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":19294173983851027608978739605542057},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":9647086991925503274154819831327781}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-29692274705361062774464952874595790535},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-59384549410722125598213053103682332677}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":434429819623627825931561150817350564081},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":217214909811813912928291738280371365197}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":11417871532527735},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-26469907977149203}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":158374422132291051},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":32730498508479621}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-5794829428036273},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-81274417018444399}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4136354137896473},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1488633072851301}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":54566695050695},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-600354643194829}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":18574681351715055},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-13435016346167}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-9572922090278521},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-48719057849851921}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-106380685333913},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1817404154255293}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":339299522946347},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-50503494411437}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3918546217878925},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":124630755843603}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":11874517705446175},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-24900272701131819}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":2344816993868155},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1868535704585155}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-16662012402053765},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-18079939771911023}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":34296595642233197},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":15742604807028515}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-2563151932477025},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11923310557272505}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":637803161053895},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-189906549809779}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-2308422140411697},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-17266114056772293}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":10523502652360245},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":2830120510742329}},{"hi":{"denominator":1329227995784915872903807060280344576,"numerator":-10264761172417},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5085781444531877}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":271983052992831},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-229248138690345}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1205068914803971},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":600853253108939}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":19424190797382875},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":232569324663917}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":42535295865117307932921825928971026432,"numerator":5131844744497228821},{"denominator":340282366920938463463374607431768211456,"numerator":176004922133536221323},{"denominator":340282366920938463463374607431768211456,"numerator":141467028370364518959},{"denominator":340282366920938463463374607431768211456,"numerator":50605006908635714515},{"denominator":42535295865117307932921825928971026432,"numerator":4207202469084349037},{"denominator":340282366920938463463374607431768211456,"numerator":55460236444381563059},{"denominator":340282366920938463463374607431768211456,"numerator":72843237582353813853},{"denominator":340282366920938463463374607431768211456,"numerator":28629798617350255277},{"denominator":340282366920938463463374607431768211456,"numerator":11926296064675742587},{"denominator":42535295865117307932921825928971026432,"numerator":2740827013689235275},{"denominator":340282366920938463463374607431768211456,"numerator":85294272124169564493},{"denominator":340282366920938463463374607431768211456,"numerator":73489701163684858947},{"denominator":340282366920938463463374607431768211456,"numerator":153310767285251102723},{"denominator":85070591730234615865843651857942052864,"numerator":37618374512818329747},{"denominator":340282366920938463463374607431768211456,"numerator":66722007246383331685},{"denominator":340282366920938463463374607431768211456,"numerator":27585928068774415451},{"denominator":170141183460469231731687303715884105728,"numerator":32788973882370924757},{"denominator":340282366920938463463374607431768211456,"numerator":90327334396483555059},{"denominator":340282366920938463463374607431768211456,"numerator":31221198524405749783},{"denominator":340282366920938463463374607431768211456,"numerator":10530083934375601659},{"denominator":340282366920938463463374607431768211456,"numerator":24640365245921985739},{"denominator":340282366920938463463374607431768211456,"numerator":74971683270403764921},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":32,"numerator":99},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1712799724219033873593572649672783067},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1944516691169659242012910052253327209}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-25241753445718867361447339266280706091},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-404267918151089304312339263165095306383}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-169714123789904532923122031008705191321},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-170956356478065469845168514426825684225}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":36879051544549709652800665629563324691},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":72139498520112057923560462829489037071}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":7055628926671675160438275980080408473},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":13234070496137790102321629490591354123}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":179306878924761603993042350021606796549},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":176461648163115133335640459703508789543}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-177698697830319372468287134987223693999},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-90316964251007582771417848359986818905}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":44630970580962175569435478845978085605},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":43953436706456382733140963167833437811}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":18558245065659622685940820765262811},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-27639931401510642072952375353688167}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-11014957199751811138689955364684766281},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-2795976282825026377838983138264125265}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":791265874861520855703413032955447488849},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":789200987342716343710590615477227453143}},{"hi":{"denominator":1329227995784915872903807060280344576,"numerator":-3570117892672889003617685150182591},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-939334354669589729158908645801290551}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":-13165415566930493389925337873589783077},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-855495901246799809109064061814924101451}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":176850888164678490712393304950650789079},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":350000021575478130436310217144784269533}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":4508291700105872842429365496655112061},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":4330452589968368092293102682132450629}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-11432625360499856130707647429366640935},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11857217898194374139703860456271858343}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-189482226545235792652320741763738125969},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-94865803177815062574267051227354711873}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":94999454294277191376211758546427117353},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":5926777640743452348631223599106306911}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":29857463752612162449746703193369932529},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":7149779169694848361915078006454888327}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":6383455053045312064461858003529029},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":13055344141423967757652467301046681}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-28572328931002245943409290190182307409},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-59650859877631935509416829422095819421}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":435099214685523966770163516785983433595},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":428534398132646819661572529887037983051}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-494705689382460797310315893123409741},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-989411378764921637079129974524168977}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-807542539474950183690748476950852260691},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-807542539474950184050222018649704320225}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-171566403134585814412600748110483107139},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-5361450097955806709350901519805561367}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":37401528854648275694422285798726619595},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":74803057709296551283973578083015003751}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":7359680911300976397850522774624573217},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":14719361822601952725454136759342785967}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":90577593303806243487224998849169682617},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":181155186607612486861810584371634790333}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-182546147077528687034607108100357234951},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-182546147077528687182856314736705043211}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":45038323850849381589729128619530995427},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":5629790481356172691264968762566498233}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-4337247366012161945097220099208841},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4337247366012186955526188881458437}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-45142146491636182264891556916235469203},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-22571073245818091155276802184508782969}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":788097077163026769192688309838356064055},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":788097077163026769017900328429490938859}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-466273391296847470408529629562281977},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-932546782593695092034297454568759589}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-216119454325535102768338598110600110449},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-432238908651070205693942003297982488539}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":356232982398389356280559309853060101819},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":356232982398389355971904705092042439691}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":74105202588155343158112863410062355271},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":74105202588155343020480711238520789029}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-1515842072073097224301058550335101837},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-3031684144146194463000885012375076083}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-189782548610388195541390717953149642785},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-189782548610388195676042107281839650693}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":190124496280539364450224225192737429111},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":190124496280539364264742306721875266133}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":1920910326950525339999516640837734085},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":61469130462416810815386993303635243211}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":20008009911273292336337055246389235},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":20008009911273270140942231552705805}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-61397839940630728970897504172574376323},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-61397839940630729021866745519420384307}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":13739060588753392653117997522440145309},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":879299877680217129645552095625732076061}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":2619711662550405},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-12342971114230727}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":155053822489937477},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":9584716493381701}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-50087088226646799},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-79477459411392299}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2218739986784293},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-138662630605877}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1603605716238449},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-157690063248693}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":38250468196784989},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":1152731143888985}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-6201543668960255},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-5985305992653125}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":7587790033421},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1632735440931527}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":316461583894553},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-95718789688291}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1762570090109379},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":351612840516977}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":3671760420945503},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-26015694951558069}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":4234476993446869},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1950305226688071}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-15195536703036497},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-8339567506956991}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":31467111267147137},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":7026647475673771}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-2272220989384349},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2737822409923931}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":309443655899661},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1375878790744601}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-2268310621703755},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-16343640907590071}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":4901375563636619},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":1337408751277711}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-634150992191679},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4770838316763243}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":126540635731599},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-54093972622813}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2292921366737203},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2390194539273539}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":4632082127881649},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":3800352168921377}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":42440915793838017957},{"denominator":170141183460469231731687303715884105728,"numerator":89839206685583912215},{"denominator":170141183460469231731687303715884105728,"numerator":71629808173174679701},{"denominator":170141183460469231731687303715884105728,"numerator":26216084358093743205},{"denominator":170141183460469231731687303715884105728,"numerator":17561168605984281811},{"denominator":340282366920938463463374607431768211456,"numerator":56302886891541672925},{"denominator":85070591730234615865843651857942052864,"numerator":18526715909468062971},{"denominator":340282366920938463463374607431768211456,"numerator":29803052730163556543},{"denominator":340282366920938463463374607431768211456,"numerator":12504864816019800939},{"denominator":85070591730234615865843651857942052864,"numerator":5707359240680299369},{"denominator":170141183460469231731687303715884105728,"numerator":43680315744319556761},{"denominator":10633823966279326983230456482242756608,"numerator":2362606545878603341},{"denominator":340282366920938463463374607431768211456,"numerator":157255725710119871907},{"denominator":340282366920938463463374607431768211456,"numerator":154318595472350931265},{"denominator":340282366920938463463374607431768211456,"numerator":68812872661940319607},{"denominator":340282366920938463463374607431768211456,"numerator":28796228996702573195},{"denominator":85070591730234615865843651857942052864,"numerator":16830514866283654107},{"denominator":170141183460469231731687303715884105728,"numerator":46368253059654459547},{"denominator":170141183460469231731687303715884105728,"numerator":16148826242206062745},{"denominator":340282366920938463463374607431768211456,"numerator":11097462683265864489},{"denominator":340282366920938463463374607431768211456,"numerator":25483522849325903557},{"denominator":21267647932558653966460912964485513216,"numerator":4812150568320735621},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":201},"tube":[{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":-28623825190020938126574549763096451},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1034021120350197715267282380348402559}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-807376115950379569147838859277738188659},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-403991486605992949526939082864187620913}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-21329092167354840110435235429954990935},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-171765527704639766376721515264101583305}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":2343730687945540645525052597960597471},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":36699984944152362912651131129342636755}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":1852919196142141052724582884935791455},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":6959814649990824242105944778442180759}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":45368191720841008337294711731276349883},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":44676014105371306834807350125467276781}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-45003256730450552058371182744430694273},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-22859110031311303448022538983828755371}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":22561274924712336187881788129833657455},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":44478983277098953088194569961704067077}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":9524648132615530000431670963081609},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-27725181959720866818761512424694017}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-44584456888902639669516540336406869937},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-5653212207878460467561591229145981195}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":789694600577903029628175718646611649215},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":49238160679542654423470842811521704737}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-920867579586650848254575047738379889},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-236047056427828572928598534623143551}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-213225343945557385942758728875700337983},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-432889765158192999393223357282073853615}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":178307671736500206440140088049265230789},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":88236908223992367437491700880329075733}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":18602824766158394434807609511800434877},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":71541572736302554004975307879079861155}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-5879841759386913472461600155438065961},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12181955581074310156928716126999890799}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-189653896705772347320655253846205536109},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-23729254826500698309075640141716054127}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":47545764185686485372270680114565981307},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":189904839674401927788754269350931739933}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":61739310203425792550182748804551763963},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":59192553435379586348791586800241219921}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":25933207403540780308014058715357669},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":7041834761833008630345151542755777}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-59130993473583783862740112163849409297},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-3854159552810450045289877863640491967}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":880632155262941819092768865896407324783},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":867551581912179410893211184791047114171}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2105719146478231968872510990210328033},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2105719146478232056699222576987354579}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-100914488803800704606547266494157797001},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-807315910430405637219356825905926227131}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-172301172939173829583239276854743163165},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-86150586469586914936726906816127888015}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":38015242098593941784091832036566761517},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":76030484197187883459556565951986768879}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":482810571504918936126494626556827427},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":7724969144078702941387730527228103521}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":91634385366695538716400560293235311463},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":22908596341673884664804598994117786895}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-92366651511487724250263328362512565733},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-184733303022975448651363084367568523117}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":22752724264971668521728676224872265729},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":45505448529943336981425189652933892195}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-4079723286710379285598517935303197},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4079723286710405497626775802463803}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-22803693274615993347392412032933802357},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-45607386549231986742311917091439341007}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":786832460614698565661498544659989632119},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":98354057576837320685305301090003314813}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-234684748938441546657149698474205743},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-469369497876883171093358720771155083}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-109343300545564023477358722416568117601},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-874746404364512188141442252578588751997}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":359128483574050408912449889230901377751},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":89782120893512602148992682643153162375}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":76400720376069872188757703225484340561},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":76400720376069872046840326768646699753}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-3112275654714617854441834189417152699},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-194517228419663616841811276426000633}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-189841136014276621314735283524659067471},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-189841136014276621452941695571866564267}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":47567171438817944530776910896770094805},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":190268685755271777932713483393431664539}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":15878687399482707523110516393090204561},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":63514749597930830025628581911482847685}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":10356485158369995056581528367159263},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":10356485158369983366996886002022997}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-31717140353517647861962295613456083947},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-15858570176758823944157162964013063445}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":444852553618216056384218677972255757485},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":27803284601138503519071796620969940027}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":9705866644085335},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-11532442357840085}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":151014079846610349},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":42324018142295509}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-52732752996167831},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-77400692782249623}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4651919396573891},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1594731781559521}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":735983322862899},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-664627753921301}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":38892492137169993},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":8143439408371439}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-1781810552219151},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-23307078377803753}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":42594197653331},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2974001134636321}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":74495148500875},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-364810507709939}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3204456759904171},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":115935075753493}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":7621013200575791},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-53651640839340251}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3820638106984165},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-515741772320589}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-6830388090433753},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-478621077697713}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":28694350842815291},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":12316939623398259}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1971823156549457},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-9992197331661525}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1203007290134057},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-624478674977983}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-8779993574811535},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-482726334526127}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":18210463626667033},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":10003656217594903}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2424064441781709},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4467997892872137}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":29574934039951},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-206234089842427}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4357802121027289},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":72933449975745}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":17656290133053879},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":7575236233571695}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":42535295865117307932921825928971026432,"numerator":5487121302213578815},{"denominator":340282366920938463463374607431768211456,"numerator":183435001945479768141},{"denominator":85070591730234615865843651857942052864,"numerator":36264058518118035181},{"denominator":170141183460469231731687303715884105728,"numerator":27155212867492155185},{"denominator":21267647932558653966460912964485513216,"numerator":2289694700030081985},{"denominator":340282366920938463463374607431768211456,"numerator":57166789790399764605},{"denominator":85070591730234615865843651857942052864,"numerator":18850508496275692169},{"denominator":340282366920938463463374607431768211456,"numerator":31014551803640348139},{"denominator":340282366920938463463374607431768211456,"numerator":13105682733382723583},{"denominator":340282366920938463463374607431768211456,"numerator":23762060219481669553},{"denominator":170141183460469231731687303715884105728,"numerator":44748715821480799393},{"denominator":340282366920938463463374607431768211456,"numerator":77774207202171118253},{"denominator":340282366920938463463374607431768211456,"numerator":161277751136626012531},{"denominator":340282366920938463463374607431768211456,"numerator":158231390623534655609},{"denominator":170141183460469231731687303715884105728,"numerator":35477831976454769549},{"denominator":170141183460469231731687303715884105728,"numerator":15026533242238834923},{"denominator":340282366920938463463374607431768211456,"numerator":69099872399038736133},{"denominator":340282366920938463463374607431768211456,"numerator":95192976693119821275},{"denominator":5316911983139663491615228241121378304,"numerator":521964372870522501},{"denominator":21267647932558653966460912964485513216,"numerator":730585201599003453},{"denominator":170141183460469231731687303715884105728,"numerator":13175509174354570609},{"denominator":42535295865117307932921825928971026432,"numerator":9883111438723371995},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":16,"numerator":51},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1954782689874775013347748351980419583},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1097591683212728386141449179044678917}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-807169103513026608876718268429612816465},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-403792016179804179534750106681469646741}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-171463855992777472582884822313674134445},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-43122331852715222720011019520685151457}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":76224901715954267670610676223934693647},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":74645075041890138352125011378576898701}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":3889166145141073804480361509988144685},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":14626328182828359115179991039383558375}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":11473624551790796517999877344605524273},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":180885985916385791592234200444848473267}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-182267735680236413278507110520924266495},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-185051849653159150839507084116230695503}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":22793092594926652502952951038724101919},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":22488725184368917238627310929380466625}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":19584934740133952870653317208573881},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-27745810188124266196259006831743353}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-2817597942289431944865819186809961363},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-45687361226683622588237604062697000199}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":394133672127988681517958621490249626749},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":24580146041452232018863372304940331707}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-464045561118643393893530701928256703},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-949347662239877269006885360841486757}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-431596370353031177977350846777275204919},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-876043506666842907141228680234027473859}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":179753085683662913104155056655372676033},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":355869294735174192612304103934517309921}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":76708667237554787788261741538314135995},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":73815928738222071379616152071985610971}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-12084799037979545434895324332843823879},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12504174424031869030026762832190476493}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-94885600863547828812266339911558035711},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-94942335280010518396556529462214264747}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":11894988563870882177423016042797839721},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":95051396987969973767147489351942442791}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":63787294196184929767407410822759394509},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":61211556714220353154051391112729975783}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":26315396883536211966948949924250577},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":15111441847512101636070471508191935}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-61141457868800264432703858012826590835},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-63705278587104909814640317411281190157}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":891031194968490362799987007310277760131},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":877996397981520103739503771860891082769}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2236105601627013872016502629879466985},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1118052800813506981447828782145499863}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-403620790520335472464433500584641549921},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-403620790520335472651758167727744770145}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-21619011326772736160869386207004264381},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-172952090614181889580757036752315207363}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":19310476947209895762391066395442949769},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":77241907788839582937076340190127753589}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":4050445749506847415602165635362843991},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":8100891499013694793005982218495708071}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":46330387499355394033067461191245800745},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":46330387499355394004033515067546174589}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-46715051149768898365758689738438615913},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-93430102299537796808262839053610513753}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":45944045761441981609733006427870093869},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":5743005720180247693149912630844647363}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1881690547651678915126337798662121},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3763381095303385289808161280015203}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-46043607942453984196201941314960819805},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-46043607942453984245655587368989332397}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":392856343436971246238430231267298118951},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":785712686873942492293389934141432369217}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-945355701759022292507436365504451597},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-945355701759022452524988160230788457}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-884997933928329927424482287917484662679},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-884997933928329927755255610201680679077}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":181001714799166683981281295853267768997},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":90500857399583341909530292082598641891}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":78714071327729677270398148705875953647},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":78714071327729677124089319534147162395}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-798034189722576747250132792865621839},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-399017094861288375585019371427700399}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-189849740666502922469365226735412540573},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-189849740666502922611196381635009008243}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":190367328755389274861660573013319688659},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":190367328755389274666256899850024578227}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":16395804218976905816434458044676201391},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":16395804218976905799160779511064501855}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":21406329969047325841773956466478341},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":21406329969047301228069333806822517}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":-1023327986247868328127149937716586197},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-32746495559931786527313410748585468123}},{"hi":{"denominator":1329227995784915872903807060280344576,"numerator":3515929555997222586569074722880946943},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":112509745791911122749912962307852982223}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":2272982781248473},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-10837115452496627}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":9175759315865997},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":11242820743395165}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-54518007309149493},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-150475487821601265}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4793259505671823},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-272180905533619}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":337443662721795},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-705275198027455}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":9757205395379667},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":10407275694441159}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-3815250949346521},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-22595666357246617}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":139626781587533},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1378643515857927}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":142040241510673},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-175723575013295}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1486425516023705},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":69104876016865}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1269920365742447},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-54598754321355421}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":6900056529768353},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1109537511306327}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-12048084231559667},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-28019005915576025}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":26010194615439609},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":10532068530124563}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-3325771907579243},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2264183077057037}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":293525845857573},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1140503551277525}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-8381624807072047},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-912543538515915}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":1055548865257755},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":4615936036780775}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-71475982390975},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2092779496286787}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":224135870783357},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-99482901541499}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4142704879640575},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":35050096252101}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":8418337243008875},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":7403340292113651}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":45424194386190772797},{"denominator":340282366920938463463374607431768211456,"numerator":187273746710063082577},{"denominator":170141183460469231731687303715884105728,"numerator":73426497403942160135},{"denominator":340282366920938463463374607431768211456,"numerator":56241021704258119593},{"denominator":340282366920938463463374607431768211456,"numerator":38197321527305522593},{"denominator":340282366920938463463374607431768211456,"numerator":58053581474455713557},{"denominator":340282366920938463463374607431768211456,"numerator":76730494412274728351},{"denominator":85070591730234615865843651857942052864,"numerator":8066351058412451447},{"denominator":42535295865117307932921825928971026432,"numerator":1716182497378102689},{"denominator":340282366920938463463374607431768211456,"numerator":24725405706374249455},{"denominator":42535295865117307932921825928971026432,"numerator":11463336862381939273},{"denominator":170141183460469231731687303715884105728,"numerator":40002108165793488963},{"denominator":340282366920938463463374607431768211456,"numerator":165378675681256000019},{"denominator":340282366920938463463374607431768211456,"numerator":162212972625027827691},{"denominator":340282366920938463463374607431768211456,"numerator":73151549105664071173},{"denominator":340282366920938463463374607431768211456,"numerator":31358090296450877763},{"denominator":170141183460469231731687303715884105728,"numerator":35456233956946821269},{"denominator":170141183460469231731687303715884105728,"numerator":48849004063381136975},{"denominator":85070591730234615865843651857942052864,"numerator":8636601975861341971},{"denominator":170141183460469231731687303715884105728,"numerator":6153320380246447367},{"denominator":340282366920938463463374607431768211456,"numerator":27243662992294956763},{"denominator":170141183460469231731687303715884105728,"numerator":40592499315126163881},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":207},"tube":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1040631815048580833875130516155648489},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-581454698476966169743189603069587993}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-807110388243673636916216080563615678007},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-807372985702844326813639914189956190491}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-86104566497484845687887498646130364145},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-173129532437011073450417790718061821483}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":38717191658969611852901994020824536077},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":75874495405993290098862407697688373453}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":509726271255806019155001786300247827},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":3838559505594118505966515310664746789}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":92811216500691136764273822113282162649},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":183007252703614277739535585900426152305}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-92231247955177996033243341017798085311},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-93585283518275278203443213365431261755}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":5752651428375373392935390074061014303},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":22724070770690576815042709652101530665}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":5042307168553491785675601157725137},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-27697456066273228285079320220584009}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-22775219135818958122373099676496061805},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-11529980261894655186283111070680919773}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":786984553860671582773018359965308220153},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":785463621400941411657820209111145595371}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-467869412832368778647975681375342863},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-477465987345911662619342141733709565}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-873463692492246771386890035829263366207},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-443145405607450467853343734331527928329}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":362376780292587152504529424823782682479},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":358767561716435214828353097633702284107}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":79023746081325190482562897480445051259},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":76109273075485947776204485334110965635}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-12407512657598944662512990170522433555},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12823412270194212215056453842960950409}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-189810345537662445508907049517707035765},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-189888444587709928107127719540441085667}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":11900705632467847052929528359783544759},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":23781605103239336478892533027482731579}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":16464502201007298657945286703535791203},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":63254387463919900624944963344629117387}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":13338976622075142211927280019108621},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":16135646028797562676250539975761557}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-63175183498967047209583019134871038873},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-65766155579649532352998737856259073527}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":901398188899819371799860237665516252757},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":888405875940500194922568297649537922259}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2369853181877607735337674720406588365},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1184926590938803914707294454748573117}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-100914828173868846673192230152077657909},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-807318625390950773768021712861958840667}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-173521018053394051736915295208095361023},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-86760509026697026017148972614163467251}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":78437077036899267996338468433658364355},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":78437077036899267879882434078202362351}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":8487465489335096975347094965991210397},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":8487465489335096935535732867311939267}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":93656720001913839611326320692110655561},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":187313440003827679104695835338410162853}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-188926621155692910101299023303286041687},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-94463310577846455128757769556522997607}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":23176736403618827539919102453727346867},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":11588368201809413753180480591840368885}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1691956184701451480954820270265145},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-845978092350732929095172960215681}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-46450142670299985372028195925590917037},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-46450142670299985423471807301410165375}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":784738003018889046766711296342381588099},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":784738003018889046578676585008111955351}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-952519720699579339745650156935280931},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-952519720699579504345526449643850055}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-895235367332881138917152326916609182167},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-13988052614576267800879503583655691663}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":364860311010210161517881050322223770747},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":364860311010210161185337493813463925741}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":20261059314639125016097774697830215957},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":20261059314639124978395555627550705167}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-13084606299062658291629975624189021557},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-3271151574765664589264542962300178097}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-47452609454766510953205845856717046125},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-189810437819066043958351213561322322371}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":190422527455170723992943747872703497879},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":23802815931896340474053831084813362357}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":16918412738561971391088194193882157149},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":16918412738561971373227360712908067761}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":22085239769238285154298959983683667},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":22085239769238259253535007423220973}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-33786539833829600465732816199205294969},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-67573079667659200987792033361945472073}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":113802637203769016497300251216619803899},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":910421097630152131811679784440207214057}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":4349762285741763},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-20524137130243219}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":142929477346561585},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":46458632595825165}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-27788405741524913},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-146417400987384963}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4879377550911553},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-721796619694801}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":155410970917221},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-752390119905881}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":38730291458597171},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":11790372542665173}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-3883693288534837},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-5474721903734977}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":5551805486211},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1301193354370483}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":68626437917567},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-170802152382499}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":700187841799315},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":33869628941595}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1131813757102113},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-55026534991220597}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":6253863772089195},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-606337569012551}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-10357398267554027},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-25582371050031779}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":23465890114387019},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":4346588239025443}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1343176506615411},"lo":{"denominator":664613997892457936451903530140172288,"numerator":-15940822592811}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":144657445071629},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-65909803048381}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-7918084014471261},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13801022446318663}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":15672248591526047},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":8400531830263515}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2131020182362197},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1967018336281691}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":26832180068339},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-194115096573185}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":984147055270235},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":533223024590071}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":16066000781543651},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":7131691077301155}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":47023845263694415561},{"denominator":340282366920938463463374607431768211456,"numerator":191193700400293420487},{"denominator":170141183460469231731687303715884105728,"numerator":74322952357681809585},{"denominator":10633823966279326983230456482242756608,"numerator":1819538018457584307},{"denominator":340282366920938463463374607431768211456,"numerator":39810364259735649305},{"denominator":340282366920938463463374607431768211456,"numerator":58964933063447608135},{"denominator":340282366920938463463374607431768211456,"numerator":78094126403842106529},{"denominator":340282366920938463463374607431768211456,"numerator":33556751247804459237},{"denominator":340282366920938463463374607431768211456,"numerator":14376927470621948583},{"denominator":340282366920938463463374607431768211456,"numerator":25720439181854967133},{"denominator":340282366920938463463374607431768211456,"numerator":93990408306517757131},{"denominator":170141183460469231731687303715884105728,"numerator":41147799269665107431},{"denominator":42535295865117307932921825928971026432,"numerator":21195042341535787907},{"denominator":85070591730234615865843651857942052864,"numerator":41566097974390438609},{"denominator":170141183460469231731687303715884105728,"numerator":37700850233240938687},{"denominator":340282366920938463463374607431768211456,"numerator":32712992204301171851},{"denominator":170141183460469231731687303715884105728,"numerator":36380486799005572617},{"denominator":340282366920938463463374607431768211456,"numerator":100252913738717668245},{"denominator":340282366920938463463374607431768211456,"numerator":35720765453703078183},{"denominator":170141183460469231731687303715884105728,"numerator":6475088795005835699},{"denominator":340282366920938463463374607431768211456,"numerator":28162298633706080739},{"denominator":340282366920938463463374607431768211456,"numerator":83356645491523487319},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":32,"numerator":105},"tube":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1105624308360244136373183995324649749},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1229909232892872132723856091963859407}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-100898482075722280203747696113637728721},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-807449598958166485023987929066851362639}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-86435160541530255490537315322274081009},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-86844008197137147019939609280192218383}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":78627579213458562782421759853482134759},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":77087944297215251843149071094308016175}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":17087114830567326051203518258391685267},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":16103412794411841089879569323611024511}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":187606338069812090881105604894085265063},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":185067684656044852142248332845415384771}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-23324626790605138517948264005103329067},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-189228917067185961338072578971081688139}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":23213494451506135547299502500321982139},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":22945192706189308019855222403772476067}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":20806349034482129471310023249636773},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-13787836854188994458201191150777711}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-22995177919910083379306060887841913083},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-23261438433079170567255157484715253501}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":785846598086650237147838338333244345619},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":784507485959572790438059582545786524003}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-471802527277643642933645408502194733},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-961111526592637352268744102981755223}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-883717211445054258911329334404656881237},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-448262218138905472021429433666955720049}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":182614837271912640548617135335731197073},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":90411239484430788757888261400929445165}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":40677759662770568371212789418470316303},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":78420577105750626055385290478389748421}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-6363681390828997042097411322377807931},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-6569602660345166401133920428337847965}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-189771449596579385906867081136447319985},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-47464609918568051116808242705907389389}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":23807448793465484793209032572632256713},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":190357077467352096479655192857796052557}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":67950571730177468494903908280147219527},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":32660088723827709081751514997967199951}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":6754580399537295830867237509192467},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":8576569360888172585645424462983253}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-16307822770620902916216284819497384179},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-4240518216017701563599356527355380005}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":455867890704237248109149508768446896963},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":449391326774689740209707664716240084909}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2506824563652043674176789963692755949},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1253412281826021885799590244605232769}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-807546013841929981351367190769096379893},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-807546013841929981741847427567713572341}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-87004956241360279295128855735213850489},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-87004956241360279445603128682577442153}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":79615771304992306934098504320140245941},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":9951971413124038351695564414283885219}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":8884700240313325014616581148378106709},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":4442350120156662486569967452556322351}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":23655549933631159334336954626853545115},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":94622199734524637277432586056349677907}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-190932365157376527231166531341727307389},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-95466182578688263695091760249750489595}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":46733112765480194843088129834184998415},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":5841639095685024346663230169173870611}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2936920235739871518906013198412153},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2936920235739901617181799099006509}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-5853293539900505137976311037188725837},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-46826348319204041157309398382339535793}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":195977142232629352484368488422533883033},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":783908568930517409744721891668441001447}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-960357892458342834210751755088311959},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-960357892458343003520204227920657271}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-452730821764324136593267471214042037275},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-905461643528648273534198812344603518917}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":22981349019941049416641488503382792507},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":367701584319056790325476238096826968663}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":41695105255515468567084872189254553145},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":41695105255515468489374933619684764049}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-3349203929307821065961049824375282153},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13396815717231284332085348086542104957}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-47431327241806181839828312338697489115},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-189725308967224727508611978880426122133}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":23804548215856790983169933221440597175},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":190436385726854327659634342982287402597}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":8723144937699803660988877153897592065},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":69785159501598429214049507288067836721}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":22746726153501625641259044849906449},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":1421670384593849899943446777220197}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-69673644627313794984421376938280056433},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-69673644627313795042638691433527578429}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":920737146278920944907797680906278457423},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":920737146278920944736625585723858816917}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":4220592192892301},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-19591143150258907}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":139335108813715103},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":46977596616024705}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-14008423357724857},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-71343690336558415}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2458881917026983},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-453876354040685}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1146556955044233},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-401553262001361}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":19081577565471967},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":194691539694905}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-3810808505353269},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-42386578525738605}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":203767348414219},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2499461372020049}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":33680350700451},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-334970901861041}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2678845615208359},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":14664030128345}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-227953434209053},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-859465907335385}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2838516279557185},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2667823823899007}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-4302580855376439},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-23285921312839145}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":21035337235322287},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":6801022628861229}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-506442125922841},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-7299850351855625}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":573080600904481},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-983814374607617}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-3705511794339395},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13057249037019551}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":3637320428322671},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":7531949465361525}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-122729693906285},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-231887141858495}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":207818216132043},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-191720121981963}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":936363777731543},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1004459955136427}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":1918120501634479},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":6788718011107857}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":48697179098990833039},{"denominator":21267647932558653966460912964485513216,"numerator":12199621227700609439},{"denominator":170141183460469231731687303715884105728,"numerator":75215473051871241481},{"denominator":21267647932558653966460912964485513216,"numerator":3766519292677533423},{"denominator":340282366920938463463374607431768211456,"numerator":41475671411525938529},{"denominator":340282366920938463463374607431768211456,"numerator":59902381002769267545},{"denominator":340282366920938463463374607431768211456,"numerator":79494922906634673135},{"denominator":340282366920938463463374607431768211456,"numerator":34889792626036799629},{"denominator":340282366920938463463374607431768211456,"numerator":15048835686096564853},{"denominator":340282366920938463463374607431768211456,"numerator":26748122951622324541},{"denominator":170141183460469231731687303715884105728,"numerator":48175175864643102723},{"denominator":340282366920938463463374607431768211456,"numerator":84650553808224665967},{"denominator":340282366920938463463374607431768211456,"numerator":173824594578458679049},{"denominator":340282366920938463463374607431768211456,"numerator":170386671821345625195},{"denominator":340282366920938463463374607431768211456,"numerator":77707301528645706965},{"denominator":170141183460469231731687303715884105728,"numerator":17059754703366139941},{"denominator":340282366920938463463374607431768211456,"numerator":74646541650093912455},{"denominator":340282366920938463463374607431768211456,"numerator":102859052728494722821},{"denominator":340282366920938463463374607431768211456,"numerator":36929881711972832219},{"denominator":340282366920938463463374607431768211456,"numerator":13620882179038134645},{"denominator":170141183460469231731687303715884105728,"numerator":14553894490011717169},{"denominator":42535295865117307932921825928971026432,"numerator":10697721183526104533},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":213},"tube":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1172304879738117895725783368508716871},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1298521991744977615156322185942862207}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-403638569925730585453247173481535329629},"lo":{"denominator":20769187434139310514121985316880384,"numerator":-49297607131735668682673906695529385}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-43362317570912372738596573476076461309},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-87083373990547549389838152371588873777}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":19951068136459030537084750030934427881},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":78285166424795172961165037606584739603}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":8942151619707241475684424337075632581},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":16873889616365272862149534052562696069}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":94764998452153901586908894160041192669},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":93533577951887165992952253492499777091}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-188671042867088494673299125128108826955},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-191226825753132648953298104680857718721}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":46802903841260604441522809009400652497},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":23151768012839774760316467359177269297}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":1343785222387510127151932441645783},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-27375937108081083461287171767145225}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-23200315274495269974703750713958451783},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-732746121282578033993975690713027855}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":784853752957470984524853107204313018209},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":783696253571651606943435000784021972665}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-475335276349831328238002832162111795},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-121145279087353686146556048926442681}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-446977958435919922096105610084579462769},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-906750421482252791441622285444638236269}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":368068859051824460041106550518819569459},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":182251902836126508434014910300933135133}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":5231436335904720659378312324277290339},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":80748821245676607620641025079396478411}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-13043886034421894303177939878105352941},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-6725544340414767093849147569959391773}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-189682055153785368660367180820033202933},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-94912351279826392829063608721789626463}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":190469516538720025448018040412417443379},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":95201276736492157775307639030428492689}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":70064089770994207555569389825746792489},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":67408046641276071930391670721283629155}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":13666913475440235954635195344880473},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":4540161938158300705515066707757795}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-33654445164341919084624836032216814731},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-34975391859218732895704636602589989333}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":461023309537100083682611189165477422887},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":909129373025257905639063940430232671027}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-165429656168666558345210338187694443},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1323437249349332517220515136825377587}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":-12623790864657650311678222595361638267},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-807922615338089620346041611278847359999}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-87210412554631694931211851010490807903},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-87210412554631695083457201032129458173}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":80777800232627993998576713562713956407},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":80777800232627993873852361546916842129}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":9292596537705878801437198861228590173},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":9292596537705878758241526713864848235}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":95557214080449273717459576632345415535},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":191114428160898547313159429922549489799}},{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":-1506853833824870619774006791603753205},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-96438645364791719746484442307647734765}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":11770593732145260793058438398928672759},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":11770593732145260774924884018940827767}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-151120329021887542804589925513619},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1208962632175116088690760894352127}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-11792902112782483038571726918895728505},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-47171608451129932209908327987445603429}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":783224461475838948438120399855442957497},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":391612230737919474120247346178397576897}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-484500479321327739773274031373716857},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-484500479321327826848598581758922197}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-28614989903337350344478627835518145435},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-915679676906795211379676825862802069383}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":5789526087500276461398827943987117563},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":370529669600017693180349685180405287169}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":85750995241200913390294453123293291189},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":21437748810300228307537572656472340013}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-3426177492942380972089416476486200877},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13704709971769523959518550684141468777}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-189596440459914269323336361721212729935},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-11849777528744641842280159802896778229}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":11900687978751537454195326395690701943},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":190411007660024599056082786969739578309}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":17979209975238316169771797296601858209},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":35958419950476632301367862157377590067}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":2923461327912968058041110865051095},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":11693845311651857912277536728739349}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-71793774763166729631332250885189843091},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-35896887381583364845747998085962405915}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":931028758300132384146638768724622351063},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":465514379150066191985452918377451086835}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":8186163826505191},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-18829069449133977}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":135943395920069563},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":47085966598750017}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-28119444315887977},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-139229631316357191}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":612967706712083},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-32649111971251}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1056209526545431},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-213309293623777}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":18681204776342969},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":6293585870279607}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-3658414502956237},"lo":{"denominator":664613997892457936451903530140172288,"numerator":-79888883939987}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":214543376983645},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2431778275780359}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":8329851937917},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-329969704291013}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2592587700651901},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-4726441150397}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-1321865569925403},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-54581478877624635}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5141039109505277},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-732169813514937}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-855425476665553},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-21079859188176565}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":18681115252144859},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":306313543063601}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1360238172539373},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6460738729011743}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1138339349884221},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-115250100160141}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-3445788056336547},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12359241838605733}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":6745349063804381},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":6664224938554751}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1797277539849345},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3505007176342541}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":202404842994693},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-190487846119433}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3567645649182975},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":235084733330443}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":3665987812778583},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":3205398205458743}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":170141183460469231731687303715884105728,"numerator":25222662407343001229},{"denominator":170141183460469231731687303715884105728,"numerator":99636626936595297841},{"denominator":340282366920938463463374607431768211456,"numerator":152203854650296359651},{"denominator":170141183460469231731687303715884105728,"numerator":31179796770311911901},{"denominator":85070591730234615865843651857942052864,"numerator":10798679356003305417},{"denominator":340282366920938463463374607431768211456,"numerator":60867474052164607273},{"denominator":170141183460469231731687303715884105728,"numerator":40467436459862402723},{"denominator":340282366920938463463374607431768211456,"numerator":36265785599149307981},{"denominator":85070591730234615865843651857942052864,"numerator":3936488944751772749},{"denominator":340282366920938463463374607431768211456,"numerator":27809404409198717959},{"denominator":340282366920938463463374607431768211456,"numerator":98788206741024940339},{"denominator":340282366920938463463374607431768211456,"numerator":87071289691203422827},{"denominator":85070591730234615865843651857942052864,"numerator":44543312333855820415},{"denominator":340282366920938463463374607431768211456,"numerator":174580761568103554809},{"denominator":340282366920938463463374607431768211456,"numerator":80069530998423729383},{"denominator":340282366920938463463374607431768211456,"numerator":35579412219022749959},{"denominator":21267647932558653966460912964485513216,"numerator":4785647733106555909},{"denominator":340282366920938463463374607431768211456,"numerator":105517804444061299383},{"denominator":42535295865117307932921825928971026432,"numerator":4771859821375984969},{"denominator":340282366920938463463374607431768211456,"numerator":14319690460386907967},{"denominator":340282366920938463463374607431768211456,"numerator":30081029159476214653},{"denominator":340282366920938463463374607431768211456,"numerator":87862339407439990273},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":8,"numerator":27},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2481210729822146295660920161496208265},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2737349068121120080819615984438429547}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-403742952312226105695833069656112140823},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-50505437299951869436792290730120125535}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-86973963063665041107731642698933789447},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-174567789681234845963407543924445544175}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":10120534583897758381438848502127486159},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":39732968687707833393563020162592648483}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":18702805459453304070374541821403976501},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":4416422204078144316456226502272935055}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":23924094919278694955594109668368287863},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":189005692815140353989322093509002666631}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-95342200202625062885526724244460942097},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-193164047926514140372184274817952860589}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":47148432810357850231536415338707663371},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":23343483046913560972306777555343262775}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":11128115374563671414100904929342559},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-6773411480702582707443565252457517}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-46780655513095262557954316690693864605},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-11809395893545762004129007639957507489}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":784006149966650541009997432313269851715},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":391515169802659615142381324140474955719}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-479197242679642433308525801090489255},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-489014278174932271277025466115528723}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-904183101346925479446153129940657565655},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-916968523164153416849971252615899399049}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":370895172769002179777949869810393661767},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":367346741157951747052979167662094752145}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":21516284648298121953609437695371581781},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":83092996279679653552562324379242855367}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-6678308904148072982621417698226974589},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-3439649224411882237814118051975621991}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-11846824094473446312857127582823449663},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-189744878240074681564489527742012142475}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":190443658798184361634694812901718112115},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":190377655370313703353605606877329829617}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":72197659520206166136061677989282522801},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":69517103943975347333825932521374732095}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":27621673681799372758367497881116369},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":9577385848881013690570148037077403}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-69407080648733833373507151433078423807},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-36036360217266724741324702143035747255}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":932333349078078533781136423729053300375},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":459724339650618384088062190628361756291}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-87182821556515829229798315056909353},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-697462572452126659979545310614374467}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":-12631987487038225679105717670770418081},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-808447199170446443869711938462350937693}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-174755900124321807064013584378518760879},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-87377950062160903686006795648808871433}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":40961501590598681336264879816830704003},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":81923003181197362543500047759348752187}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":4855573444149798382132241275365609069},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":19422293776599193438589043755506643439}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":192923565106942287095658937813795598865},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":192923565106942286971911560317140809893}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-48690323117225304595424654275494500775},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-97380646234450609273277944630240159105}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":23700347566621721540260261378158440877},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":23700347566621721502572963789142513995}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-911185671529229310689972881837751},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-455592835764622890032015922280375}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-47485332986289804148977048510662821087},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-47485332986289804206790113422680210727}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":782685678242827798169173378929271344685},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":782685678242827797966514785230962510727}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-489291730799857370174258841093378089},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-489291730799857459738195616199049945}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-115736544396133412267296281309353204263},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-925892355169067298503600204069088467625}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":373346948126078360591556238808100488499},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":186673474063039180116923907868700811319}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":11015701085939364492067160466745174987},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":44062804343757457885776611075054988061}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-7003911823688395777259436411026150657},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-1750977955922098953588735642495217289}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-11839120135202140309999194574447662857},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-94712961081617122558529877587913552911}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":190348496118637972526118949860633637615},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":190348496118637972309651157360441706921}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":74067779948728047008561459435044406969},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":74067779948728046929645962290809519245}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":6001227355447436308642003078598113},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":24004909421789715139049055399035443}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-73932550017448739009139294399457191995},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-73932550017448739071306823551371194155}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":235324644751494336603327019509329598011},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":117662322375747168279112423194875397455}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":246604185576373},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-18217687479846273}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":33216699260555409},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":5844522450898151}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-56037270596262569},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-68060862218233371}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4844843040349425},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-134907413836263}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":972017220032681},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-904396160088687}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":9081437385015663},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":769305194331269}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-861390845944763},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-39415949499390119}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":216252825087497},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-597774087060385}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":265466510454675},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-81638840021889}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1266943887132101},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-36987194215529}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-389001098682039},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-26877545683184337}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4639432964422525},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-802115131274257}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-5059029617479063},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-9480713980905491}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":16397622917460571},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1485589306403907}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-681696337559101},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5642180977713279}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":70826394940499},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-433501183019729}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-6370068981149737},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11703027362519549}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12496741428220821},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":2899728877836921}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-408401802864669},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-829863023702365}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":198239037538529},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-190298990458945}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":425148768664061},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":437903140025901}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":7009310155427111},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":3006062760261233}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":52269263069609054181},{"denominator":340282366920938463463374607431768211456,"numerator":203429948457804572039},{"denominator":170141183460469231731687303715884105728,"numerator":76979980616314694453},{"denominator":340282366920938463463374607431768211456,"numerator":64512366061929235065},{"denominator":170141183460469231731687303715884105728,"numerator":22484511233143917867},{"denominator":340282366920938463463374607431768211456,"numerator":61861680315112013311},{"denominator":340282366920938463463374607431768211456,"numerator":82415819231269020599},{"denominator":340282366920938463463374607431768211456,"numerator":37685993914429262363},{"denominator":340282366920938463463374607431768211456,"numerator":16469078048027451883},{"denominator":340282366920938463463374607431768211456,"numerator":28905247018524454953},{"denominator":340282366920938463463374607431768211456,"numerator":101305531312260688953},{"denominator":340282366920938463463374607431768211456,"numerator":89560012828360912079},{"denominator":21267647932558653966460912964485513216,"numerator":11413001599872453175},{"denominator":340282366920938463463374607431768211456,"numerator":178847498313197106551},{"denominator":340282366920938463463374607431768211456,"numerator":82489550549605634797},{"denominator":340282366920938463463374607431768211456,"numerator":37094506046612174777},{"denominator":85070591730234615865843651857942052864,"numerator":19633413628285391287},{"denominator":21267647932558653966460912964485513216,"numerator":6764409225516230741},{"denominator":340282366920938463463374607431768211456,"numerator":39456905649675768469},{"denominator":340282366920938463463374607431768211456,"numerator":15047565209443679767},{"denominator":340282366920938463463374607431768211456,"numerator":31082939787162396637},{"denominator":340282366920938463463374607431768211456,"numerator":90200342991762440323},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":219},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2620907216444447126048639257720779165},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1440290019493312600397949295760421419}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":-12622562596258612369023057256236264727},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-808630097935935474916781479240336752569}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-43592082063360980610671700221292157521},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-21861662101454824580006976255534403969}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":41053717301004152132268836331363377123},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":40315031540237313026332552255967689527}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":19542604512438619583466845814004610611},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":2309851753356652160852273420337070813}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":96597425422200038564818130897191183247},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":47720817521238483222276612089780257665}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-6019902359189193050216479364099680333},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-97520513924673397424191317096536455469}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":23731643624056836574170801826646559423},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":5880006417190232747897968818129399115}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":23077793916830823133768688411351387},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-13362065630881639090519684290814255}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-47129811012239093686560366734977467491},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-47547785401147478363825773942008677229}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":195825968971434534861758047100743326665},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":782509731786746229357914305126693070583}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-966907142368605711181358450317856073},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-493922652554551697416626187795188463}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-914401682666154427607147861673716227643},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-927181625072562261768830150103337234855}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":186855496361548517320269918616429319381},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":185088094626504438731275389576231720965}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":44220505288047922197935408685482575319},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":10681513081054351220911556759568127699}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-3416273200819869983061655198733055865},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-7030632244089959746678534853017384193}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-94687465013747491803300605283482267147},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-189621052730183079017580484455060359767}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":190422116744513433031778656771944423731},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":190311025899625095385244314562035752859}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":74350368068764903992192265694358480087},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":2238951496322110215399878386299201617}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":27878945153194138733638925597788393},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":5032994906853334316698434977720469}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-71524951855657352859501727256605960797},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-74213180930751120577806961343421528185}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":942598617651399642454167138469947309799},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":929743218372213799694987914097783463483}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1467796141492748309162985971398115929},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2935592282985496726691184346871597443}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-404559218109758727346287379005219401295},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-809118436219517455107983265153698236287}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-175017374027720589963159319820499001547},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-87508687013860295137312971124796717395}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":41525624329915198300682756550482293333},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":83051248659830396467912822261971828111}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":20280671184446684304841297182000105277},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":20280671184446684211239147814281597351}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":194671887062646721701560278207745865347},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":12166992941415420098485255032682389287}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-196584304507585774876285857404576398737},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-98292152253792887522095115395014958129}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":47687536100634747170012307875363169309},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":1490235503144835846615825183123151551}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-286407874509873776563782979345979},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1145631498039529544872424173792835}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-23883479289349432335536830585833480599},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-23883479289349432365574736366328021619}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":391146070416380489329600529322601341517},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":391146070416380489225673755936048898803}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-247310915331206475034098031452330313},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-247310915331206521095495372575186149}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-117012817153387723566299006133930359215},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-936102537227101788904666960161646688393}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":5877433750437165821291536273899204545},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":376155760027978612196269851765038864693}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":22628270606007487328616904565361652121},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":22628270606007487286131432115053472001}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-14305691751110731860003845876902779741},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-14305691751110731937339070790021225341}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-189215846169585927708719147366627988957},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-47303961542396481967449932119206936013}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":47562737831974639610569954532156697833},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":95125475663949279110137900614603773339}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":9529632318888537983254684750972810553},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":38118529275554151892240748099990021921}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":24595033376754676827039304775300631},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":24595033376754645215658084444398963}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-38044521096975016317248068911349350635},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-76089042193950032698726704763527616251}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":951549251503738120814298480339670812213},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":951549251503738120629095046302480364885}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3802038400893025},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-8928692768878605}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":130259419344767047},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":23106160400027025}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-55763114458899385},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-66684883864793019}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":593620678350459},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-76591768948565}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":112111619193457},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-478363939184545}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":17541471057086447},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":2933793869594677}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-12740048326282229},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-37980434872323597}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":214291012187627},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2373892504720797}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":265225689356663},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-323770392901011}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1247418178886923},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-42752774788705}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-3305296782645977},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-52577099070357489}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4176691424329099},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-879649306068491}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1624241116048975},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-16927376504822013}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":14180625556054973},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":127587233069283}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":290784581645},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4843214352246759}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":567801690207241},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-820355561091547}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-5837817861738317},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11091331645983177}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":11564978604929065},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":2465985375762499}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1471411360533067},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-197026245911661}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":195026964416055},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-190993591419345}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1623491277050641},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1619650573702603}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":13419159663267533},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":5580942722258167}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":170141183460469231731687303715884105728,"numerator":27084937735433955581},{"denominator":340282366920938463463374607431768211456,"numerator":207662230022357360349},{"denominator":170141183460469231731687303715884105728,"numerator":77847253943955936647},{"denominator":170141183460469231731687303715884105728,"numerator":33361966320449251579},{"denominator":340282366920938463463374607431768211456,"numerator":46800147873443295589},{"denominator":85070591730234615865843651857942052864,"numerator":15721606239773980321},{"denominator":85070591730234615865843651857942052864,"numerator":20984891624863434519},{"denominator":170141183460469231731687303715884105728,"numerator":19575828457976352813},{"denominator":170141183460469231731687303715884105728,"numerator":8609507074043537811},{"denominator":10633823966279326983230456482242756608,"numerator":938644905810258117},{"denominator":170141183460469231731687303715884105728,"numerator":51951895066899954973},{"denominator":85070591730234615865843651857942052864,"numerator":23029736759480352535},{"denominator":42535295865117307932921825928971026432,"numerator":23391327012245693163},{"denominator":170141183460469231731687303715884105728,"numerator":91593827459204681369},{"denominator":85070591730234615865843651857942052864,"numerator":21242130241790895925},{"denominator":340282366920938463463374607431768211456,"numerator":38666634477088469785},{"denominator":340282366920938463463374607431768211456,"numerator":80537663798207755117},{"denominator":340282366920938463463374607431768211456,"numerator":110998691945782920293},{"denominator":2658455991569831745807614120560689152,"numerator":318571487496985887},{"denominator":340282366920938463463374607431768211456,"numerator":15805497599887533133},{"denominator":170141183460469231731687303715884105728,"numerator":16057234902212129075},{"denominator":85070591730234615865843651857942052864,"numerator":23149449477531179745},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":32,"numerator":111},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2763547398859594795290075842047010947},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3026576308348712195924776040764638879}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-404175126326056372813836203623818170161},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-404659858917724861989303820932658626693}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-43678152343217111370389123043862876143},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-175145516887402061306127412007100812085}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":83233618430517595930327830789859157585},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":81777379264606225500519182733845012081}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":20403667036631089816917940168986220497},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":19313252303262316063219166131895217593}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":194936113721294535042835931539578998277},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":24087493574279560203837217631011192293}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-194528437485084341154280993030584880005},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-196856987323253113428457231545492855401}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":47746574586914742732873768476715818899},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":5920283010354440101647020904265433409}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":11984887646094489814535823229013257},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-26262661442216328023703228803907357}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-23723751818124972268568024823582348089},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-47825797136648540655546036083122689711}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":391373468897362305577711988195099854705},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":782134342275756481292918003979939317715}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-976342624869851764531390224477472363},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-499375496084240761351331301273527477}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-231153638049279515114982940644459732077},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-937392581916610437244316639348682730711}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":47064831813105320150089295517702012711},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":186497268153107835618764655057409826063}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":22707407849981140514957752171868737727},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":21956290429867349879325033628183376521}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-13968845557325969532418621156863026881},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-7179313228917094876710567804866257829}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-189161380157477863361262695474557915877},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-189455315719429398645481650942526266433}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":47590983672550960030884050418622126935},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":190209548974545164149363685734963062047}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":76521293702139795937279065932708990799},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":18448791827365018704421682077121192947}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":28102603465068228808537490799448601},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":21088611036356146275474531842618495}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-73661584855477318725351536643438595035},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-38185618237595760781614556002300654539}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":952845068591776086074406838261528895705},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":235003908929666593784849639309152212365}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1541967187324261996816989636418747381},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-770983593662131026488708466725329267}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-809934899705180821438330219063940379743},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-404967449852590410931174444415550229707}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-175207575240060941264144089590405528113},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-87603787620030470789512272817732621445}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":42081216864944565205075041825405074757},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":42081216864944565136077079585382314295}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":2645034706671162464697298970886069833},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":21160277653369299620197167321216574819}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":98179753614694900217972361223435262501},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":196359507229389800308041935804592098221}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-99173149911226378766590801167854697329},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-99173149911226378852111218900329823875}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":47942387764735956301256214975919057955},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":23971193882367978109962775600316017147}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-383013627042709664864041154469387},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-95753406760686414659394421455317}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-48015948982685091257547651899553024511},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-24007974491342545659979635166160040815}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":782043697716309448499169082490342446991},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":782043697716309448285972540584035187845}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-250280867736539011456129964768362755},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-500561735473078117666333069993691433}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-946313051120757316901923686577833460395},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-473156525560378658642711285039493865251}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":378958401973796458050022231121577949935},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":378958401973796457674805400961583306163}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":11614057949973070105667461014235263157},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":92912463599784560670319728264322007897}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-14597850221328193820774892149055503033},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-14597850221328193901372166832903693719}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-47242076386317838215918040589350547069},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-188968305545271353028844497226597817147}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":95060234741765363770159511141598656729},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":47530117370882681828166277406462806741}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":78423746419369541174771593727485754699},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":78423746419369541090496235749034052119}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":25154587931657389411141116935027335},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":3144323491457169527718273000462065}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-39131157818346912897625843818914816231},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-78262315636693825861606423455661171395}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":961783415257305950789896117337027364297},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":240445853814326487649943810748962242761}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3591167339326899},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-1099036094238313}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":4005467787640757},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":45694940052368491}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-55442860258178265},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-65585192335793471}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4620654013300409},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-73862253258487}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":206177981406995},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-502494782414543}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":16594508328120983},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":11082967450316731}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-5852869900313297},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-36590264826946137}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":210328211153183},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1183865949520123}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":262784184373309},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-19820416056643}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2438678498270225},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13132940954315}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-6836543901647645},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-50295993546373037}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3717412067240607},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1890707252244739}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-710801542201449},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-14957442829824669}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12022802427808333},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-971211362178957}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":177156669477931},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4063398718473263}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1129432415956747},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-194031230137439}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-1340066166631805},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-10397208153053759}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10652790412193171},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":2043014325056925}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1316685693540297},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-187307972667427}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":95490409610947},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-94347317033291}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":765311452272033},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1506914998356131}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12677439349840667},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":2604076778214829}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":56148043840938677749},{"denominator":2658455991569831745807614120560689152,"numerator":1656000741164093531},{"denominator":340282366920938463463374607431768211456,"numerator":157402364260323153049},{"denominator":340282366920938463463374607431768211456,"numerator":68995614981889481013},{"denominator":340282366920938463463374607431768211456,"numerator":48689697372190763389},{"denominator":85070591730234615865843651857942052864,"numerator":15985085074134062693},{"denominator":340282366920938463463374607431768211456,"numerator":85507975469961966773},{"denominator":340282366920938463463374607431768211456,"numerator":40664042857588415115},{"denominator":340282366920938463463374607431768211456,"numerator":17996596812845036141},{"denominator":340282366920938463463374607431768211456,"numerator":31204583310663916289},{"denominator":85070591730234615865843651857942052864,"numerator":26644135307082816719},{"denominator":21267647932558653966460912964485513216,"numerator":5921895232948193805},{"denominator":340282366920938463463374607431768211456,"numerator":191742673830704424167},{"denominator":21267647932558653966460912964485513216,"numerator":11725119879568895515},{"denominator":340282366920938463463374607431768211456,"numerator":87507593912081856185},{"denominator":340282366920938463463374607431768211456,"numerator":40297684563255842091},{"denominator":340282366920938463463374607431768211456,"numerator":82583648962854551165},{"denominator":170141183460469231731687303715884105728,"numerator":56911836473896001793},{"denominator":170141183460469231731687303715884105728,"numerator":21068419434145641011},{"denominator":340282366920938463463374607431768211456,"numerator":16594507628739021169},{"denominator":340282366920938463463374607431768211456,"numerator":33176590743510403465},{"denominator":340282366920938463463374607431768211456,"numerator":95056702527692491121},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":225},"tube":[{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-181810777353384521146814700393266127},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3175170890967595138118400372308740735}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-809003327230026922608792888445073242201},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-405077208562466121723305790949852795267}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-174982994556317159485904718794750238067},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-175326789270351464258450726853214617315}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":10542841091293135359646559829317255331},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":82907750874217653533550637976239664767}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":21285943457042986525103181980410000541},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":20168974265269317287476477107042524157}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":6144270802399634684171862064899061961},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":97227900274982161436896734275188280423}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-196359015669204399298961850629341828605},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-198611904053018155072201916182664274371}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":47997788092678775898250427614170413865},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":2978316478567143715408427977682047409}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":24936770251360095390765020451229861},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-1606527979975115130922747510619675}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-23866583330696961452877962268495452631},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-48071085834443340558933288684728209069}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":195583816607244133102055506272494176477},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":48869000654176312182375772677578733295}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-61677422493455315155001131019064181},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-505443887095346809521878096162357451}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-934824572776471031790726867677768734797},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-236901054320694649796844669853871717117}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":379320449950307629586508125161467728275},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":375804127814386499152910043365544184789}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":93230050862948349843792814322383411929},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":11276399630240988077798117612232391841}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-3566852741746231168162720411954016405},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-14650218808242996546180521739659951271}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-188910628203150515952861540065372541687},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-189249759276967640305015082989103128265}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":11891903536085532730211460399307814179},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":23759425510333608909043485748120740887}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":78709506596724127325169072326026530171},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":75962342101595434502182876386083405855}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":28289489376527387252875108550982253},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":5505218996037970833308226115487485}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-2369251635355217761313828110597077579},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-78545950957197611086578880176005414395}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":963075341838170983539788531026017791023},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":29695892962497257717885978922915842369}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-3234704532459285958203777521466658713},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-404338066557410759329591455740506895}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-810895065470933101329823149812023035029},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-810895065470933101762585024654382383575}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-21916115496092797201455008159741599079},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-175328923968742377929872136152384676109}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":85256483386902438615417422209645461219},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":85256483386902438472755355208050164867}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":2757631185190936601356995363133953409},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":22061049481527492709575531727205364807}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":24748321776525957735001542775318499063},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":49496643553051915437485834370067611065}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-200047289777943269819100021569884554131},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-100023644888971634996681758578178523301}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":24082383793420551801038497066312162999},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":24082383793420551758812776564180681137}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":235116943619723285272070040810361},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":470233887239408964621127730398549}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-12057948852099799167809729309111622185},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-24115897704199598368030732490483554915}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":390970063330133799288792190864888046969},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":781940126660267598358897209059708957947}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1014368411343257341657613364105113519},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-507184205671628768288774317459481423}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-478263345972850161688935924859887709915},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-478263345972850161885388417234292520363}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":381757124860747556321388787430698124437},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":381757124860747555937194045135870902239}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":47661408082931274097595756655028370131},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":95322816165862548014970914784699402383}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-3720959106399924663931791586332426055},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-14883836425599698739708175170823593661}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-188685393109608104360781043747334353595},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-94342696554804052265065686854281765473}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":47489785344085007606795478115373100351},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":189959141376340030193761664745818108055}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":80626906765762112963737052833549874185},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":80626906765762112876660955619443613379}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":25679973387225175538339330338942781},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":6419993346806285176670890058514625}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-40225713952646513950313477719248053751},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-80451427905293027969168959506343859741}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":486001852350300383570071712174419223173},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":972003704700600766944978569761221028595}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3330026636151613},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-8732103244510031}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":127096509521606873},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":45171080198080261}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-6854853563136907},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-130361728814457099}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4459431185572683},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-15984878777701}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":190215389969671},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1051518580375933}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":15596776104987515},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":5067905880560779}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-5378427624420399},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-17583856418239923}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":193899348958587},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2360447398571573}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":259029681456121},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-309889059834637}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2393720543762007},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":23689304970375}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-1630262185610559},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-11955410019179869}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3260649925041715},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-127801420587027}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":490838551136545},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-6503682840257819}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":1238641466531755},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3076672520985331}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":727953675100601},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3304392300420081}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":141359542072085},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-367464909107475}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-1226957733864397},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-4870386578914083}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":152224072864419},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":202682358341269}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-585298597643683},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1416969645709735}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":23259021505287},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-185868470128507}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2889549886415705},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":700648707684285}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":11993073396550697},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":1213448461620957}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":58204414932348036579},{"denominator":170141183460469231731687303715884105728,"numerator":108169987353258955483},{"denominator":21267647932558653966460912964485513216,"numerator":9942392124191953801},{"denominator":170141183460469231731687303715884105728,"numerator":35664369922844875515},{"denominator":340282366920938463463374607431768211456,"numerator":50639309398863003923},{"denominator":340282366920938463463374607431768211456,"numerator":65023973490914347385},{"denominator":340282366920938463463374607431768211456,"numerator":87119542364442426711},{"denominator":340282366920938463463374607431768211456,"numerator":42224443328757716781},{"denominator":170141183460469231731687303715884105728,"numerator":9401338523402482853},{"denominator":42535295865117307932921825928971026432,"numerator":4051261107080114341},{"denominator":340282366920938463463374607431768211456,"numerator":109322936039366429375},{"denominator":340282366920938463463374607431768211456,"numerator":97456292487715011373},{"denominator":340282366920938463463374607431768211456,"numerator":196445743272288984355},{"denominator":340282366920938463463374607431768211456,"numerator":192090878245286991413},{"denominator":340282366920938463463374607431768211456,"numerator":90107919112853358297},{"denominator":340282366920938463463374607431768211456,"numerator":41989571509669548905},{"denominator":340282366920938463463374607431768211456,"numerator":84672748509503403385},{"denominator":170141183460469231731687303715884105728,"numerator":58353437073186107709},{"denominator":170141183460469231731687303715884105728,"numerator":21768608468002532175},{"denominator":170141183460469231731687303715884105728,"numerator":8707820957365678369},{"denominator":340282366920938463463374607431768211456,"numerator":34270257907688352551},{"denominator":21267647932558653966460912964485513216,"numerator":6098678603377104715},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":16,"numerator":57},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-3057016979938680593900636861321568463},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3326190927037114591234058777457575901}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-404900907666060667081367869467982717019},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-811132659062716206918680538016691635531}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-175181800814845343860652737284489089321},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-175439545067001317895566258144630221689}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":85434693935562835328403875725549175083},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":42010535742407137077396539654615214181}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":11094684088856287893783189490649680669},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":10522967130887801134133627335102396183}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":198236659692390963863919952034453796449},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":98075467366750391067583300211802440567}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-198128578237285075160352513988300051929},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-200305794088961898888643395263370223663}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":48216448612681506128570637308495649065},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":47911936559408672896742763610977937591}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":25983441679549262923764166893980891},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-6261162419412699966275928886837299}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-23993130209141896182140143720097731563},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-12070786515574195324238482458686955355}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":782068719089054204940641598436730011725},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":781818505361606640525916441171877619937}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-998537033450246954352289422560308179},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1024401408409337869074591588668481031}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-118129322078434012841235956074411152215},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-478909660780162122225124013110854194459}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":382118624834298740679269836488196772975},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":378607266100407315118753796769845892567}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":95641335711851907995972071050817690069},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":92609255587332633189691689932597681483}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-14560324797698683338511176112228163689},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-7467789516996894080574167140739150787}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-94312383044978524490557447144444973361},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-189006476595861831256370008908456831145}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":95071889654622451087698333269022043857},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":189910681052103155824620226188599600709}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":40457034758465920058972938160516481445},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":78147043852973730087446275441142700305}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":7109080603827581152848500454977503},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":22924855468498793007858704862890521}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-77987419422604709787189067846574253873},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-5046023847718491866738453972506549013}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":973292072096674519532712980569422290713},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":960504675608487220718337716354449351575}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-3387725328365328461178889804768006009},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3387725328365328581881769371245967099}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-405998655915427323368063257381746267851},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-405998655915427323588874801153881496335}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-175383932292868089043261698123571710539},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-87691966146434044682386464629857610061}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":86333349918796672761435390877073485167},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":10791668739849584076747700948836065575}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":22982907121757438670140526634935005109},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":22982907121757438564837388745566177069}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":3118019862609120206990032299305463037},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":49888317801745923278766314233035761733}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-201687323893012128875267663515953726861},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-201687323893012129052837060141794578819}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":48354220854134568956482334901095430523},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":24177110427067284434405739683303672241}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1418916715189801376304398040750575},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1418916715189762099485200224236585}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-12103504216078561840752772477004446725},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-6051752108039280928790228715861957779}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":390990568366121694205081395173281884803},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":390990568366121694092918840194044355239}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-257281896332119890246322529065523555},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-514563792664239880735292530634555935}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-966746219781132497422003564575861096137},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-483373109890566248912249775167955221129}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":384554131512477313832932485914703747677},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":384554131512477313439609358125143673257}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":97743222091403562382449615642829994751},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":97743222091403562196903520109457176289}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-7581594823502070861449238013553867715},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-3790797411751035452597207118062682563}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-94184600119431345894723771272766682887},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-188369200238862691963064568321411230143}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":47442262756326750537534743307108580261},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":189769051025307001910833290911991667173}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":41422798000723143553699575333946738927},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":82845596001446287017438448737993439035}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":26167465377175005475853523137527545},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":26167465377174968935531267508687971}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-41327715224281115826254724349078202495},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-82655430448562231723303852317420049819}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":491106373947443518137261036675361592247},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":982212747894887036074182823399276039869}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":379475209040757},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-550535423620923}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":126826563820369369},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":22287312148815567}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-26885919326208489},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-130392559749955955}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":533649845873121},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-28775023619825}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":705676533760835},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1097704031532859}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":7308233816977573},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":9079817508781945}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-9965096788455521},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-33810167247032447}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":89537151235087},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-585728816307445}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":127546162724835},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-151652176663813}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2361284611146467},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":5060580382879}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-1477515043117683},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-5668993592620455}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2809020794749229},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4427452410858627}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2401090646360451},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11098949364686107}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":7870716572380021},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1295603088217653}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2203149782299703},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2579909416082407}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":17832810605103},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-347056623401893}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-2239973133578761},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-9131905167535079}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":4422917560620919},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2425766621373507}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1035400768645193},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2667972302296267}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":90627835540103},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-11483458028241}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2736766522681161},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":325622033860359}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":1422239397399449},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":4514761713113873}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":42535295865117307932921825928971026432,"numerator":7542449426848589965},{"denominator":170141183460469231731687303715884105728,"numerator":110385208901186929683},{"denominator":170141183460469231731687303715884105728,"numerator":80358652603761492651},{"denominator":340282366920938463463374607431768211456,"numerator":73724641943714508499},{"denominator":85070591730234615865843651857942052864,"numerator":13162666813600441793},{"denominator":42535295865117307932921825928971026432,"numerator":8267291069102966193},{"denominator":340282366920938463463374607431768211456,"numerator":88772775777691137515},{"denominator":340282366920938463463374607431768211456,"numerator":43834166772460193043},{"denominator":170141183460469231731687303715884105728,"numerator":9819065200284434173},{"denominator":85070591730234615865843651857942052864,"numerator":8413552377363723987},{"denominator":340282366920938463463374607431768211456,"numerator":112142834034953283109},{"denominator":2658455991569831745807614120560689152,"numerator":783117415905474257},{"denominator":340282366920938463463374607431768211456,"numerator":201241242860019149781},{"denominator":340282366920938463463374607431768211456,"numerator":196655037330317411893},{"denominator":340282366920938463463374607431768211456,"numerator":92770656237087218175},{"denominator":340282366920938463463374607431768211456,"numerator":43744258516008732221},{"denominator":340282366920938463463374607431768211456,"numerator":86806186908488743405},{"denominator":340282366920938463463374607431768211456,"numerator":119649631123971392769},{"denominator":21267647932558653966460912964485513216,"numerator":2811220917448949617},{"denominator":340282366920938463463374607431768211456,"numerator":18269978632314653755},{"denominator":340282366920938463463374607431768211456,"numerator":35396484670438202551},{"denominator":85070591730234615865843651857942052864,"numerator":25041548349747632863},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":231},"tube":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-801877419652483480059612890004181701},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3479458217103454299891708975492790339}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-25335756407564768489201021640023337815},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-406126404665338844204168631797242902009}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-175277601195688346396532072356265361077},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-175490066767900243190627138676954627535}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":86509469695808827297883543433393811721},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":85117262685912839714407778494231620155}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":23113859795227783812275931147289785793},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":21944070557783015920386598213971178525}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":199796283254938816729224267614392713413},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":98892747714840988931678283610516026313}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-199837131795313504293934417045391212395},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-25242338952701394943198807511412671775}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":24201052436052722215402277018239351827},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":48138396777367287860605663894234629281}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":27114514504886527648746433566767499},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-24278381085852849773089795482144509}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-48206272649033334119339432691856884391},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-12115375060672989909583568984682418081}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":391051047181386693087531049344222064221},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":195465075984487923495657660403444990557}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-505791271335068401953492212615837447},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1039441229401342181413271614942805587}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-955247363287907176816735554062248223313},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-968040649865838642428098508438496932927}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":48114422071023692828506008076496305393},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":190703104002182556485771799141539740205}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":49031285428763288121733676516740478837},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":47509199488949939105902321811916100589}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-7423562091575228120332516726363019815},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-1901780825955360048910795022467428747}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-94152942084719031236850637009939594443},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-188727560769626998091956940584975486237}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":94992997277131346513616684812725985931},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":47429365693759016756679700046219880709}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":41567019257227621113568077281488464279},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":80348336571462876282163711048048438853}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":28539701198289598921342987240873175},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":23796502055872566245083788154585633}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-40087372200011917277432511748160141159},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-20735394863178942003121085179763819651}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":245874471877259699671061174570058697663},"lo":{"denominator":2658455991569831745807614120560689152,"numerator":7583801353730007700317309893344576597}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1771407241210835781823184391770897101},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1771407241210835844389152487985922677}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-203309979752102842086208831898335485295},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-813239919008411368795429200905031359577}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-87687602215707363770721621338463117723},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-43843801107853681966543501039400073597}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":21848253059835575662897574488883809813},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":87393012239342302499216493504346996307}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":11962877706516589766431909884781252621},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":23925755413033179423410996185257744859}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":50264953851674426110549802082887030923},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":6283119231459303259612842759035008181}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-203266489821348039652198525285183058243},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-203266489821348039833158770679985876313}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":48510320960247371027250026733701197333},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":24255160480123685468129202580645913147}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1233944650063446410865346965385063},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1233944650063425906731630998262373}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-24281080242332934604297322153074341717},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-48562160484665869278473013655006889319}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":391083184945487492652950062158527891493},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":782166369890974985075790207321280115131}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":-16336776120151734512002888177352337},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1045553671689711214976776929435490473}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-976974357609206064736938213904786608137},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-488487178804603032574606438268541242173}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":193675787187935607931719772880689428435},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":387351574375871215460836519023620392643}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":12521597821192887056523897555995292269},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":50086391284771548130596153942282411223}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-15435451558224574348582369276916029245},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-1929431444778071804963961187564946109}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-23502726961069868607511326854272771531},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-188021815688558949038065546152585943799}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":94776137156409288784670644639470691457},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":189552274312818577324028376232116829603}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":21269716109463451659594758462653314883},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":85078864437853806545447286832571100513}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":26613215602454567710579093100606869},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":26613215602454529392962180086619351}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-21218342319462478148913240369033096247},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-84873369277849912668766987017203929055}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":124051645652769766913237273473239987581},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":248103291305539533775062556486625392297}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1368039918600707},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-18037803750803989}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":127388703355655981},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":43778661700987213}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-52151480106594319},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-130986559525965529}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2036721810259469},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-48074603678251}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":330982863324071},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-575862144981541}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":27341028559944899},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":1983997097308159}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-2324269683139131},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-32748407586487229}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":5607036447029},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2332163185241577}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":31633835787691},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-297742257728559}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":145612177672913},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":12375176367227}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-5041744249975789},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-42951067718677911}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":300159009491249},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2404223349732399}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1088919887759731},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-4678928553040355}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":6034376938381107},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-7328240371970457}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2963088422728795},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-60426159877219}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":582403280785765},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-658327615201093}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-2031754918196829},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8572397802485775}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":250614037776899},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1607468035410351}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-112766874418031},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1257706090068381}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":44408672734057},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-182687476194357}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1299467429200995},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":603936475406831}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10824666435559395},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":261017047268911}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":62554213114502422167},{"denominator":170141183460469231731687303715884105728,"numerator":112627565817508687407},{"denominator":340282366920938463463374607431768211456,"numerator":162325963200627343865},{"denominator":170141183460469231731687303715884105728,"numerator":38092336602684574499},{"denominator":340282366920938463463374607431768211456,"numerator":54725504947144074579},{"denominator":170141183460469231731687303715884105728,"numerator":33642208750564287409},{"denominator":170141183460469231731687303715884105728,"numerator":45234198516487221841},{"denominator":170141183460469231731687303715884105728,"numerator":22747277496014456133},{"denominator":170141183460469231731687303715884105728,"numerator":10251929154747553823},{"denominator":85070591730234615865843651857942052864,"numerator":8734511131840113523},{"denominator":170141183460469231731687303715884105728,"numerator":57518001918076741433},{"denominator":340282366920938463463374607431768211456,"numerator":103100691183654773057},{"denominator":170141183460469231731687303715884105728,"numerator":103065237273909689143},{"denominator":340282366920938463463374607431768211456,"numerator":201294832060224056331},{"denominator":340282366920938463463374607431768211456,"numerator":95496987918929357951},{"denominator":340282366920938463463374607431768211456,"numerator":45563748544713383501},{"denominator":85070591730234615865843651857942052864,"numerator":22246302803804709929},{"denominator":170141183460469231731687303715884105728,"numerator":61326625216412775723},{"denominator":340282366920938463463374607431768211456,"numerator":46465066870428683251},{"denominator":170141183460469231731687303715884105728,"numerator":9579314147711714233},{"denominator":85070591730234615865843651857942052864,"numerator":9139079309895494467},{"denominator":340282366920938463463374607431768211456,"numerator":102820656722869537319},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":32,"numerator":117},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-3360247722117231775122576864333862551},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1817511892299099317842852034826020789}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-101478604428760032207495916419769011505},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-813513599437824148421559163212533273103}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-175268322612349914187255741059742080849},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-87740843711254367301162442217556705971}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":43783605287794036207551625316604931023},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":86196254290264294858301424786072458711}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":12029854067390701693984812867334975101},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":5715815641188693951677896097832460137}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":201296189618628724302792991010349191271},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":99679806802844900380436643117336556805}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-50371167574213010574706620290632400219},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-12719450391153306753952393906109225323}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":48554436122306905983280130918298189511},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":48331974713226531411648295616527999973}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":7138223674863600348854294285075505},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-5904927095025986087771032183185931}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-48392708298276434435171709186023744321},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-24302896979327281856782757103470457279}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":195574671146840086639947521196365816301},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":781945853637230392810954079655155620447}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-32054678923416145637375390052223525},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1059528323340945666288786628557311445}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-965465255233534499543606479810363250579},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-489137450354757239163788662633159225301}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":387716416257698127208900274464535606475},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":192101383270393055954844072477104326141}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":100494025459350613799199534573963538019},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":97437577272742778685537296035731663257}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-7563652518939409964712358044180087099},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-15486151129132037864162313276812530963}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-93977412527505407632123615630071189819},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-94207620962978672464799914119610732075}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":23724904582173947190275617233351871197},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":189497380336545823801545293682031739811}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":5335554503816030174448712914573122469},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":82565231994822931931467230949749019477}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":29134702464481261317633759266102203},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":12055071361182757120553744794802485}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-82377031626272236572748462192226887845},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-85161019849172187370358325052498803739}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":993701604147330283187709283813676849557},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":490468104155641115419673274887781127421}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-462473176988241793627735748558956503},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3699785415905934478742854556435333591}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-814621068197059299835833841402134385277},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-101827633524632412536937265971202206607}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-87652718579156285963116632921350701921},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-43826359289578143063565321693914042703}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":88435475195819013955404170289464088869},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":44217737597909506898989692650154604033}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":24889483831613533999089706459878715685},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":6222370957903383471339174800609972481}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":202506457616317813474743140886632290611},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":202506457616317813337797863280077098283}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-25598114191789867032495149025270704903},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-204784913534318936444398838076383837893}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":12158167416420854162935811451062127951},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":24316334832841708278663382987239730601}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":905512447324771295963698362416703},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3622049789299042381744895574631281}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-48675801839762389482654640786314463153},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-48675801839762389555182284266327035273}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":195623850542552884795769563195894669471},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":782495402170211538947037433615020255121}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-531901469629440254643503086988815603},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-265950734814720180345283908273797497}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-987213789218353280995417773253005495407},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-493606894609176640708830823477552224195}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":195075776606087054400320021230906811141},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":390151553212174108388603703909490599967}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":51305309606993273318723356319093061613},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":102610619213986546440864817469242949713}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-1962520835360175577644743647371969265},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-15700166682881404716059947164579841181}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-187645324427974675110020059873217888961},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-46911331106993668823111663845358233875}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":94655438808004211244223381952016669917},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":94655438808004211118501083905268974785}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":87325756992741901199590234182999253895},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":43662878496370950551799182115930447361}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":6753313212295359707801585774808993},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":13506626424590699332691018708861935}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-87104285641447597221648440733173204539},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-43552142820723798648575729863326880265}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":125325946013368110790001265544538397593},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1002607568106944886108915227505858426025}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2414864674345129},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-4662541948965933}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":64170947705376381},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":43105960492785295}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-50354135319671081},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-65780977773057035}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":481064166295073},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-571271468278021}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":623527714382521},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-301232494533525}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":3193355353940171},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":422687540776855}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-4402467431373537},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-8000486580651203}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":189896550958015},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2315740032923927}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":251577542946667},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-292108711540879}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1146142995328715},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":25190765660841}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1980288287203081},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-40691034662004277}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1001679358648227},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2607621644495699}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":6307755418189503},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-3828001697914063}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4233484376916757},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2365399117992745}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":928839727341043},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-650585879114823}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1196209439800327},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-155729344598403}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1830608688481279},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8058493308927739}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":904061913667325},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":100244267515277}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-386488875820879},"lo":{"denominator":2658455991569831745807614120560689152,"numerator":-18547694462159}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":174191523593279},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-90885596581993}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1236906590720911},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1118580139728837}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":2582109639954755},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1921276996268347}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":85070591730234615865843651857942052864,"numerator":16212186083852390947},{"denominator":340282366920938463463374607431768211456,"numerator":229789525216282650055},{"denominator":170141183460469231731687303715884105728,"numerator":81986703278182080995},{"denominator":170141183460469231731687303715884105728,"numerator":39355091301089060549},{"denominator":340282366920938463463374607431768211456,"numerator":56865589399873154569},{"denominator":340282366920938463463374607431768211456,"numerator":68463246882188050319},{"denominator":340282366920938463463374607431768211456,"numerator":92207224431379170465},{"denominator":340282366920938463463374607431768211456,"numerator":47206987096592584329},{"denominator":42535295865117307932921825928971026432,"numerator":2675097888226284249},{"denominator":340282366920938463463374607431768211456,"numerator":36262700787776618185},{"denominator":340282366920938463463374607431768211456,"numerator":118002044355235412323},{"denominator":42535295865117307932921825928971026432,"numerator":13255431928569454433},{"denominator":85070591730234615865843651857942052864,"numerator":52778738742910616919},{"denominator":42535295865117307932921825928971026432,"numerator":25751415216967133411},{"denominator":340282366920938463463374607431768211456,"numerator":98288439319137789847},{"denominator":2658455991569831745807614120560689152,"numerator":370703823667132395},{"denominator":170141183460469231731687303715884105728,"numerator":45605549558070770339},{"denominator":340282366920938463463374607431768211456,"numerator":125719082776163086939},{"denominator":21267647932558653966460912964485513216,"numerator":2999695900749963893},{"denominator":170141183460469231731687303715884105728,"numerator":10041367085741188709},{"denominator":170141183460469231731687303715884105728,"numerator":18875415940109710751},{"denominator":85070591730234615865843651857942052864,"numerator":26386051370735184049},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":237},"tube":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1757549033447518420373714273346749983},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3792262222161384069736828716153186771}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-406527048281089897279866118713172174365},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-814912321024495532410763136897297017671}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-175198391815785055040365627106164177975},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-175412074947440617195837739201014075931}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":22151898201763695537978077411016091799},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":43629029421464902380014034622243463351}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":12513011122340138687951185370342756457},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":11901751771425084269900421606270482229}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":101367876602297020261469686458499968223},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":50218400023955083404254730771532761831}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-203071380071969977158470344493850193071},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-205022477565750602095752150208155589239}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":24336417424807316967060945815434631453},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":24246131930714393079359008765723652471}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":29848142052864669852192193311037103},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-22605930287955248928590425590912091}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-48545132908203107908454184996554967337},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-48715408672830720909858775893468872751}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":782645831105066889938266918821741387071},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":782113096422742551202181683576892945409}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-130228475357045721026561893611045077},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1079086491189818173769389894486994583}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-243922955919588942349004456310850848163},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-988517162986858722805221709658212291947}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":195258929839206589142000723542899626221},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":386999764897810997369373748994597935381}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":51466286773487851375450336047923838271},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":49933069563803069992279022475043182909}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-7700247401194690228685185033564382487},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-7875031180370659684745179982989076063}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-187575142229920181425478660325770553401},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-47017861518213036359866022316642003893}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":47396371373846795667903643646451343935},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":23656671708712641456110215464523587879}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":21904200964838251599741663816938680341},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":42398435584399169947528122825496279345}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":14571851025674118595347125646139217},"lo":{"denominator":1329227995784915872903807060280344576,"numerator":97276866736187671355498921384475}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-84593422294922467581405167849128958131},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-10924111515524614715485387740017496393}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":501948230198625695270271056096676722007},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":123892155442004582784193890903786652671}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-964611953042550222013514224664559069},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-964611953042550255629466583696826725}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-408069420136746404286902172182923895351},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-816138840273492809042628227074657747683}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":-2737147192614677441166061377893458885},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-175177420327339356566032740726483527077}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":22365192212499766536096883758672473833},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":89460768849999065981778045856896989363}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":6468491690247984498712353936371602921},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":6468491690247984469175527250128824183}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":203893482065928028175172229907610442805},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":203893482065928028035802441406331830027}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-206242759695932427182920494830373953465},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-103121379847966213685461798683965970289}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":24360448668006513571181479552869475987},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":48720897336013027044414733572898085837}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2443167602025944085556520747324459},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":1221583801012960877718584054503561}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-12188636306772248950849842015057167571},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-48754545227088995878660181815697374861}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":195741936116078421902917108374226458495},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":195741936116078421842390512659728558141}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-542017640516265145968223491295578129},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1084035281032530510082506426249143725}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-997467157083453311935659130891393835725},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-31170848658857916011502055717503205301}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":98239028194497748468976195918546905819},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":24559757048624437090892426230455209537}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":105055875246640326885632106313023592339},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":13131984405830040835416672084675984187}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-15956882843556500768743143996597139575},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-15956882843556500867555657786468159727}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-93620903240449261220487075184628639845},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-46810451620224630656987172422405176485}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":94523458214275004002134037975723128371},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":189046916428550007746564714169162627417}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":89585313902094527441938394207505294309},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":89585313902094527342794625858180413487}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":13681742158064767139601197868525411},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":27363484316129492191909666208787065}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-89347216701324312620953984071282092405},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-89347216701324312698917566334325107063}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1012798557759090372049125896837655630879},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":253199639439772592958110528167347897673}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4116986051553263},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-19416804371905965}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":129583716653742917},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":5299356389742997}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-24014023474635237},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-66049045865158179}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1803068407903937},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-831857401831309}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":588586562609557},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1253728651843733}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":5952355505261003},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":5677643939542229}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-8540870924711755},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-7877126355094621}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":105222456776723},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1142984555464783}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":250230939483241},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-71424572435673}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":140033136467153},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":22954538478249}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1427442994873429},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-19239109484224681}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1601394819143807},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5612963713256287}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":1033137592718077},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5971337758376293}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2461264611341335},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-5803586682144051}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1118265825667913},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-341822616294103}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1224394187652047},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-587440856302473}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1643144568118777},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-472249112764279}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1614893085331357},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":1806827383999}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-647159680234829},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2236117688494625}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":170340757497425},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-180088261600445}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1176697320295943},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":519849918421643}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":9825384545120705},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1767002501156735}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":67220137822852805697},{"denominator":340282366920938463463374607431768211456,"numerator":234368346921637079019},{"denominator":85070591730234615865843651857942052864,"numerator":41415092812065139069},{"denominator":21267647932558653966460912964485513216,"numerator":5081407849486727087},{"denominator":170141183460469231731687303715884105728,"numerator":29536366107439165415},{"denominator":340282366920938463463374607431768211456,"numerator":69675828361598555497},{"denominator":340282366920938463463374607431768211456,"numerator":93990067451531160191},{"denominator":170141183460469231731687303715884105728,"numerator":24486432279704095781},{"denominator":340282366920938463463374607431768211456,"numerator":22329851388023704369},{"denominator":340282366920938463463374607431768211456,"numerator":37629309567181093313},{"denominator":340282366920938463463374607431768211456,"numerator":121035379762506449455},{"denominator":170141183460469231731687303715884105728,"numerator":54534711271281396843},{"denominator":170141183460469231731687303715884105728,"numerator":108098103907552153249},{"denominator":170141183460469231731687303715884105728,"numerator":105402973887232160311},{"denominator":340282366920938463463374607431768211456,"numerator":101146786463540229491},{"denominator":340282366920938463463374607431768211456,"numerator":49405350977413532815},{"denominator":340282366920938463463374607431768211456,"numerator":93485134811847717669},{"denominator":170141183460469231731687303715884105728,"numerator":64424227359312959973},{"denominator":21267647932558653966460912964485513216,"numerator":3098193105978644407},{"denominator":340282366920938463463374607431768211456,"numerator":21043471150254582943},{"denominator":85070591730234615865843651857942052864,"numerator":9745283571029908257},{"denominator":340282366920938463463374607431768211456,"numerator":108338746394360616475},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":4,"numerator":15},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-3671851935918496671176260482002746611},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3951186735792873449632513347668545187}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-814418136091840863093634116046531542995},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-408223728572012615257815683701768355131}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-175064846992358236659361235065201950335},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-175332169398974165098139070543375890371}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":89630812679649310295906627054387075319},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":88302659919837869742654135972186861087}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":13006534273876093221152819433024095093},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":24764641085375905823473483439925272611}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":102057855695425718720681848671887440013},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":202327651641369632881846103695330316361}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-204597329578879867190453354722591134455},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-51618292283317639471382931829828231647}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":48757045432113049436287591537915724455},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":24309425068040062007610003667103090667}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":7810554345965132090611427808918837},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-21470676153291518325169675283587167}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-6082888381456672924677215909243319177},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-48790054932743444249786860198602395227}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":783136243436881556389068859347370113491},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":782424197585025981453478386067089909129}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1059710238749391701086311617293441157},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1100637243844279783093254985112086091}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-985929355327266094794441214620465245429},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-998773694238137956804206798746844489653}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":24582762286828419330468552757489747733},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":194899518640693687477696677376447043355}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":52689425066185716717460727011732665433},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":102303038000832670108191857607771212301}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-15666194538133779172700726282738726867},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-16005915985610033657272953046085743845}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-187168692777544566192357149696123401199},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-187698283500244687414678822924136578817}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":189346856771395431796664933487955828241},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":188987065217525338714483239847754199729}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":89877276435557778852037363185582240287},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":87042254832429025798216252992667050153}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":29098044825161636186597022613571077},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":1603170701218688256087631515223041}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-86822911210385996749937829608785210685},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-11204581940125250183380492331705236709}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":253522056058421480261901206503390395025},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1001331939648418104449060827427333269399}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-1004652045894371746658570062044701421},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4018608183577487125990953778759363873}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-817791214195298654819246787193606615821},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-102223901774412331912163550006638510249}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-174994037468980199590958546276259313855},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-43748509367245049981455295501739644047}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":90468947731659959744006267203972310575},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":45234473865829979788037795105195117551}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":3359882972466826714179126968160328637},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":26879063779734613590733585398140526743}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":25652650801466296867408543979181026847},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":205221206411730374797404664213744851085}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-103820116109500869743541166388389448447},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-207640232219001739678740644224058781937}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":12193665788938300297926045786692241847},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":24387331577876600545057232779775988453}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":6265716875866040723269475816747489},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":6265716875865994138672226303336323}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-48798023941140434218969345928166495903},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-48798023941140434297049549469801946193}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":391791421461955279359385047921332175151},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":391791421461955279235235614958968419167}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-138301783528469584865541655662851469},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1106414268227756903292738083692468393}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-503868530108237255736410572136670928053},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1007737060216474511915587028808127170991}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":98941810123135199038778987977339810813},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":24735452530783799732733824112502199455}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":53753858338218774805970961096502665787},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":53753858338218774701894452978175311857}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-2025643949497591417441058190213191837},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-506410987374397857574797050325584731}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-93406667883489474975393153281514586185},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-186813335766978950142407610841389447217}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":188762433967624527958080569117687387203},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":188762433967624527693988709559530113055}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":91856571438913912988920630837303557431},"lo":{"denominator":1329227995784915872903807060280344576,"numerator":358814732183257472213009423476733263}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":13829848639088266227267184115398299},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":6914924319544122092523783724249147}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-22900299053331607729638564780492758929},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-91601196213326430999052240524356991501}},{"hi":{"denominator":664613997892457936451903530140172288,"numerator":1998024851426214382078816287764917003},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":255747180982555440850483929385021862959}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3285210330510017},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-5070126733410731}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":131048495690206451},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":10385447542292063}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-45187082227699103},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-16542304282706341}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3341153913811637},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1141188273531183}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":280120717538061},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-324041324908605}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":11096736289265155},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":1179022138416331}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-8378413780356133},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-15674330617741815}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":246646444478861},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2244893485321709}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":250279057902489},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-140214163418577}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2182998494323109},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":11977939661993}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1913848241828827},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-18184724083654789}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":593332953057165},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6036999596749161}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5128949283826535},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4296174829293283}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":178138682016363},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13765376588348173}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":653557924435185},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-20172636376239}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1259916824710731},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-273568464959607}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1465890323317603},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-884889303457345}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2851234423408549},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-401036879966679}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-514770805740447},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1051274573406533}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":20885299834161},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-44688077311325}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1120406979630899},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":484433693284209}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":1169306659753915},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":203486829019161}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":69666553906658202623},{"denominator":340282366920938463463374607431768211456,"numerator":238986053076990213985},{"denominator":340282366920938463463374607431768211456,"numerator":167387742189332655353},{"denominator":340282366920938463463374607431768211456,"numerator":83963097325697366325},{"denominator":340282366920938463463374607431768211456,"numerator":61348786970203695905},{"denominator":42535295865117307932921825928971026432,"numerator":8865388139729906169},{"denominator":85070591730234615865843651857942052864,"numerator":23954417649978094693},{"denominator":340282366920938463463374607431768211456,"numerator":50793613023643594955},{"denominator":340282366920938463463374607431768211456,"numerator":23292033271064335761},{"denominator":170141183460469231731687303715884105728,"numerator":19519511124755112791},{"denominator":42535295865117307932921825928971026432,"numerator":15516525645300126951},{"denominator":170141183460469231731687303715884105728,"numerator":56090295293221698287},{"denominator":340282366920938463463374607431768211456,"numerator":221375665230694184265},{"denominator":340282366920938463463374607431768211456,"numerator":215680144089003819173},{"denominator":340282366920938463463374607431768211456,"numerator":104073853541356860711},{"denominator":340282366920938463463374607431768211456,"numerator":51431616517479273375},{"denominator":170141183460469231731687303715884105728,"numerator":47904289236144812823},{"denominator":340282366920938463463374607431768211456,"numerator":132042677507775261845},{"denominator":340282366920938463463374607431768211456,"numerator":51194315324459384741},{"denominator":170141183460469231731687303715884105728,"numerator":11021023349656470355},{"denominator":170141183460469231731687303715884105728,"numerator":20124177363953315601},{"denominator":340282366920938463463374607431768211456,"numerator":111206061565768164477},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":243},"tube":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1915159719942692603354321545476704023},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2055801581366771010081389484489217395}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-407959524118545745184329107495705715271},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-818116968601104672420119506536751776585}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-174874330393090435838742122409355449741},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-21901387123337543469744240097979209397}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":45318461766329487360687176152954885545},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":44665042498185093616467005781335381499}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":27020702998725171079380149512866311391},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":12873275811733011538202274349625744465}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":205436386081902529206845630936816821583},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":25465256035796913210433038623992753099}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-206062678588056869822802578900119173373},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-207863489666812443423981736003643718739}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":48806730681609918914345657054266243619},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":6088920037201671549025023284384602211}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":32740061201010674415784187764629267},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-10104471136984301764458880701103145}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-12186557850394270790802537848823390783},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-48829369656696209565102315845621379097}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":783769359515835828345894462889862110641},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":782878676125255671705525115700028551049}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-269889135163454182210038278437395223},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1124343944440952359803089603142078995}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-249045125147693444918846141785858568133},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-252261766379392275569532550606001662227}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":396137342122464897347578076613861057851},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":392602642850827226355023346451105468057}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":107831737050298422381916777730009438597},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":52373723078672491358412054824724780045}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-7961975803029689502262067078264971307},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-16253263981030596646714230358178656665}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-186737549490890468720958005331094984561},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-187297835035343861950947654862681703377}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":189085407544113008610086841635642401997},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":94350248194241501275949593496352102501}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":92149326075703864319990405449745184305},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":89300423660582378789772872325892855001}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":14496927196889395984569485345372735},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":3293644258325327306481815358477723}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-11133066988385044805813687915427558891},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-91891343849519900190954308603013428343}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":512139741727262018326949453308660142217},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":252880724837121657824181172718821454637}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-4180070442751294077999022616878963669},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-522508805343911777797921777498562717}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-819576065115753891389627683237890614445},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-409788032557876945938488143501542256425}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-174758266420650072535250571717914511193},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-174758266420650072873652938081812153905}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":91460090063961516276347134529503208331},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":11432511257995189512869503645641529277}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":27904619966261961728806749552416366265},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":27904619966261961601413579550220903345}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":206489981914632671596119336704490886137},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":25811247739329083931461294894027435437}},{"hi":{"denominator":332306998946228968225951765070086144,"numerator":-204079663077737902804966482656125047},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-208977574991603612667690489565184645539}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":24396827657945682983133557843757080069},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":12198413828972841465230813621997339015}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3882598086764804623062604537161453},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":1941299043382390167236902694798065}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-12201475129985566374543084761407653389},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-12201475129985566394790129652903573177}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":784340078970110460066415729167811601075},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":196085019742527614952949284685127241869}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1131107224008170757212253288372949907},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-141388403001021373497143588725604609}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-127253256497745484231356168596403730595},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-127253256497745484288021672590668980657}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":398586864088350918041384160527299153527},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":199293432044175458800049369718863611069}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":54982666734603343290595022959132311119},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":109965333469206686367041594894709204153}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-4111132162219669672748429256370453949},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-16444528648878678798057454875447658361}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-93180989469128628269134452226410168817},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-186361978938257256734638375134424828181}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":94229729880584905109717520987024059485},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":47114864940292452487205596029867294351}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":94138562639833474759902666978463240957},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":5883660164989592165885537965397249177}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":27897561112582165880741086073770055},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":27897561112582119720992949322072189}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-93865255211875526590034143840147121011},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-93865255211875526673142694488098779261}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":516590321838419890799608782762391738607},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":516590321838419890685457936474453822225}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1152223434464703},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-21109596874598263}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":8259368432125631},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":40687125377143955}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-10452649610901343},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-65836969094022607}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":762088993757145},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1475675076295235}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":534873393428279},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1330585690321659}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":20783101531869337},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1946449863074573}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-4205269762584849},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-31477446920783001}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":293864317836047},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1093276007069289}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":251037417313535},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-137901690803611}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2111247410103897},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-7401295871409}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-565621194001699},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-17285004193138653}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":175863090822467},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-405493711143959}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":1532323032974813},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2554970282058803}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1056320235299421},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-15896122697306827}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5963829571622065},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":514613785192861}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1303923860784773},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-482769633816661}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2598837206313771},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-3319041242831441}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4931114386133247},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-405801759693659}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-374710824892481},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-491271153899173}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":163630076642731},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-88692266648905}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2140138367886255},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":906060616026407}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":8940230174431441},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1517367077230541}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":170141183460469231731687303715884105728,"numerator":36090234389841502599},{"denominator":340282366920938463463374607431768211456,"numerator":243628570497828516131},{"denominator":170141183460469231731687303715884105728,"numerator":84578125756038300717},{"denominator":340282366920938463463374607431768211456,"numerator":86693290666659825149},{"denominator":170141183460469231731687303715884105728,"numerator":31847826135777928245},{"denominator":42535295865117307932921825928971026432,"numerator":9025755459404105153},{"denominator":340282366920938463463374607431768211456,"numerator":97690872208958492053},{"denominator":170141183460469231731687303715884105728,"numerator":26335345195798207363},{"denominator":21267647932558653966460912964485513216,"numerator":1518020336171756559},{"denominator":170141183460469231731687303715884105728,"numerator":20246513378995458109},{"denominator":340282366920938463463374607431768211456,"numerator":127292575830652179845},{"denominator":340282366920938463463374607431768211456,"numerator":115378852034845146875},{"denominator":340282366920938463463374607431768211456,"numerator":226654609199788071593},{"denominator":340282366920938463463374607431768211456,"numerator":220635290643554961991},{"denominator":42535295865117307932921825928971026432,"numerator":13383937612985561805},{"denominator":340282366920938463463374607431768211456,"numerator":53530975578235620565},{"denominator":340282366920938463463374607431768211456,"numerator":98182715718162570717},{"denominator":340282366920938463463374607431768211456,"numerator":135303051766577016841},{"denominator":85070591730234615865843651857942052864,"numerator":13216558644789568739},{"denominator":170141183460469231731687303715884105728,"numerator":11539851780535439331},{"denominator":5316911983139663491615228241121378304,"numerator":649275910704685925},{"denominator":170141183460469231731687303715884105728,"numerator":57073946769963965601},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":32,"numerator":123},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-3990307435400722369688075971484099305},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4273314917168368539150116539407907541}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-408777412502886890251274254416167006195},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-819918716901022523669531290246036791147}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-174631770184321980539998682041193449211},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-175034289389497779857579237803046174247}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":91626006497192389803793304196477079239},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":45170192823300400330942366428244556457}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":3506096131274370261014630910434287775},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":6687274131865310383867189013858547491}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":206698132823947329507133227877271981429},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":205057103477039602051879268006794808207}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-103733813006977669188600682511369169829},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-209193688064419349476011040364120656459}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":24411042808388560069548556074771267115},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":24382460721018802524298982157030401629}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":17173326173330629552491203868578357},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-18815703249409956620045670847309039}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-48776549820308754328354675750218323371},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-48834973025532819905558088667799864193}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":784544552541490132628816976598267114165},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":195868996574933762557663758899502167045}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1101529884964503266657977607718422047},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1150373717597037389321531784539063539}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1006447865519953556416572579422554291355},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1019339812485163106979058225731406683307}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":49869897880365834501169220281612050097},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":197706290104582293401558782974912903137}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":110290282584247730853621589578247986561},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":107198542686680862576029718642914999447}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-8086658523773384335288369864005144059},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-16491662531886395360093995465939498343}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-93141883558200475138286987803491708275},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-23359022091019285432604196319526865433}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":94401591524877678768170322903756436987},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":188395692228447061753739881108281261823}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":94431993407455256037816675626156757841},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":11446301680301164900381770087156349165}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":14446550287599917491164285146510099},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":13420378255881600484583081136925513}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-45658663442418084100697883175582856139},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-94156020169738795372980691860195691099}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1034472813011162331735010705446843762613},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":255428178508084869507898512993194652783}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-4342636476223342232843849330524470051},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4342636476223342382392063816252893301}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-102686395281192495944150819072424921553},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-821491162249539968049879276767197202321}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-174473179950920657436743535367215849671},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-21809147493865082222346146392939843419}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":92434296960158324915603140629536034499},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":92434296960158324736609534200843498491}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":452351034681251301868948896284554479},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":14475233109800041593690157628896591927}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":25962524223277906833378330241549041647},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":207700193786223254519958872502779096833}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-210255072762798888172981042327847665913},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-105127536381399444186112724850746502503}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":48777591173061120792726141624262293423},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":48777591173061120683512506186059925233}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":2347450136294337919606956380290603},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":9389800545177301038401714779789603}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-24388933483130275178504999994576464075},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-24388933483130275220498583104158901953}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":785238768935917222480557453344981654721},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":785238768935917222219491480398226434303}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-144785664557445049903156179350195001},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1158285316459560636564415975519891781}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-257084159468127287627925101609027311699},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-514168318936254575487891889382307413645}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":401416849243414538518565454112040932527},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":200708424621707269033602428981597546625}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":56213970354069521725193360662861895567},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":56213970354069521615048941110460474351}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-16674574268987851573483203882563179493},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-16674574268987851684896023955780910853}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-92944897102868411497901496439793965683},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-185889794205736823197024695543213160935}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":188140008210906422135107160071135200171},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":188140008210906421857838819022085600119}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":96430318040371039856227507409625422005},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":6026894877523189984190580459774018059}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":28072629715312980396478961088286819},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":28072629715312932080703632664020759}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-96138422700090458021738851464412441223},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-6008651418755653631721034244709054651}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":16302763751924016311911849852232425019},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1043376880123137043728020683604522147427}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1318704537159511},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-22081747617569119}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":33372468367208377},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":39405473623677319}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-18712835981521171},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-65212570986272847}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":86466524819453},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-461743237212433}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":258245158514855},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1363060906274321}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":4915146032850819},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3197605941257297}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-4308233514758285},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-32165026336190859}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":362404038094067},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-264638794105791}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":254026997912763},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-272876722063589}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2027128823772891},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-36050777024691}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-468867738257793},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-33248675891684293}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":224657519320559},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-3494380974086049}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":3574514376708313},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-435780454918501}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2757469911460521},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-9013078221151375}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":6688552758171031},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":539463384241531}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1364130088600117},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-25865262991647}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2271802053872717},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1562561390646363}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2104040086104153},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2466862316349225}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-112740886270031},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-920524777881059}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":161020052671593},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-88332446189713}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1026765640889961},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":423498255709219}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":537460161957697},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":353225389818185}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":74762407016786847309},{"denominator":340282366920938463463374607431768211456,"numerator":248289319893976336853},{"denominator":85070591730234615865843651857942052864,"numerator":42741579538286674291},{"denominator":340282366920938463463374607431768211456,"numerator":89494496263474731889},{"denominator":340282366920938463463374607431768211456,"numerator":66115267276597499385},{"denominator":340282366920938463463374607431768211456,"numerator":73525653225711545181},{"denominator":340282366920938463463374607431768211456,"numerator":99610429407169332401},{"denominator":340282366920938463463374607431768211456,"numerator":54605577961905713897},{"denominator":85070591730234615865843651857942052864,"numerator":6329937400877674557},{"denominator":340282366920938463463374607431768211456,"numerator":41992533494393526741},{"denominator":170141183460469231731687303715884105728,"numerator":65258298284650448479},{"denominator":340282366920938463463374607431768211456,"numerator":118665976560625419557},{"denominator":340282366920938463463374607431768211456,"numerator":232034101355044455119},{"denominator":340282366920938463463374607431768211456,"numerator":225672663731157498523},{"denominator":170141183460469231731687303715884105728,"numerator":55070807369703288615},{"denominator":85070591730234615865843651857942052864,"numerator":13926380262365158111},{"denominator":21267647932558653966460912964485513216,"numerator":6288053881878641151},{"denominator":85070591730234615865843651857942052864,"numerator":34657708263320130315},{"denominator":340282366920938463463374607431768211456,"numerator":54588302242728955501},{"denominator":10633823966279326983230456482242756608,"numerator":754928713179362735},{"denominator":170141183460469231731687303715884105728,"numerator":21449122479040517927},{"denominator":170141183460469231731687303715884105728,"numerator":58582983344720069029},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":249},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-4151620108710336495663897861886175039},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4436123449119912319015143212790805785}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-51207709679424204428273810738881981639},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-205462614330113369056212020945219383219}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-174340251792915781767318553535321352811},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-87402356245199163720511712748990191211}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":23149541373906286124389834503096574629},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":91333637238221112948000105715545865343}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":29097096026240831018316405192238625489},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":13886061313132154721989966006163730689}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":103950670942457755101318315761630966535},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":206333164140156800479362995311101071815}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-208812410618674678260339803976219524501},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-210464054347964020379798544413721505215}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":24403113501418165191681812224424018127},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":48748666617921742629483718177725703781}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":18035813751707619076108012982446371},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-17290339711331282782156579266848625}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-48747727033036944883924802253943559115},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-1525386382522172607318334673823689665}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":785461130667058302774643438580576991775},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":784215517670449588371480882958387714159}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-562898594299851761281669494559776119},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1178897542684375869052479782630273375}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-508367004805359398652091255661698283539},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-514827216661584781385425441801353044173}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":401791575820526482451841149316678713521},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":398230785006998077061016249206841139145}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":56376852311417060038304123468509643179},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":109655514452136971510423077756783277735}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-16413846006104360247466468112451926335},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-16720672433847544682738955043727565387}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-46452342252633247895322456203571155701},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-93211690020668865320282996040499273031}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":94251108461307201537475208423403806129},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":188074645308168474519796670318235934931}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":48362184075398591571981310556101857315},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":46925625458196531299873525064018494341}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":29117021282663810413265914042575935},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":26997323083484385047785050808676839}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-46790152118450466332252871755274298189},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-48214906993323435959894872303755293577}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1044670773768289457443946238986931002217},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1031903962555567595140579165367013576303}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-563263339799675697748580398466549457},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4506106718397405736840401363634890867}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-823534166524239182375018574965718051941},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-823534166524239182881041682795006164267}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-174141946337650397794075241005837274241},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-174141946337650398139809038276416706765}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":46695845795632603182054057767502601233},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":93391691591265206179367114943233923355}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":15008209797552048167889633815170175321},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":15008209797552048099279065363466311471}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":13053266355752147759936708589967992045},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":52213065423008591002301305146416962161}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-211473052176452527135414166078516933571},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-105736526088226263669296404967372429885}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":6090777172305494928748717529246028525},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":24363108689221979658393832695551318735}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":2786144974325197885763612466535503},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":5572289948650369383907305598645157}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-48713644941553294430043776991089776705},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-24356822470776647258561709805669506533}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":12285596302244805654099401946803433151},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":196569540835916890398680151480652094845}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1188123670233007168422933139587576983},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1188123670233007412517771492798194863}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1038671273240073835051797952686195518613},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1038671273240073835526843943707765498617}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":404258997193684843440328188479485938395},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":101064749298421210744681326846711645349}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":114894779744115015054576725147549734179},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":114894779744115014827998667614517930535}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-16894853670795922517571395564694993417},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-4223713417698980658371997962141949787}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-46349707537775139454026147570586995329},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-185398830151100558022285288806776683285}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":187806077127033599112489100478364264403},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":187806077127033598828427654091441897831}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":98730866419529114281209349861852447911},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":98730866419529114168483662294408552731}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":3522543041857759597694524433405799},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":14090172167431013113204031779570275}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-49209863173077439457120611674155623203},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-49209863173077439501404556491699217375}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":526789990608423834759973311530045059515},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1053579981216847669279416823959692719735}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":76253178599641},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-5788554750322531}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":16839628429095655},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":2357658381198617}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-8012666977208117},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-64186324752336137}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2477746926933733},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2238797818462087}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":251575056556135},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-696635180865723}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":18766551110171893},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2645922358014963}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-9033389414300877},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-8302607635226637}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":448902729657319},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1016975575202445}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":258292576986521},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-135245259625847}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1928417639759635},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-147473733055715}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":4974984415447},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-32267622064747167}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-126926977309517},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-3763368565234837}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":16346740172628865},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":777482249021887}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-2196050469899447},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-2514801903870125}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":7389228497973491},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":201336511515895}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1438817070145683},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-340347827929215}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1944779804685737},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2944673458380251}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3496516509132225},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1663374258947485}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-67643313963599},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1716437836219975}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":19892504687255},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-176461190767065}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":987494104540571},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":98647076766083}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":259649871198827},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2621659030793513}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":77414149472093403261},{"denominator":170141183460469231731687303715884105728,"numerator":126481528333988631239},{"denominator":170141183460469231731687303715884105728,"numerator":86409368822245898179},{"denominator":340282366920938463463374607431768211456,"numerator":92368142023512941645},{"denominator":340282366920938463463374607431768211456,"numerator":68609620241466441991},{"denominator":85070591730234615865843651857942052864,"numerator":18720749528133483393},{"denominator":340282366920938463463374607431768211456,"numerator":101577233407550660263},{"denominator":85070591730234615865843651857942052864,"numerator":14149948998623191065},{"denominator":85070591730234615865843651857942052864,"numerator":6596838881946576685},{"denominator":340282366920938463463374607431768211456,"numerator":43538783364438210505},{"denominator":42535295865117307932921825928971026432,"numerator":16725551946925558333},{"denominator":340282366920938463463374607431768211456,"numerator":122043782735017383619},{"denominator":21267647932558653966460912964485513216,"numerator":14844700680113949157},{"denominator":340282366920938463463374607431768211456,"numerator":230793577389174097445},{"denominator":10633823966279326983230456482242756608,"numerator":3540191859322280583},{"denominator":42535295865117307932921825928971026432,"numerator":7244676069935920677},{"denominator":340282366920938463463374607431768211456,"numerator":103088376978658313601},{"denominator":42535295865117307932921825928971026432,"numerator":17753413945118458711},{"denominator":340282366920938463463374607431768211456,"numerator":56362019386460819401},{"denominator":21267647932558653966460912964485513216,"numerator":1579837891583745023},{"denominator":85070591730234615865843651857942052864,"numerator":11070837977936529483},{"denominator":340282366920938463463374607431768211456,"numerator":120262055981774915171},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":16,"numerator":63},"tube":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-1078514887329351454425586913044006759},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4599828818376769969117362236637201627}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-821222420639920283479279200714025893055},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-823909836736117124218552717168737431193}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-43500739063602817983225773113683860265},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-174525427028310589539420957908830587557}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":46776763202673909900028875350783599239},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":46154969066457523753668754950435807271}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":30165499459902165630251520665696400009},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":28815462526233185138172403301468020331}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":13065402433458776738619342008946732719},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":51887652747969225482824423630156110813}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-52524327904909310522268777275007051387},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-211674923051253702928134439179199553645}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":12196731869766127474571352564108516327},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":12173391104757654710673181533434900503}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":37931344425380992660909486406128875},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-7820682092878074811336353070567979}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-24339398770309439042124336370613835007},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-24394437340110368129206832863387423589}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":196629584052399057565299061324001078037},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":196274148698599333109269959902423243759}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1152529199863534320557117435544241553},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1210090365823795107238435229094170549}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-32095045149157975883131038165914585601},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1039993375767594450775265070378668559315}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":404636312161071419346571403900803893601},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":401059131141452662369497463725791531483}},{"hi":{"denominator":1329227995784915872903807060280344576,"numerator":450082997875227934595626108594658123},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":112117573291703564560499837356661527997}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-16645098134297139915327897916951816515},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-16939859481204256496880955374042190743}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-46329062179533401328167930537141220621},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-185953521482137180739730581720287775825}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":94092271543993414371166541534056744183},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":187739194317182762670073855297353861969}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":49512974836176129098991081326674698321},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":96141914525706459919167856523496693027}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":29632099220797905352148664986303343},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":26749921612199446195010813291078917}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-95852445928986397515491251073022179705},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-49356106820013501288983626393950769665}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1054875911255893260839277343490999439291},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":260524802499318810456692485843199966095}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-4670280723556781257307619436663753281},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1167570180889195354401550834248355427}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-825702628053630322287362258473770934069},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-206425657013407580700687619903951601417}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-173767829859198538486322867584414301201},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-43441957464799634708962722099180608231}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":47166209162224994804022571231964062047},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":94332418324449989417409017086679122341}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":15551141827066313923400127659074646795},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":3887785456766578463054606735972568403}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":209946640402099248146570142067797308599},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":209946640402099247993996100362500422835}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-26578985367728958579481579838579316311},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-212631882941831668843061557537652204861}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":48639309974549394770051989183156502779},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":48639309974549394652739729172025454651}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":6517301665549005303448424452440591},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":13034603331097955621933571822584113}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-48612985930783261354186794955567963389},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-48612985930783261444454928886949408197}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":787457445827490281847192801070433210169},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":787457445827490281572848810944305029135}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1220801496103775960561052690198110135},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-610400748051888105798299115970221451}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1049032360979901935520946303775049064687},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1049032360979901936007160121567264982441}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":101778760581412689528596443714126124599},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":407115042325650757642370970045541087779}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":58682559667425102045382181570124099211},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":117365119334850203857744303432588049097}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-1069058586910533546847928878357378433},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-17104937390568536870146346593257046449}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-23111390564868520374161683048885246305},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-23111390564868520400567832934841018691}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":46864911557722735528305535768375682767},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":93729823115445470911113827563766583839}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":50519617777168381355426900869940123373},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":101039235554336762594474284480972192397}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":3527004606391247554228795924674361},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":28216036851129927553264087755212839}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-100708193186648025468083301080215908475},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-25177048296662006389876241903154569527}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1063792478471622107459789018658354822213},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":265948119617905526803226868857601954307}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-702826682223809},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-6082795259145075}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":135530018089005925},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":35514473019957315}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-12757565481397101},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-31301454335507059}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2180320746747985},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1323418621004345}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":247108980337469},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1421203628584463}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":4527548411610817},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":571101811391087}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-9686793689158783},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-8632594529007813}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":550713807086191},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-241687266079479}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":262880458785843},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-268170453940889}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":906093445826063},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-239956922081163}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":300340161418323},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-3956489257719625}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-368237077625159},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8103154547022179}},{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":143680229929785},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2400192465593549}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-2978999193824547},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-22151661347900737}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":8057279203814099},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2107149747435869}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":765140438107793},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-261096984744839}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-404750985179287},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2774111859028729}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":695886797726611},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4199618558586971}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":49469543823305},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-792923540506689}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":157572421606611},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-44108228383161}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":950904734291279},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":366461435478105}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":8069250812583003},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1212665487091273}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":80137477772987655967},{"denominator":170141183460469231731687303715884105728,"numerator":128822051399241605747},{"denominator":85070591730234615865843651857942052864,"numerator":43678541265741112211},{"denominator":170141183460469231731687303715884105728,"numerator":47657824554815061269},{"denominator":170141183460469231731687303715884105728,"numerator":35590371502194871741},{"denominator":340282366920938463463374607431768211456,"numerator":76279107959448003421},{"denominator":340282366920938463463374607431768211456,"numerator":103592037622295400951},{"denominator":85070591730234615865843651857942052864,"numerator":14663721974899415763},{"denominator":21267647932558653966460912964485513216,"numerator":1718263507067799073},{"denominator":170141183460469231731687303715884105728,"numerator":22566520446891927879},{"denominator":340282366920938463463374607431768211456,"numerator":137156018935952502855},{"denominator":85070591730234615865843651857942052864,"numerator":31378522357668820113},{"denominator":340282366920938463463374607431768211456,"numerator":243098913457625249411},{"denominator":170141183460469231731687303715884105728,"numerator":117999652787000789743},{"denominator":340282366920938463463374607431768211456,"numerator":116507054789101885547},{"denominator":340282366920938463463374607431768211456,"numerator":60288846580839015547},{"denominator":85070591730234615865843651857942052864,"numerator":26405658733483604847},{"denominator":340282366920938463463374607431768211456,"numerator":145493752390110034987},{"denominator":85070591730234615865843651857942052864,"numerator":14547229059092424295},{"denominator":85070591730234615865843651857942052864,"numerator":6610029034288380349},{"denominator":170141183460469231731687303715884105728,"numerator":22855124411451185821},{"denominator":340282366920938463463374607431768211456,"numerator":123437949654054302263},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":255},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-4477426324203963805227542472328897007},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2382115133069190786419273713670313969}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-102906212149351392644127498673093558975},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-826094390489091553373005842995421017653}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-10851447543363326286293583074989343873},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-87099794593482820045410725320186712291}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":23623059048301252607011933579056485153},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":46634704428858169520312411828727224299}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":15626890722232989773065607319948731007},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":7469733736293749512206946956400153107}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":52533470244195407650008055393331989241},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":104354929774642333860667776782462626329}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-105661325283336050177808503823602877709},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-13301666666529773009599286860080892587}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":48740011820571157787256291180056299157},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":48602067399299174214590783918198845139}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":19958858300133396028956986411278511},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13846754376192460875127609822083813}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-3035838781194728425990579835906996449},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-6091153179394684588269235013026408931}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":49232209004289089089990666530651392087},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":786118476596450021167483932504070918317}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1181900608055624570333429007130458689},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1244131229829450551228468132678386071}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-129671579133549871874851995094003378909},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1050359034785147575528635877894688649125}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":407495116596267982555566439268816989537},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":201949714185587802623982590688923642715}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":14711522864155446033585633523118176905},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":57291978584883698889516755875622813031}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-4216659496362378079396617117256075053},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-17148794838913614317435737226707976709}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-184806637891292031914594319172787634269},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-185464629291079283145362063454889161571}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":187852146683941989772186113129936904053},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":187391451114858083175215988813233763111}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":101335362080819512081853053473575774013},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":6152592375794941872242941439385322901}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":30091703082304246812457727882643979},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":13181799702072565529203888335115693}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-98132844871284951842239171652756191223},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-25250414904996055640564921602320871875}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":532545377203504430798252866344738195271},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1052301006417940870133073611634269727917}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-4834957733430193731277385861674507629},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4834957733430193897169834925517774777}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-827993983470002075469464427060948391709},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-103499247933750259499277580771475585699}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-173354191157228003043003260226633946201},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-173354191157228003396412814653620129495}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":47628320916046818297414748475607603903},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":95256641832093636398147653378534154727}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":32207848826633755752910577464118456767},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":16103924413316877802623605366553747051}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":3296622196545432606278702648396131977},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":210983820578907686646391140616584404801}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-213731979129473159583188589445067247301},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-213731979129473159794525274963535368871}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":48516674458116492621801987258255444961},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":48516674458116492500254656573312516691}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":7532478127343843602463186402356401},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":3766239063671907483382525332989833}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-48475671376290023486736793759993845245},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-48475671376290023580292028014681339391}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":788775731710008373069796491741393499611},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":394387865855004186394310808128733932979}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-157062779689612294010396687274610025},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-628251118758449305124071231920051505}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-66213890572781816414124787777270687197},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1059422249164509063123585270401077002815}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":102496662437406784660779632319841193887},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":409986649749627138160519662603760627227}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":59919128385760475403548198821834553449},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":29959564192880237641869377776158058549}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-17304401644272276875103055153559647135},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-1081525102767017312531817088542125967}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-184368702985184436469003466394778390447},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-184368702985184436685433500952618837193}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":46775668905573160510883253620818352167},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":46775668905573160436365755892248169939}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":51677226492407735313753206769651692455},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":25838613246203867626840892823064158345}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":28174933526932415792520783727139743},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":7043733381733090124429015198386469}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-51501425168727546440616008456403134491},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-51501425168727546487796831044062366943}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":537008442844806756003123319576189850877},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1074016885689613511752850026253141696491}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1616382181434789},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-25613126694162017}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":135808240214573175},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":1014979974294555}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-2191874239016589},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-60382112242702203}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":468481321160617},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1538365986327361}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":122577232063225},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-725626582966837}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":17793126514379605},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1959489885522935}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-5239497713438569},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-36120049619035951}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":669200345456029},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-454469755046795}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":134812425145867},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-133509424615601}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":842915539638835},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-355791717247403}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":601607957959415},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-31640098128676291}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1198486468223857},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8723928280706143}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":10214885545676445},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3966620334342033}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-7419819118467259},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-12055273720984605}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":2171290560809411},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1277472829357711}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1640121720207867},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-90096833204827}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-631979246871091},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2618247744409367}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2078188559069139},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-159376104584265}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":279064713712147},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1449550275534173}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":78340494403873},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-176814302970645}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1837217064653655},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":669152188031031}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":986860594031933},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2192181615864963}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":82934226159665269959},{"denominator":340282366920938463463374607431768211456,"numerator":262326445114909573233},{"denominator":340282366920938463463374607431768211456,"numerator":176653162598206455799},{"denominator":340282366920938463463374607431768211456,"numerator":98338446457711877943},{"denominator":340282366920938463463374607431768211456,"numerator":73830712584458388045},{"denominator":21267647932558653966460912964485513216,"numerator":4857187351379349533},{"denominator":340282366920938463463374607431768211456,"numerator":105655522232137981377},{"denominator":170141183460469231731687303715884105728,"numerator":30386210901394321265},{"denominator":170141183460469231731687303715884105728,"numerator":14317714906943307633},{"denominator":42535295865117307932921825928971026432,"numerator":5847074539493185567},{"denominator":340282366920938463463374607431768211456,"numerator":140571316888919498973},{"denominator":340282366920938463463374607431768211456,"numerator":129078721761915370261},{"denominator":170141183460469231731687303715884105728,"numerator":124393050703497249201},{"denominator":21267647932558653966460912964485513216,"numerator":15080692998352520199},{"denominator":340282366920938463463374607431768211456,"numerator":119806378161226175239},{"denominator":340282366920938463463374607431768211456,"numerator":62702098973863875407},{"denominator":42535295865117307932921825928971026432,"numerator":13526628876302835637},{"denominator":170141183460469231731687303715884105728,"numerator":74515703172593740823},{"denominator":85070591730234615865843651857942052864,"numerator":15017639204007188151},{"denominator":340282366920938463463374607431768211456,"numerator":27647235613820907737},{"denominator":340282366920938463463374607431768211456,"numerator":47180238555220921139},{"denominator":85070591730234615865843651857942052864,"numerator":31673863774512701845},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":32,"numerator":129},"tube":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-2320760025205623795507817849166309819},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2464563390933292126967735441310350257}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-825402748920499828607589761441409243221},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-51775096265737797837832170597875181009}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-86602119336391725718336791340854865057},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-173830451102133548546870589276059761631}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":11926807752573480480634291888675580923},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":11776523905887667365680775466088379451}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":8090432749380275597599033039678062053},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":3870293132552849647971838951667638451}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":211164163279356025668551881008810809333},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":104905680041202025237300506689842786859}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-212488791628865932922856617923106425475},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-213919704758523290052816823579364220047}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":24328792299818428712004043069836806289},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":24237419174381115442223559386762885073}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":21016602739156956324800012736218905},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-5950271254581254019963179074491879}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-24215690655778173737111451705303935289},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-48633164221808474107814043073101051883}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":789051260876950925692368121356254406549},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":787280355266439098892902220654196958805}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-303522542774533144619194846085852605},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1281203421154566399319510243867152011}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-261932496099960144060061383655670342839},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-265188437550113542261813305986833762277}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":51296205506890716323546424313478316197},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":25422088744454040596078738220476118699}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":120165811488494628928127548315731506383},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":117053931317778601072146164867902858781}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-4269508847422706766411933153383007787},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-17347055398467923904839024816369013389}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-92141280252272497140536770649500723643},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-184958742742770737529372566187478144839}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":187507005167429598172676325846797534981},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":187033415802043037578134500312872751407}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":25912876291066985561709377504434395379},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":100748983375455520410878370288106787433}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":30476531671530706902197963197094369},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":25898539491862956187923158404006961}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-6276283006513480771362359755455091005},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-103297178928539023604653203817602724475}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":537658907137459890605942476424834641433},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1062511885604589032324132199917265070429}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-4999937237597127392714590961144775261},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2499968618798563782175926208023879391}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-207601388288486613419915703402864782973},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-103800694144243306776722224047971466595}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-43226121857247084180916780349008103191},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-5403265232155885533782722064423497601}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":48082273085815880139230451006907677177},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":48082273085815880037789933819010896543}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":2083305799099182501758212415095962683},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":33332892785586919875006111765009274361}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":211964329692954346566332553887850880475},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":211964329692954346407932880702652877725}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-26846725072573935721338071415102773775},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-214773800580591485986267877622472973341}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":48358145807481701032575705450817179385},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":48358145807481700906665218909662963299}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":538773058992233537403081356595791},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":2155092235968926695013456719870543}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-24150756389504244919467678939903650699},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-1509422274344015310496217046138454493}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":790232066242772080422091735354967301517},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":790232066242772080133957858075340454239}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1295413733004674964433843787279640275},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-161926716625584403740084851324944741}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-267460807156529892030213792276025639565},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1069843228626119568630027393642812221041}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":206437706427649136204249755136763068057},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":206437706427649135957570980332767624653}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":61156759495612564045148163412023263327},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":122313518991225127843917651176980646291}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-8746414334516299908741875016636323405},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-17492828669032599947884599782929562109}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-183833577897449810067105485681377813969},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-183833577897449810288831590420861160039}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":93368552104329985685829051085789985489},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":93368552104329985533183817175104733187}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":52837773394869550479827355872661671725},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":105675546789739100835635845174306638691}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":28052159259579406694511595827291627},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":14026079629789674446898455118782847}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-105302725712773929815726995943510047857},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-26325681428193482478279378873509834171}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1084255697658155573120139976794650957751},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1084255697658155572860061207481182509079}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2371083738837741},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-27017879698602893}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":135674636370824655},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":28525005825388357}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-3983364903703939},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-115290309312841483}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1568784049853613},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3515511631079097}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":7704272638581},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1483764117521111}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":17810320089642231},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1762442921585403}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-5713557323297039},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-18972792076447599}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":807215264694065},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1686639011207937}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":277870892079013},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-133011172196027}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":772537169051879},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-492267199300333}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":807329980770731},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-32314219006386575}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1620463514937557},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-1174594908997831}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":22443328054992327},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":2716622450981925}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-544466817602363},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-12981516651433985}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":1157454681936089},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1463748432227347}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1772742016575719},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-24911248801963}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-434754026471553},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4958256573695233}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":691419516842611},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6024550959316095}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":472608680125457},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1304010531455597}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":156493742194499},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-88711660569817}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1782060206857449},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":595570026833941}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":975421119626851},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1900792856113441}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":10633823966279326983230456482242756608,"numerator":2681447104045987787},{"denominator":85070591730234615865843651857942052864,"numerator":66750978642720895571},{"denominator":340282366920938463463374607431768211456,"numerator":178636330543007038431},{"denominator":170141183460469231731687303715884105728,"numerator":50718987520028157139},{"denominator":340282366920938463463374607431768211456,"numerator":76561655019479869135},{"denominator":10633823966279326983230456482242756608,"numerator":2474744145437967905},{"denominator":170141183460469231731687303715884105728,"numerator":53884196958036120505},{"denominator":340282366920938463463374607431768211456,"numerator":62953996343439157041},{"denominator":170141183460469231731687303715884105728,"numerator":14909061764103907475},{"denominator":340282366920938463463374607431768211456,"numerator":48470775127542919143},{"denominator":340282366920938463463374607431768211456,"numerator":144050377865319844985},{"denominator":42535295865117307932921825928971026432,"numerator":16592441170472679535},{"denominator":340282366920938463463374607431768211456,"numerator":254577607227778317151},{"denominator":170141183460469231731687303715884105728,"numerator":123335074510942414161},{"denominator":85070591730234615865843651857942052864,"numerator":30796542938309355793},{"denominator":340282366920938463463374607431768211456,"numerator":65199488681322565863},{"denominator":340282366920938463463374607431768211456,"numerator":110861007995481296971},{"denominator":340282366920938463463374607431768211456,"numerator":152641530215688751643},{"denominator":85070591730234615865843651857942052864,"numerator":15502136243975640463},{"denominator":340282366920938463463374607431768211456,"numerator":28900190384263195899},{"denominator":340282366920938463463374607431768211456,"numerator":48694666530174632659},{"denominator":340282366920938463463374607431768211456,"numerator":130036433368683773651},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":261},"tube":[{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-300383747720166906278936268857934441},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2547158831298951404303516851089630617}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-827679027068554226316822732793669152659},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-830828591083032717843239673267438287601}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-43187415090260035965872007769006785171},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-43355340311423330280573336601644372495}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":96320390319317614846997885685286713743},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":95138447555735416570497627322336841997}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":16744562218359721262624778548214218715},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":32065484869957568169691394226180360893}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":53034454518212423459113754404357489799},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":105427799317568176257080910352743935181}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-106798071573408914187032900588518369189},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-26869312871671392558161710207289821507}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":12134861910154615856905679265043530331},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":48311715815598755369415421240010613253}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":44282911204979028225458439297038685},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-9797629018760712632751520536762393}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-12063123790015354390139096608796517505},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-24250234366824378791242438661702809969}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":790525122970591358699369417921730773727},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":788581354903276929909649638050436070033}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-312320215068489574528272673901415127},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1321494632703358837813916522494601875}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1058115854152564546225960359697985133641},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-535589902136004855113161402441210246597}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":206630738709226054598039969499572558469},"lo":{"denominator":166153499473114484112975882535043072,"numerator":200011123051096965734001556252139643}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":122641463452003340736016008822546097073},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":119526789362578462770973233336083665481}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-1079929113371488610937974860760797483},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-17534224117228408775962169387018378245}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-91873013518732505127831262773785186327},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-184437889201597706288741387353071250537}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":93575540649479299774828975666001978185},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":186667024532299024488408585043721734909}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":105973407017481075123553032887748838113},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":103063458092297069994453630870643804459}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":30781405030493365224126604490786763},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":12675086082146125216898048891682965}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-102714522655423691284013754265200917065},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-52798899737868853628098189271115590341}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1085559582723718336888369302385344078599},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1072734363796935197848903439771894403417}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-5165019523760357186567953311336127461},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5165019523760357364105262039291423729}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-832934538401367429903358889820477474649},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-208233634600341857611702719599400551885}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-172422272406442199534652883768071542403},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-21552784050805274987011667326916102313}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":24264083459118264625721598676833645329},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":97056333836473058293649801608386690809}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":8619295208058276720411706058738336609},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":17238590416116553361446653355524933547}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":106444366528074201511895200192805096685},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":212888733056148402862352425455754024889}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-215757854418040845288198085544176536365},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-215757854418040845508088240767478098367}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":12040897118217539118907766394551741537},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":48163588472870156345226078841124035475}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":611470599158941929681673492117121},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":19567059173086079666357105076784677}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-3005646985338794815160834603665759343},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-48090351765420717143009258416005548215}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":791825422520236158897278162424424349267},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":395912711260118079301028466729472764949}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-41804012286472653078008357846535157},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1337728393167125171501186115617544329}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-540148765243388356660909011369920662097},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1080297530486776713842784069369957977121}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":103945712712994012002290048479444625015},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":415782850851976047504866926108658311021}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":124790263673328847518728590678728231269},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":124790263673328847265424952833517496363}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-8834903523902574019077371215119830197},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-8834903523902574086861751493455916255}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-22910968372968157494552982004780927665},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-183287746983745260183564220200627933487}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":186364848093505647368134276503424737935},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":186364848093505647055475851385000142597}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":27000386593361408057735390700719726497},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":27000386593361408025732672934039289707}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":27842742359724489634312845242502755},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":27842742359724429233086648400073491}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-26901712188159301115095483429186635683},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-107606848752637204560892992903620243131}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":136813923601825909773476932776796398697},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1094511388814607277920883633292220576783}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2801623186984537},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-14345692107059529}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":67430628252017811},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":23280486307304781}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3414141160603225},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-108165260827417577}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1267083825637205},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3958903089757361}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":505903859626463},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-760886523503443}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":18336318200518977},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1666321372987183}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-12465415997579109},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-39996248974254251}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":959859193183835},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1546251402148233}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":288305851492387},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-266557434761195}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1394946250611675},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-653053360574391}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":117569564118593},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-16971781255151151}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1990153321676067},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2534784216645835}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":24443967009762959},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":3398840199209187}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-1230296508274577},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-27697235881956707}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":4885953176626469},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1614826284691159}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":968393231359473},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-12464674101457}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-431996530926005},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4711724136237795}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":697551803792153},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1745389405929291}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":85235565652185},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1148529415786651}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":157192865169613},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-89421914312221}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":434312116635117},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":510821436508411}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":7796066069217795},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1543405693509685}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":42535295865117307932921825928971026432,"numerator":11094463685433010109},{"denominator":664613997892457936451903530140172288,"numerator":530605866998953127},{"denominator":340282366920938463463374607431768211456,"numerator":180664437722634627649},{"denominator":170141183460469231731687303715884105728,"numerator":52307841778008123985},{"denominator":340282366920938463463374607431768211456,"numerator":79375744923498422995},{"denominator":340282366920938463463374607431768211456,"numerator":80710652466514318343},{"denominator":340282366920938463463374607431768211456,"numerator":109931312195162443429},{"denominator":170141183460469231731687303715884105728,"numerator":32600620156621899651},{"denominator":170141183460469231731687303715884105728,"numerator":15520725395846177403},{"denominator":170141183460469231731687303715884105728,"numerator":25108464189435553165},{"denominator":340282366920938463463374607431768211456,"numerator":147593172423227784161},{"denominator":340282366920938463463374607431768211456,"numerator":136498384840491756015},{"denominator":170141183460469231731687303715884105728,"numerator":130237100085876327085},{"denominator":340282366920938463463374607431768211456,"numerator":252137706472652214473},{"denominator":170141183460469231731687303715884105728,"numerator":63324273897856716071},{"denominator":340282366920938463463374607431768211456,"numerator":67783399420430625127},{"denominator":85070591730234615865843651857942052864,"numerator":28392010554346900047},{"denominator":170141183460469231731687303715884105728,"numerator":78162686502249271505},{"denominator":340282366920938463463374607431768211456,"numerator":64004520326390371513},{"denominator":340282366920938463463374607431768211456,"numerator":30200445080074317603},{"denominator":170141183460469231731687303715884105728,"numerator":25127458189960917085},{"denominator":340282366920938463463374607431768211456,"numerator":133462788130887452341},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":8,"numerator":33},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-4971085479361812813032405928026711065},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2629801530857479304927127030092048735}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-830075866995724312112010461084887584221},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-833372728577945727788533984151579805375}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-172262992489252414927838208190347626199},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-172975764644514550653625872736021651297}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":97210225838640643899345438690129925749},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":6003022471372756644836480802021282983}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":8658931441543229830985570578540514813},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":33188133565521808825124314792989714311}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":213055415574355575332879327328914024293},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":105921548964177104930358304305477305411}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-214645159041290443519851630390145831661},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-53982893608575216507095259374471540373}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":24192716126283946621845942687479195461},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":48112567801705971132530088332569531105}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":1458498577685045085036550757214805},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-7532911531055839931603924591904913}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-24018303673021191225150957675723138437},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-48330946716004724100943060179098046271}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":396067947130911642834102205891251524347},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":395010264898105417537298564820659902119}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-321915005246332083479327119656186073},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1365197141178794639082659366150448567}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1068532540782774292516977361656031062731},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-270409854804056762138938858484430690617}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":416172125059028493673927863313502421345},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":412509111499328247275276860126980757351}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":125118499945216823509426659210787748651},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":30500463610195401525826384732222096075}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-17468710705491000105806243011821900207},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-17709890340906997222581311027306110685}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-183199033180199247922556323905196268695},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-183904082866033206107306620278048731917}},{"hi":{"denominator":1329227995784915872903807060280344576,"numerator":729634050191816246848897636815376343},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":23286773805581885122090108586524483883}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":54150048567819063089453532140372606317},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":105383930084639209130827931695921990969}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":31000966260768051982243642296020783},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":24713911465771708126502370646776247}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-105013856262906826106799669511238372131},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-107902550761577863196072931634931873837}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1095818531086327769196074815590514385475},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1082970938388358662156059695224698605529}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-666250776830365579413630446372012627},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2665003107321462409452926378674197919}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-835578018568726431522364592212643542379},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-417789009284363216037559398584054381715}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-171911196079183647839029534498151063409},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-171911196079183648204621472830167044165}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":97932224778478331040722177354299430621},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":48966112389239165412485374747892529161}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":35640466291017083654710434362722320991},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":35640466291017083490157928273902734667}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":213757634963405879019653048899739056333},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":213757634963405878855090182236080281349}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-54171174161637157230720200675123414739},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-108342348323274314573599745212613896553}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":47932896328189445677790551626078871063},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":47932896328189445542756401990316646305}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":22049041107335542810261011914665021},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":22049041107335478196505306840102147}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-47842060118736624240885199000728255143},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-47842060118736624344920142984108895493}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":12399292173085758462189117894999138383},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":793554699077488541277666993864514313727}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":-21619427979744737363354465481826427},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-691821695351831735988833296649753595}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1090787323636244245425263204900421195771},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1090787323636244245958234721240944325435}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":418710406296971913659043299814059920847},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":418710406296971913143634934281013536737}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":127267880317443814090252293753404473931},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":63633940158721906914927115452489204789}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-17834932016980911935846038332643053493},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-17834932016980912076760680286869724483}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-22841649003208294024353183914895977489},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-182733192025666352427501252310529174817}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":92993899461130567388978735253045132241},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":92993899461130567228890559235024650049}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":110331483263845639712254288175574227133},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":110331483263845639580132070427570970941}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":27541619884309281377781885546310089},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":13770809942154609139216830709127965}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-6869640697454602352216529970790366881},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-54957125579636818869595286836325525209}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":69049150742102410228011613867784417289},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1104786411873638563374226236805281941443}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1411462297283057},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-30410099251814057}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":33266701420530793},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":16488836145376929}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":16809325108406187},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-99067738142359573}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":243819676755121},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4396515759549795}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":65643033377471},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1563393999052895}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":9601177852894567},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":442940125357043}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-13555660706250409},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-5295239206326771}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1126112783711157},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1398459957816513}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":75053992387293},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-133568530325491}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1229544705704693},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-416114453754903}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":49383674711117},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-36299026257058759}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2298127614389485},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-10903903251639681}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":6596400425528295},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":4013160737145899}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-10773932427577515},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-29261420300565323}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10203568684799361},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3448635708026991}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2119416434199375},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":20511858194869}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":41629413063919},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-278785651325975}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":19703152904953},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-3985721548189443}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":913468657318837},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-981131338535057}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":39585444801235},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-90302089678623}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":845374215102821},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":418582656982997}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3905495167878907},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1133494805024149}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":91784611005857523439},{"denominator":340282366920938463463374607431768211456,"numerator":276318813492964237403},{"denominator":340282366920938463463374607431768211456,"numerator":182738030634382607497},{"denominator":340282366920938463463374607431768211456,"numerator":107873028032023901009},{"denominator":170141183460469231731687303715884105728,"numerator":41137604387638378415},{"denominator":170141183460469231731687303715884105728,"numerator":41136359017113603505},{"denominator":340282366920938463463374607431768211456,"numerator":112144940735894885195},{"denominator":340282366920938463463374607431768211456,"numerator":67515812531510348543},{"denominator":340282366920938463463374607431768211456,"numerator":32306594176022181359},{"denominator":85070591730234615865843651857942052864,"numerator":13004110276220928231},{"denominator":85070591730234615865843651857942052864,"numerator":37799932781297263269},{"denominator":21267647932558653966460912964485513216,"numerator":8772324219588292677},{"denominator":85070591730234615865843651857942052864,"numerator":66619144632536913535},{"denominator":170141183460469231731687303715884105728,"numerator":128847469511293349075},{"denominator":340282366920938463463374607431768211456,"numerator":130195653957724645991},{"denominator":85070591730234615865843651857942052864,"numerator":17614070445188607669},{"denominator":85070591730234615865843651857942052864,"numerator":29083909848940884423},{"denominator":21267647932558653966460912964485513216,"numerator":10005261277805990017},{"denominator":85070591730234615865843651857942052864,"numerator":16515040393500925287},{"denominator":170141183460469231731687303715884105728,"numerator":15774752319542372993},{"denominator":340282366920938463463374607431768211456,"numerator":51862410987115978837},{"denominator":340282366920938463463374607431768211456,"numerator":136976453791869000757},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":267},"tube":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-642019593245844875091743175584037907},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5424784523902740859074022272287289749}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-416295242666850045597885134561063296835},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-836031016010373478271656473906612147905}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-171747898040316719531055547384011718509},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-43124300722891813317496606693563881169}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":98084190663843523009475888453008264505},"lo":{"denominator":2658455991569831745807614120560689152,"numerator":757360371268131128408873372770690441}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":4475160884050822858237529436783961291},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":34330057916658276040336981046355969451}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":106958782571905325180081888471086858867},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":13298401148733842904606669968169050525}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-107818170156483859370791095898135442217},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-108425740681849492103870563538152074095}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":12048849806094229177088931796092915287},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":47877291709309314381109113321747966701}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":24602737524161296728692392297959973},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1275321668010239966815062947505885}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-47783593316603782191877288227764861863},"lo":{"denominator":2658455991569831745807614120560689152,"numerator":-375972156543058497602617446294543295}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":49617653987325812504678340872369240837},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":791596862378349842882857319825836021115}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1329419548248787946781455370162463147},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1412507997432157463929573980405826365}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1078982283354216474522719974453144905941},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-546067377339909431256850227560542916459}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":52387877296374508089332797710242889823},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":103853485837465678064833524366822687113}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":127596314057579745794342375573304783433},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":124478480297300969651100794506982991627}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-17647157818792226735264660612511797849},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-8936825054460719882082738295383583873}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-22830444812549010282950740334173020187},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-183359323481895613285781809059102047659}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":186414630992636810555694557999719049561},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":46479200500331294670022936308949797215}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":55315303631001136074373952139827680509},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":107709428496939338764506556764765885745}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":15564903516489226329216161935993067},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":23985040359090728913601459318429613}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-107317558096060209335333035047343565705},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-110210464661830160585822019542350080421}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1106097108784287962784091190386958581243},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":136653010824469233561454793615780887931}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-2747350393990794406843184142523556185},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-686837598497698625438280357425704793}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-838332948238827007742948000026999707653},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-838332948238827008304955918781945367867}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-171375004117823232519636534405106615327},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-42843751029455808222368008709613834531}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":98792455402677752737695596832548574869},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":12349056925334719064408391139811128517}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":36822490913160768947725257631480199251},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":36822490913160768777198458265654622179}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":53642919983193299144405257748209624537},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":107285839966386598204922296108527040463}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-27194366728700013172032468600283280833},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-217554933829600105605109926966694838799}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":11916498145758790698615458624424930009},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":47665992583035162654660477153626249957}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":6172953375206420037118893873188991},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":24691813500825612918367721891266085}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-47556539772916318869916121904771747737},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-47556539772916318977659644285514978523}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":198854679295602651405595621882980539945},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":198854679295602651328150825644609741997}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-358340215443279250591437511477805715},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-716680430886558645505261991912952437}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1101314712158733018635029530858343603985},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1101314712158733019180219359581995590621}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":210829721308216419568112082596781596533},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":210829721308216419304759520689908112289}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":129745791300474473572849719318348294255},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":129745791300474473305183390247819028261}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-17987805756691394771568700580904299981},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-17987805756691394918012197349386162507}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-182171877492926373933134095001997246813},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-2846435585826974596429210355292248585}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":185607822183885711033214711961410497941},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":185607822183885710705368006456648050845}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":28166097980414822750220272100768648637},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":112664391921659290864524744940404920691}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":27143643549923180428205476883209503},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":27143643549923114530034042908283743}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-56111983821269155667563496930259772507},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-112223967642538311442165522903169130771}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":69692699775714586177370871492899510991},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1115083196411433378556768087493847608435}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-640126100278241},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-32124418139294023}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":129947323055570711},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":7989939975800385}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":16287254456514593},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-21946365095117803}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":349472417126379},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4828469572252645}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":275674243751929},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1608777639873051}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":10187654515814795},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2086387267939157}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-14675775212048171},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-44889627161457351}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":327793335213421},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-621367362294629}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":313031421595959},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-267547413486359}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1049511068652299},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-64257685162029}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":170333180009261},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-4912627919772785}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2557184088914963},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-5839020237386749}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":14111944966137371},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":4549323838095843}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-5729715164556619},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-30608855983415179}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":1317426838240383},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":222791238574067}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":579959641758431},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":106436426611721}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":551408943358411},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1049663936817947}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-324460307861177},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8977591924836007}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":582321745789855},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-400451822391253}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":159852235664569},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-183035016524051}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":820098623771137},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":158629499977545}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3920332937929391},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":678927056021625}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":94895155330310172457},{"denominator":340282366920938463463374607431768211456,"numerator":280942980685932944943},{"denominator":340282366920938463463374607431768211456,"numerator":184857570232027611199},{"denominator":42535295865117307932921825928971026432,"numerator":13901433768728315083},{"denominator":340282366920938463463374607431768211456,"numerator":85262319619849100081},{"denominator":170141183460469231731687303715884105728,"numerator":41939537463505181697},{"denominator":340282366920938463463374607431768211456,"numerator":114409982156239591477},{"denominator":664613997892457936451903530140172288,"numerator":136522268980476589},{"denominator":85070591730234615865843651857942052864,"numerator":8403690909345800945},{"denominator":340282366920938463463374607431768211456,"numerator":53870722373355993011},{"denominator":170141183460469231731687303715884105728,"numerator":77434885815941247747},{"denominator":340282366920938463463374607431768211456,"numerator":144317826540764411739},{"denominator":340282366920938463463374607431768211456,"numerator":272585351740697951789},{"denominator":340282366920938463463374607431768211456,"numerator":263342987194046333273},{"denominator":5316911983139663491615228241121378304,"numerator":2091088705590941625},{"denominator":340282366920938463463374607431768211456,"numerator":73220641683170720261},{"denominator":340282366920938463463374607431768211456,"numerator":119165308836008016213},{"denominator":340282366920938463463374607431768211456,"numerator":163919188416726666721},{"denominator":85070591730234615865843651857942052864,"numerator":17044297239441663955},{"denominator":340282366920938463463374607431768211456,"numerator":32948914273361368569},{"denominator":170141183460469231731687303715884105728,"numerator":26759301526100499643},{"denominator":340282366920938463463374607431768211456,"numerator":140579347326862365131},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":32,"numerator":135},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-5301155182633417954288028100576575287},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5589665502728484764498180605548577019}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-417609988565907285815478853306852536127},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-419400195750466585272513280202033258973}},{"hi":{"denominator":664613997892457936451903530140172288,"numerator":-334390889913371439842205065155474585},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-171989313906243367205222859682343412187}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":98942523207192724707227368999783625297},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":3056874043672189526189167096385568411}},{"hi":{"denominator":664613997892457936451903530140172288,"numerator":72237400251531671125235367954722797},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":4436376583074814156742482946488694709}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":107362458268438004100906813664108232717},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":213650159233020308927676465870395899167}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-216570236633058370291761562910772333421},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-108857418383980478301476979304481166607}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":23984619390793260206172405937599690757},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":47605814247615773066802211583017532559}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":25944315266285284497480538040216577},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1248825723993250933319294795220367}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-23746679326797553111669630055070336129},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-23940402362987285401436787329442863235}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":397881821505687775197599273241505427187},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":793309260862612206931274598884789891927}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1374756075440925266697200480388499675},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-182953653508538064034006423231145081}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1089467259022307390356062792887745426719},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-551333952580837970524033455407739930841}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":422055509292931363679430654054776285093},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":418338728186309751972990965172926202969}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":32518582970563746629916545926786527183},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":126956052365798127975430680349290525721}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-17813801525268223013218339082010687479},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-4506276610598778059873832347327773015}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-45520391268248561563233218128502667495},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-182805595020407697558008850310033814861}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":23254739832495495114654594574126384551},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":185536721282935699524443897922826212701}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":7060248261485700406612140110575345043},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":110038984494965021032836273367497881463}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":15581217278353806614001247327325011},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":2894844448625496550481350490765873}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-54812329746268431936170374489279273979},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-56260288079952300751789026160204256891}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":558198870951905163473607732413896223095},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":551748132046254183710835938945889095149}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-5658909075792004231311207848262384047},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5658909075792004427521843592184658661}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-105149519306336680304805855806211560873},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-420598077225346721504822255207247637205}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-170817536954415973377931353963882957259},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-170817536954415973752101933750218071581}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":99637277535103112526964560585616254097},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":49818638767551556148846981275825750603}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":19011492643893041668570229661633342781},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":38022985287786083160459430696326401639}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":215331554034426991022728000082059950781},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":215331554034426990851647222111224467685}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-218369224829974852335353341174069996205},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-109184612414987426284419484292729364431}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":11840707413438891251575474679045374207},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":47362829653755564861591865939091769353}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":27500514173937659230166580081956245},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":27500514173937589295176756539858951}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-11808430692067773462047993777120081385},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-47233722768271093959756497168110337947}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":199354054458377659266442619688958528285},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":797416217833510636748522181597115686957}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1487088116739920396815951039191955815},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-371772029184980173397491682952926649}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1111881732710424654856747495788109795837},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-138985216588803081926796164210192058549}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":212315620811976704021133311896367036061},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":424631241623953407504081089822828581237}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":66111726454935023600351564088617009379},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":132223452909870046925590313416841382875}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-18128037663629286313912522155346473597},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-18128037663629286466072963788272056755}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-22700718642014657156192455567435198233},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-181605749136117257493661824462675753463}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":185226755467154800244647819234347886221},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":92613377733577399954487980007418916427}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":114999310560799785106586226569035893661},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":28749827640199946241467368478228947233}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":13321793126128098607616297743650269},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":6660896563064032103590917810853933}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-57267518337275174630528385105020482199},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-3579219896079698417859628611720175763}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":140675518425186836159814315140588969899},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":562702073700747344494980012068052613203}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1953121576814955},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-4215501124595915}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":62324832908003013},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1785955343016179}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":49906486631322703},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-73549481836169185}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":214411474233189},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5206765020916907}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":575198574776713},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-825776006742941}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":21853486131359191},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1304023047846695}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-3949620853915773},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-47332687603442719}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":375631724797687},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1072898888771657}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":327118301119335},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-267211949229093}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":213967720667207},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-19432828695833}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-50799928428933},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-21486712863019359}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2772044649703285},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12419798980029485}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":29792316936220561},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":10032996634795525}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-2980186796682139},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-31538354371310111}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":1338131920375229},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3589344425263715}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1266799369051595},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":174466742912473}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1098841873381239},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1959869593167107}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1316758228108703},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-4974298531619913}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":713293236901777},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-302895097708525}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":161963000824991},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-23138200619357}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":98940458515913},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":50948914602277}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":7878513105307825},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":172800509056557}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":85070591730234615865843651857942052864,"numerator":24522358107062790281},{"denominator":170141183460469231731687303715884105728,"numerator":142767807085910941305},{"denominator":21267647932558653966460912964485513216,"numerator":11688972619308363201},{"denominator":170141183460469231731687303715884105728,"numerator":57316240611498842401},{"denominator":340282366920938463463374607431768211456,"numerator":88339400938176010663},{"denominator":340282366920938463463374607431768211456,"numerator":85530766265399908647},{"denominator":170141183460469231731687303715884105728,"numerator":58363523301800238257},{"denominator":170141183460469231731687303715884105728,"numerator":36176864337825441267},{"denominator":1329227995784915872903807060280344576,"numerator":136590616197835447},{"denominator":340282366920938463463374607431768211456,"numerator":55781211243855405133},{"denominator":42535295865117307932921825928971026432,"numerator":19825358133276238683},{"denominator":170141183460469231731687303715884105728,"numerator":74191091984572356145},{"denominator":340282366920938463463374607431768211456,"numerator":278801029286562623759},{"denominator":42535295865117307932921825928971026432,"numerator":33635369772670056833},{"denominator":170141183460469231731687303715884105728,"numerator":68776424762363724441},{"denominator":85070591730234615865843651857942052864,"numerator":19019760312616299055},{"denominator":42535295865117307932921825928971026432,"numerator":15257322583883403259},{"denominator":340282366920938463463374607431768211456,"numerator":167831613690337461121},{"denominator":340282366920938463463374607431768211456,"numerator":70357360139725442061},{"denominator":340282366920938463463374607431768211456,"numerator":34400260927819052479},{"denominator":170141183460469231731687303715884105728,"numerator":27612491528331703629},{"denominator":170141183460469231731687303715884105728,"numerator":72136697819002570379},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":273},"tube":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-2732942001268341466193050864061130549},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1438512964246435436347191274586879565}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-837961641891458012664058115039862929303},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-841674705365147963452956962712207457245}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-170651998407415174929776758820035627083},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-171455338085646350440549287973726778857}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":12473184646512785479243286284389919969},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":12335264956314933907204513870982606473}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":2386765050457654038363531284083646381},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":9167685231230145087726891108671795115}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":215478161245500321082520273220120303361},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":107235479893457313500884758152855402797}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-217447448012172652242849794372177516035},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-109261153093223591788474668237020783385}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":47706870503552531125642057740298908507},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":47298091298378847813839827513330279349}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":6840824477562505596854204647730159},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":283095810492803468017005948837495}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-47165839024067716478985454676045190323},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-23799975483616415183200610576562658359}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":199444540671943297631452396154375332109},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":397578278285351825700012413275992505327}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-711935677579336425695872826477033445},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-189845802662889295141473422937796379}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-549994793889721987781298736011131204557},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-17394387993317725098233094659125798473}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":425030780078042657885951572021104702037},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":52660606195642857336239428327472698447}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":132552009891588851872042694903443123129},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":129433989234795097908865689486191544881}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-17968243105810140907278293476792454399},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-18163869614622679550182362318887654661}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-181514996067558458602289505206944394171},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-91122432158983626839578062465506553099}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":92829024331999121429589338170374018005},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":185155783862872924599539034746395910879}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":115299230554610663215518684782526767449},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":112371632073553582825525418046944353767}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":31093278571453858052068374036835057},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":22230173736898363747911966760581121}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-111934194702430662541786661047923785907},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-114831924103507150475189986974858121425}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":563361415861408406942485818967205379471},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":556894951799528720649039401933613448325}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-1455609934694061673595268078566257729},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5822439738776246897153860031616348597}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-211041083509574163050047083390919056211},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-844164334038296652780491997021057511673}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-85121364238309062126812536048918760663},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-170242728476618124632216973873546184841}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":50233478682407464650429968341369686273},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":100466957364814929064579413399219921161}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":19620834629754472193237434360427382113},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":19620834629754472101727496032299325161}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":108018993149428562916238265802502174171},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":216037986298857125657998570621067792667}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-219128282600514597130192652743517267461},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-219128282600514597368418188818503181039}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":47023388992567217598753334997568225689},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":47023388992567217448989687956580218173}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":30480288594816595543167366815006723},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":30480288594816522812231201289831357}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-23436785583755377001297235224572052975},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-46873571167510754118095356876339699345}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":49971616154708177005947174989638679373},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":799545858475330831770312122177523152179}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-772518929068747830364844704023520729},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1545037858137495965843923747660281425}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-140311293981340548858090956953628031845},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-35077823495335137232343599301800562659}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":213813500521622850322580819600680437279},"lo":{"denominator":1329227995784915872903807060280344576,"numerator":1670417972825178515997307940552439697}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":16837544543739438756220642230112645917},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":33675089087478877441755856032518964321}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-18255244606253233960160350742235673847},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-18255244606253234118231023774915513049}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-90518366267465225220292310003559757521},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-181036732534930450690623915488760519685}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":92423203335497620303867815921688492545},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":184846406670995240264081661517885485633}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":117335281979706464988606148770926607111},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":117335281979706464843399145933197373357}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":13018074608269984483299757916304511},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":26036149216539897155901058355588955}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-116846501253586285695593132555583314103},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-14605812656698285726195091731256647293}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1135751643696950950451408646946281591009},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":283937910924237737538819824402470542083}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1039389739798785},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-34744818554865409}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":14364169342844643},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-5626704616807653}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":33152367075243321},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-13552621495419245}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":117246894531677},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1347330951305631}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":286095798108923},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-833471587512517}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":11818264431429617},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":834833117541379}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-8448058868006787},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-24611341002780713}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":211581690796813},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-442609654690183}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":10650150547755},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-266405468958881}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":162716912243721},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1475812367641291}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-398172718348333},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-5911351982713299}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-743514130642123},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12968496220658369}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":7649518015110975},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":5460429406805687}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-6134561252432747},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-31484656777746553}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10494381559192149},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3574657457231719}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2730026234973737},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":16066955809159}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":837199818774383},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3610014320906177}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2014286873689461},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-5367218456794163}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1679780235199571},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-390913004252991}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":164197145836013},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-187070586926561}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":379240903025461},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":4802890540941}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3941228859389155},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-23917382588323}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":42535295865117307932921825928971026432,"numerator":12671192643033515691},{"denominator":340282366920938463463374607431768211456,"numerator":290088748346702457189},{"denominator":170141183460469231731687303715884105728,"numerator":94617846638894124973},{"denominator":340282366920938463463374607431768211456,"numerator":118137508356409848591},{"denominator":340282366920938463463374607431768211456,"numerator":91508818760742435511},{"denominator":170141183460469231731687303715884105728,"numerator":43614415946885965489},{"denominator":170141183460469231731687303715884105728,"numerator":59548302377679091431},{"denominator":170141183460469231731687303715884105728,"numerator":37440267292038063161},{"denominator":170141183460469231731687303715884105728,"numerator":18182582238809672081},{"denominator":340282366920938463463374607431768211456,"numerator":57749379873589488609},{"denominator":340282366920938463463374607431768211456,"numerator":162398489765853702363},{"denominator":85070591730234615865843651857942052864,"numerator":38138029987489393761},{"denominator":85070591730234615865843651857942052864,"numerator":71280980601918364725},{"denominator":85070591730234615865843651857942052864,"numerator":68728948860707928883},{"denominator":170141183460469231731687303715884105728,"numerator":70683698496680837405},{"denominator":85070591730234615865843651857942052864,"numerator":19758525009717226501},{"denominator":340282366920938463463374607431768211456,"numerator":125017005533841274849},{"denominator":340282366920938463463374607431768211456,"numerator":171822625087725800295},{"denominator":340282366920938463463374607431768211456,"numerator":72602466072244890595},{"denominator":170141183460469231731687303715884105728,"numerator":17952586797436064373},{"denominator":170141183460469231731687303715884105728,"numerator":28491540294276604363},{"denominator":340282366920938463463374607431768211456,"numerator":148060542100279615599},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":16,"numerator":69},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-5630148715142484062795440773621776847},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1479438080409421436988277330251148323}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-840813341579642254712764534588619340587},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-844641470290154131969587651000327549001}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-85048591703959120685680556630617080041},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-170897576237360166238850914048885534587}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":12576665061454630668279278081993511929},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":49764414158855226535039188814530203393}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":39409081496813386847855376904271937243},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":37868974597894160528526547539996535955}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":3377781779944761784577149558959339703},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":107618750357100286350196369285545760017}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-218268626534525826220545589088088685849},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-109637304744508043684311553874439266925}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":47408243199796309036307390638318931841},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":46954107739388868736252473615967837269}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":28862281401871391675921234307520469},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1623027473354695652309575189899597}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-5850125011377899214966914227499576183},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-23640901532871541437657203336673890309}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":799924669638536339125047505253417870157},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":797137500966285558706686034279857304873}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-369243197217647229406293620681302017},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-789063033781951854766468924184714993}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1110551342786269033721924974807834849789},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1123855242027825245070150182411561054715}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":428029685442871407939652431212754803933},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":424253636755184740789017607201834194765}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":135028829467659693310303002571460106729},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":65955872201724487552533340522107248137}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-9055045512912027724310935261853081949},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-2286194675484545512691048080135750667}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-180945774290750894525529738016695577553},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-90839539837245648911727139378282511813}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":46319215410655054989691636990734878109},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":92387899943983011408789631438023252921}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":117635425728053341896409157987886802599},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":114706408875549389751365064326916425685}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":30916698981129412802262600987209025},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":2649292236731989330944005797197731}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-57122600820832445073348569333202116675},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-117143551970519481290293451903748288275}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1137074753183894747227658129090775697629},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":140513426678209057537110307084322962651}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-5985104711435139426912884981214116971},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5985104711435139636411248219045066271}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-847234051123996682037668801198667573671},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-211808512780999170656745036533431946585}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-84827302146306952621629602327561765517},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-169654604292613905626360205766600795711}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":101281774361410802690857737461174390123},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":101281774361410802447396531722807067921}},{"hi":{"denominator":332306998946228968225951765070086144,"numerator":39529543311946806183071291464277907},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":40478252351433529341916839520285454019}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":108345875097231658139865095919806481307},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":216691750194463316101760293608281236445}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-54958219002810207337507383130714206523},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-13739554750702551849568787951096590241}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":11661920218465935839745934670041202265},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":23323840436931871602008984281307713753}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":16818144980212012718025561939595891},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":4204536245052993726939745292398329}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-11619019232810183217250094167212582959},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-46476076931240732988555993477058038053}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":200451552361023111694265506213892194233},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":801806209444092446444519648161817102703}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-803714201723106809716803000419385911},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-803714201723106966551299107251028277}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-566571231665577647560919370591689360529},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1133142463331155295704966248168136300959}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":215323916021060930752953362393778382659},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":215323916021060930472101874190213256153}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":137176028717599259886807838635610143361},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":68588014358799629798125093259497353121}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-4592262790575529932662581253264603781},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-9184525581151059947414908980889119613}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-90233365799669628680659762772648037657},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-90233365799669628808704654310051720181}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":92234276084358605085522154782610453501},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":184468552168717209819248904612660040085}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":59835677201657531731848890189307964921},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":119671354403315063313867009852872418661}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":25315969802942646265858149353372249},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":12657984901471285667425784452091541}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-119157409677189001945720170423074167775},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-119157409677189002063310599268839937643}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1146128036454487330030868087054544886617},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1146128036454487329726974047671433470511}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":214905903129215},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-35522369902495525}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":51962499352778717},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-22910498465433287}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":85181839665468975},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-8325573683564461}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-139051993762273},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5557012670205179}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":143230517930771},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-420968724748923}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":3208214619304131},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":2172027889438855}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-17705765011816983},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-25533718513849785}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1900559831979387},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-11159055787175}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":355607657543163},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-132904119783437}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":438746877272481},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-862798949070713}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1703204843083289},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-52070856814340089}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-3093391008631627},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13450154455667807}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":3908796014627039},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":11529369618751461}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-764517800906815},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-7802315635486193}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5095776252899737},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1703964181266619}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":730696556755481},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":335859343295311}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2297304262991531},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3244811944747051}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-333221709580123},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11533597416899611}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":976223036930647},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-43118966290161}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":168460786859073},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-47350628381883}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":358734677297225},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-32845204177417}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":7785461756583243},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-994287865903975}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":104731312981012662279},{"denominator":340282366920938463463374607431768211456,"numerator":294592254718944610973},{"denominator":10633823966279326983230456482242756608,"numerator":5984101827766836529},{"denominator":340282366920938463463374607431768211456,"numerator":121727893888845439647},{"denominator":170141183460469231731687303715884105728,"numerator":47386476535541100993},{"denominator":170141183460469231731687303715884105728,"numerator":44487144142539042707},{"denominator":85070591730234615865843651857942052864,"numerator":30379714127834091897},{"denominator":340282366920938463463374607431768211456,"numerator":77481577689073511483},{"denominator":85070591730234615865843651857942052864,"numerator":9452488968205361889},{"denominator":170141183460469231731687303715884105728,"numerator":29888363115858073077},{"denominator":170141183460469231731687303715884105728,"numerator":83123428061655875179},{"denominator":340282366920938463463374607431768211456,"numerator":156829317725108124275},{"denominator":85070591730234615865843651857942052864,"numerator":72888470748282414381},{"denominator":340282366920938463463374607431768211456,"numerator":280841999714701408639},{"denominator":340282366920938463463374607431768211456,"numerator":145275434246236085441},{"denominator":42535295865117307932921825928971026432,"numerator":10261056626364756093},{"denominator":21267647932558653966460912964485513216,"numerator":8002632529956238327},{"denominator":21267647932558653966460912964485513216,"numerator":10993329285275644009},{"denominator":340282366920938463463374607431768211456,"numerator":74914322801902244621},{"denominator":1329227995784915872903807060280344576,"numerator":146348923275681255},{"denominator":170141183460469231731687303715884105728,"numerator":29397232054162056533},{"denominator":340282366920938463463374607431768211456,"numerator":151942629816744464443},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":279},"tube":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-1448457582343929255879834431622194651},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1519981105845253433034170351307011543}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-843770194453912599112716305286089759269},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-847711590297753129987436585862931159463}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-169525372385796224522561728741246858065},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-85161217354465834544422667344068791439}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":6339123279468388102325257297942804515},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":25090100032684863361349722639613641217}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":40647442368461846338793450668237516815},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":9771368061850766547104346327186825857}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":108412534513129642218617463518377422149},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":215950532662479108015861197441655536313}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-13689656777419555700512968494607473111},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-219972250056729950428059062012673291073}},{"hi":{"denominator":1329227995784915872903807060280344576,"numerator":183880069511242721102758996622093811},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":46574209771768946566776623957401371901}},{"hi":{"denominator":1329227995784915872903807060280344576,"numerator":237229649214730555392686334929913},"lo":{"denominator":1329227995784915872903807060280344576,"numerator":25546126382515920566500104581189}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-46399147018164742628961478631953486089},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-46926284961882533172443565814496306991}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":802200777184648980510210280450910618101},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":99906358438453601905457096376740245113}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1534550228637276246722228161074845427},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1639426523639470386796838431773550179}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-560577391240885445829788313052213545051},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-141813809521413235463885864893921935141}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":107762874879032008073522793948415859495},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":213623250606462720481056508323419940599}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":137503690741055652426195657198175849137},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":134388874750899938360448731322617718683}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-18239005704008868873775142595809509465},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-18401394726452519737627221861047897733}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-180376433647405350145945895772542648123},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-181110099077988795195588140146009533809}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":92448052163125704641798730652893002281},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":184399127773689722524979168880719065397}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":119971146725089906827357926428240591329},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":3657575253722134519467477537169131551}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":29644692041604926743198464172892411},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":10494524776344158158599466756090945}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-7284798642184094294343774621953938665},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-119454008061353278570427777795442717715}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1147452101945624155600291205107857832461},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":141806449097553963138229191233221397157}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-6146719613141082341266611565867200163},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-768339951642635319706037385413939713}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-850401734813572899184492349802927728053},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-106300216851696612472837282018845166405}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-169057279524492186546750340237652056109},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-169057279524492186934450082377361021155}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":25520505042377516239533495759659023003},"lo":{"denominator":1329227995784915872903807060280344576,"numerator":398757891287148690262962140231721615}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":20866217096243798092397292567209167799},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":41732434192487595988523729926031427281}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":27161708145584684114992657292060848313},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":108646832582338736369191256271376597349}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-110241915849220555273606334755667946141},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-6890119740576284712351127506778582599}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":46235744137014657043099322095313611501},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":46235744137014656882779276237178348269}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":18486839859995906193305093363916931},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":36973679719991733780159746988902333}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-23020630876026212645959940560083218533},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-46041261752052425415651696633409670621}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":100524468769640129634594292318509073123},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":804195750157121036736423608438414178383}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-209310488755495333532967857630145121},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1674483910043962990705382828389247323}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-571919942673401689864191965003556413691},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-17872498208543802817571657019044609519}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":216847378393008241479636376785545098959},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":433694756786016482385528715291868611175}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":139650033944305624906977405689049301993},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":69825016972152812304206023478443170657}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-18469089838604774855013509695707986311},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-9234544919302387512752882688733289481}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-89948813510765382136928386631003008483},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-22487203377691345567016684000098448311}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":184094934926486771448727458525186582495},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":11505933432905423193039309529175590551}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":122006582335235485597293461884112078365},"lo":{"denominator":2658455991569831745807614120560689152,"numerator":953176424494027230021106644134795763}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":3059703748725225913976263435313867},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":24477629989801729146580914264719761}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-30366704081091246225031063324738209889},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-30366704081091246255361825728768221681}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1156535647495259369327078875699975057851},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":144566955936907421126903367437813917509}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1900246041159823},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-36060615258850029}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":22899344618928029},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-36983751941171531}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":53378424984743047},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2698796577290699}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-81785666382943},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5705725708708111}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":579591341130049},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-852898559180673}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":28051391865041991},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":5537688860181529}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-18182125496315141},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-26400947970638061}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2114423943706769},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-279232232970415}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":371588735007687},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-266885212044305}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":122936681918229},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1982913409253799}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-1440406053629313},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-57552063156370799}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-3103567460700369},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13870115607674359}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":15894876375029641},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":738622876343049}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-11756376179130785},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-30681247913756989}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":9785668497091539},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":383598979703619}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3115642429219009},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":406293498323703}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1497294593702469},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2826475544228263}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-3267787374968935},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-6173839276280095}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":280594447398223},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":6600471431313}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":21805012206953},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-192907776241751}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":83690911341135},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-231860994257313}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":950005746208171},"lo":{"denominator":1329227995784915872903807060280344576,"numerator":-6660658306731}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":85070591730234615865843651857942052864,"numerator":27042965832018038461},{"denominator":340282366920938463463374607431768211456,"numerator":299038662608708359769},{"denominator":340282366920938463463374607431768211456,"numerator":193791095051715158077},{"denominator":85070591730234615865843651857942052864,"numerator":31351287069534022779},{"denominator":85070591730234615865843651857942052864,"numerator":24533571227490927115},{"denominator":340282366920938463463374607431768211456,"numerator":90768116045364365671},{"denominator":42535295865117307932921825928971026432,"numerator":15499299433445861869},{"denominator":42535295865117307932921825928971026432,"numerator":10019835810607850977},{"denominator":42535295865117307932921825928971026432,"numerator":4912863247861992471},{"denominator":10633823966279326983230456482242756608,"numerator":1933274792601095989},{"denominator":170141183460469231731687303715884105728,"numerator":85069734917679138263},{"denominator":170141183460469231731687303715884105728,"numerator":80607718354800278091},{"denominator":340282366920938463463374607431768211456,"numerator":298091073712506805667},{"denominator":340282366920938463463374607431768211456,"numerator":286862556703743480269},{"denominator":340282366920938463463374607431768211456,"numerator":149279320927751749045},{"denominator":10633823966279326983230456482242756608,"numerator":2663899161450432771},{"denominator":10633823966279326983230456482242756608,"numerator":4097982463657030255},{"denominator":340282366920938463463374607431768211456,"numerator":180044713083599771211},{"denominator":340282366920938463463374607431768211456,"numerator":77294809741525242709},{"denominator":340282366920938463463374607431768211456,"numerator":39082430922671946899},{"denominator":340282366920938463463374607431768211456,"numerator":60660739350272165847},{"denominator":340282366920938463463374607431768211456,"numerator":155921315511483764637},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":32,"numerator":141},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-5956597640208025962821545350372197285},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6241668352479160603734939459768138587}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-105853577914599642453459529161990998427},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-850882901388792563727601910124300594413}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-168940172179122169642921973050042880869},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-84866992819278715923371115934166018433}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":102224442464791714943160377122026345175},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":101177033461035145503422770878557897609}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":41903699528187664997982167015574628329},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":20159934665897090467843679221569814239}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":217420589356921150971780788495853500225},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":6769086502040666701547993560374776419}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-27468224236020373564724481831434012873},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-220616615118941396840132631166296078505}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":46702116478608064795638256672024771981},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":23078880215582425214546539476224199163}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":32030670199961689058364294325083971},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":4942010316308027292582873340498469}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-45959671480687150437812481886482915783},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-2908340957164723468387135104743893891}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":100575850705900930287864349835494316297},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":400747516044095390119015648929732957839}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-798131365408439558227922681349675825},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-426979864277556036558362386267574453}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-35368785288129034802802148815600081901},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1145214470330390928011368550741940367539}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":108525566860062244373380892274113401823},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":53783000735846800443729359895955392503}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":69988739182927766421367298753834807813},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":136864756534459673679974140609250465693}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-18354521859391916213063471541831742961},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-18499814888493951388932004055075209033}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-89903799007515409306326331522952152595},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-90269984332131208753413356964119630777}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":184517688969001114215420163353010131737},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":92013160483081036885830813837070569973}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":122306365488775024529522083098929756203},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":59689287696909756033841556290598398603}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":14618677891776819572398628532279599},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":19719722396942574795745569181898861}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-118867861395638405518668444924031125457},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-30440836052786092447296424428859573271}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":144733088162984088463781747234786954547},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1144823962137888954395498499626335090353}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-3153552060063691807193348940607906917},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-197097003753980744930593926263901849}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-213415919285141590385930405516948502881},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-853663677140566362150662354638241051409}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-168454956088714623565659783522127133665},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-168454956088714623958048739541832646229}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":25716999370479926173354218118850893165},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":51433998740959852217534983194935289015}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":21501952474027782145272155614361640493},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":21501952474027782043675664162309318721}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":108922299107280454644903773659111120681},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":108922299107280454552280536186066743539}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-221082035920808879528090406081652588147},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-110541017960404439890586875337120215829}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":45787645885109781881098983919521511367},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":45787645885109781715268836867775993111}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":10124407134205698761709812296605415},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":20248814268411356677715484835315121}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-11392294211623310386799376092283845665},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-11392294211623310418807531979231475815}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":806712865060590871092613459722281618503},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":806712865060590870744414129847513728359}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1746434599443560930561429977667115849},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1746434599443561261996400252500762319}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1154584357756234478827040738945061843407},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1154584357756234479436531727442771572895}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":109192176505060415604788963960681555841},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":436768706020241661833180207305105073557}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":142121973699299726893832795855171183293},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":142121973699299726587063189144638873791}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-9277500636617604678102000524973355721},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-9277500636617604766609124563171641853}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-89665637338335346985992348757240660285},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-44832818669167673560146940081375382119}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":183727262576889493433963018358819832083},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":2870738477763898329146837211244761895}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":15542503427448622220641099487650265223},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":62170013709794488802817423314715559389}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":11757832778169835413259369617034003},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":11757832778169794654814038280031055}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-30943445611664145087953124732794792887},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-123773782446656580476981258035963059765}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1166976767598393945464051730354288329621},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1166976767598393945144045671164324497329}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3974327880039255},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-35882291333159021}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":76683926253211333},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-6677901702661155}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":65462392566723335},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":14086119155633341}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-448506344856371},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-724886699621269}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":287666947542835},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1731807158205097}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":30657249976562615},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":3459169919878549}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-18313859859855107},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-54153776817531455}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":580074517088309},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-411307036204687}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":388348486954401},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-268093507779489}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":60692272495513},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2243177158574017}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-8597279411091361},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-63547366274890875}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-3060433963170077},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-14177613764728621}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":31999688613823321},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":2956320177225325}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-2709695424205191},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-29734739727122529}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":1152417437096517},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1275619980800527}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3296614787341407},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":488641316112369}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3740469153501783},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1177154998395163}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-3843915712395611},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-3281058291392359}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1274725680555185},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":146422352861321}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":181146260351417},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-196099496304021}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1227548521582861},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-414621886183909}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3666180280958503},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1231170988219271}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":42535295865117307932921825928971026432,"numerator":13959528196250990441},{"denominator":340282366920938463463374607431768211456,"numerator":303405312715286269655},{"denominator":340282366920938463463374607431768211456,"numerator":196136058676863849617},{"denominator":42535295865117307932921825928971026432,"numerator":16146347218642555053},{"denominator":340282366920938463463374607431768211456,"numerator":101595337881525676387},{"denominator":340282366920938463463374607431768211456,"numerator":92611368017975974383},{"denominator":340282366920938463463374607431768211456,"numerator":126523752337815083581},{"denominator":170141183460469231731687303715884105728,"numerator":41456853861660240083},{"denominator":340282366920938463463374607431768211456,"numerator":40845375918760528763},{"denominator":170141183460469231731687303715884105728,"numerator":32007579919589862767},{"denominator":170141183460469231731687303715884105728,"numerator":87036094946976022657},{"denominator":170141183460469231731687303715884105728,"numerator":82855963273758021981},{"denominator":340282366920938463463374607431768211456,"numerator":304735407044902403733},{"denominator":85070591730234615865843651857942052864,"numerator":73244594072448856005},{"denominator":340282366920938463463374607431768211456,"numerator":153381469305498569209},{"denominator":85070591730234615865843651857942052864,"numerator":22126430012865667903},{"denominator":170141183460469231731687303715884105728,"numerator":67149242007967478949},{"denominator":42535295865117307932921825928971026432,"numerator":23034759782606368561},{"denominator":170141183460469231731687303715884105728,"numerator":39872923166278903819},{"denominator":85070591730234615865843651857942052864,"numerator":10189564177114668807},{"denominator":340282366920938463463374607431768211456,"numerator":62583558467188060723},{"denominator":340282366920938463463374607431768211456,"numerator":159998132243712738371},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":285},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-6118335714704160495386550976095433901},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6402174699073378954187154674789840963}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-424992571151551815754932009625009059783},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-213537766851949077064036830645022737221}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-21043239692333187945403118357522393253},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-42284079936284899049479885530901508919}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":25752170208795192193078871209227294661},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":50989528936662215461159310664293050011}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":43177201990659171869447861485712160505},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":41571904437135198668421048397286539639}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":217965215063246775801172941887493276705},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":108609524254640441754591787852278634151}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-220403333270677652895652693073947196085},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-6912759923384757169101639226525340703}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":23147348024190363009390759661124333687},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":22852588467360018130979774625960682099}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":33783764861759322599512573333410257},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":13425711182249783724881580943875907}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-22741476163010235329978662671218700995},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-11525824033180660652682212310852293327}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":50446263905530939723934084983141339973},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":401934293282373073987849484580825393817}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-207826721934477546096431287140711645},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1781315121157243363694373737257115681}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1142492574549359394980080269963679835513},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1155965682523799242463116868198986498647}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":437180115483719645656784430555952465687},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":216653747354246954344361262231317243917}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":71224565133171486612270552897791343281},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":34834755810464257579432760043729374195}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-9228157673973967083129143658213766003},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-9292030127258170526905254455104409751}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-89620870339238162386435143935145713177},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-44992625820467536683012900953794658169}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":46035824316952275946521247902487361089},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":183659673854585780412509662961344081301}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":15579960988658776663637870076589976965},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":60857007524615813395439641204488639187}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":7176482938591002136623539561660909},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":18327230532138817923386727542834263}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-121177559648295200671827484748223750749},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-3877191450281032592337349001765355727}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1168311091423121362695105298200973308735},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":72201704052288002274008083990452200253}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-808260286632968571473438054441814625},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6466082293063748802311227325605225213}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-857016031308327240380030752646479193259},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-857016031308327240995524919305852578935}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-167851919423640522544573324964847884577},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-41962979855910130735436088662449309101}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":51820009446698238130331334910860951303},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":51820009446698237997302370377627172435}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":44292345752886256215382204133843669425},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":44292345752886256005062503972461363721}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":218345465536615499561188196796308272357},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":218345465536615499372153136243984083769}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-110814218203578703334768967323095142017},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-221628436407157406927789790684688945159}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":22651740569632964218234813332388154577},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":22651740569632964132484905182012695387}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":44213317681104459382024663872696261},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":11053329420276093625958429340119991}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-22529951352174023975726335446617468295},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-45059902704348048083913913569845768191}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":202338959837812613949640435360864736477},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":809355839351250455442422480251733669887}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-455879244421157454569369433703438417},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1823516977684630158928921777515846393}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1165377539276825037318460451548022358803},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1165377539276825037941453838002214864701}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":439870516691120451405902605654618650465},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":439870516691120450807503138273923783041}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":144591488250703083523670892495607318003},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":144591488250703083208495556211661972767}},{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":-145519018907273964521206363342001913},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-18626434420131067642465171381513151663}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-178769503970889813379215491376280224393},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-89384751985444906827143709189183225093}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":183367205448954239023816374455259609003},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":183367205448954238646618063153554760219}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":126670759311836290722308135482531923985},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":63335379655918145278883515846063655933}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":1401535999068749582902215564347281},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":5606143996274977084206818708068763}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-63038688483895284779617306082695691643},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-126077376967790569688365549897454733471}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":588726827361472287862528028185457732117},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":294363413680736143849174202714871487675}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":6647865227583601},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-35358529825275739}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":15094708426742177},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-36377711658522403}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":158035008875066233},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":40084636248317059}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-58042508107763},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2925271735919875}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":575930995913387},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-111097323037727}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":33497631327017821},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":2118493685308427}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-17932835101426187},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-6900603901202041}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2522535347742181},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-138326091017623}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":406111634137397},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-269523325083055}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-119335133881019},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2503730647351707}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-11803324670605725},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-4386202797567199}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-359018160787643},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-3605612952513871}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":31995343893742957},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":5698011716369309}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-2336673209621147},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-28467832535556797}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":8528685812735369},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":906305923890181}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3482466656984443},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":557357832893169}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2277148926761011},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-917571559011833}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-1083877157839303},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-6945062344525317}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2868696589930041},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":535263904970013}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":188658528199455},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-49836601528555}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1099204177968601},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-308799827776045}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3498960503378735},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3324832390334413}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":85070591730234615865843651857942052864,"numerator":28810214561877231109},{"denominator":2658455991569831745807614120560689152,"numerator":2403754032821677235},{"denominator":170141183460469231731687303715884105728,"numerator":99263269828080650663},{"denominator":85070591730234615865843651857942052864,"numerator":33256567857882572511},{"denominator":170141183460469231731687303715884105728,"numerator":52579336668304447171},{"denominator":340282366920938463463374607431768211456,"numerator":94505018447869202237},{"denominator":340282366920938463463374607431768211456,"numerator":129107292021195235491},{"denominator":85070591730234615865843651857942052864,"numerator":21437127139152642619},{"denominator":170141183460469231731687303715884105728,"numerator":21219378827888248961},{"denominator":42535295865117307932921825928971026432,"numerator":8278678642568585057},{"denominator":21267647932558653966460912964485513216,"numerator":11127527664738587705},{"denominator":42535295865117307932921825928971026432,"numerator":21289993358511146149},{"denominator":340282366920938463463374607431768211456,"numerator":311486393566865750779},{"denominator":170141183460469231731687303715884105728,"numerator":149595086560249448803},{"denominator":170141183460469231731687303715884105728,"numerator":78792155052495097557},{"denominator":170141183460469231731687303715884105728,"numerator":45936957941228203881},{"denominator":85070591730234615865843651857942052864,"numerator":34383192195139335013},{"denominator":21267647932558653966460912964485513216,"numerator":11787148646426473605},{"denominator":340282366920938463463374607431768211456,"numerator":82269385178859826045},{"denominator":85070591730234615865843651857942052864,"numerator":10623652521157870971},{"denominator":170141183460469231731687303715884105728,"numerator":32282305232057457373},{"denominator":340282366920938463463374607431768211456,"numerator":164174461379016210825},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":2,"numerator":9},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-6278863713587211776379658449560583233},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1640316944747232539112512641772408421}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-853236054322437386020393961192062302183},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-857512282503727141253670567750356140041}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-167746816581602020344035822934037220405},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-168533638256171579915161286075923610827}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":25944750344084512159519935247184928201},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":25691693706746083214239442241970633665}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":22233815040112692072899803661695721425},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":2677579301391182338386900511970636639}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":218459868793595121391579323339170401767},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":217776234816890441072670155353682357051}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-110504002568323514980441744462242289531},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-221748312978265525632952658297141414355}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":22925550073402611959001661254203636743},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":45216557529850803548959938818572907853}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":4453414149032573266605891590959577},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":17169974201854633202503481063531127}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-44969073498363045012419887939777728981},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-45635854996285485748875710380944951019}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":202449825089233146628316849457972307161},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":403184963902720895607270772135790266633}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1733832888435928403328124384662829131},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1859849998512253675661178115682440753}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-576615434319555395606439742313068546765},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1166765759810347667354492025616361336745}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":440285867295814173752561016875126807127},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":436377910322955827175471228219655630321}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":144918291158313797854346050393885080125},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":141811271759409274224031759872608933581}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-18544025770113155100529247267388926059},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-18653780801333697657276782893943524333}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-178680687468451016273984069262907686015},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-179403562144250658459099281799014539367}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":183774641542159904322168333446172818937},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":91650425944727897720057592385833102975}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":126970184664756773117163389353780475323},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":124047787725681444771020563860167495211}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":28044584270682202576357104324616347},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":8403204181016278383436995706138023}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-30871233332922224814053531681539164275},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-15796678060170713776524730822169818253}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":147349189178920801531080228543463606593},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":291415948959793695533105968919347579583}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-6623482854621606063661006229456515763},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6623482854621606301430124615897646135}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-860454810278605091457417419049849657475},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-860454810278605092081416321107525100571}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-10453283414112437231474913382405655843},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-167252534625798996105888435277074660551}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":26099601434282207226002478462770378509},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":104398405737128828630058110700430625107}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":11399357286319163721471472398674652039},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":45597429145276654668229631335355285611}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":218797234165288827774223540902424629215},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":218797234165288827581296994574941541605}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-222124044179640345280816594153725412069},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-27765505522455043193043323448366975511}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":44783372448275399231804227240607485219},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":44783372448275399054471365208026996529}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":48125940842955168757891734799347833},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":24062970421477540294121781640134395}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-44513548794809876140629802105085157047},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-11128387198702469069412684906065080297}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":406061427244522331409582677394587642609},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":812122854489044662455024416711186529295}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1905974048500035401163953354536510571},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-952987024250017875628827664721244741}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-588110502331737629823223460816947462103},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-73513812791467203767697312117508275627}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":443000929617077190072969300108246270901},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":221500464808538594730974894144186336583}},{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":1148892634995339911076817240159640367},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":36764564319850877073511021651683063601}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-9341523358181973627103472314153090525},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-18683046716363947444914066271666312255}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-178214116135197356107292099539325073507},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-178214116135197356388978463076950110545}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":45754098639134146262196824436546170981},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":183016394556536584662787703396312265351}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":128997856557806342499187331254706879013},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":128997856557806342329450046071953538577}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":10599417551384534349490697583107855},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":21198835102768980111888340498613649}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-64188338645759727223477880726564715395},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-64188338645759727290084407716669979875}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1187968532154447692769498681297905817277},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":296992133038611923108146126547525626929}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10012925912662085},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-34422315040917297}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":10640010570436035},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-95712554470335297}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":188714077591617507},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":67168500905188467}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-358089056857731},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5860564801679575}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":584281784241823},"lo":{"denominator":20769187434139310514121985316880384,"numerator":-112363184143}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":36554556560938877},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":5046220758652487}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-2100023216202185},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-55854161238390691}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1359182673901497},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-159234522115433}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":424954602947613},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-271505498606801}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-295299428982367},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-690263643800725}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-15269315513393123},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-9680035389505691}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2500251885178807},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-7296309910301705}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":31748701031089397},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":5207250447874309}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-223479606492339},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-26850396904780865}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":7704660542034921},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":101039194543969}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":917374639939951},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":606402939229257}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":680196274985111},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-320045792607883}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-4701153194714437},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-14638942658866631}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3201730709999971},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":773237865987139}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":197042775759721},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-202402201496909}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":956715745680827},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-842234465665383}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3299340169113107},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2153667074358865}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":170141183460469231731687303715884105728,"numerator":59431170786371887747},{"denominator":340282366920938463463374607431768211456,"numerator":311930314730461681829},{"denominator":170141183460469231731687303715884105728,"numerator":100542068895474434505},{"denominator":170141183460469231731687303715884105728,"numerator":68486575168726516771},{"denominator":42535295865117307932921825928971026432,"numerator":13603364563696880113},{"denominator":340282366920938463463374607431768211456,"numerator":96450042106219726853},{"denominator":340282366920938463463374607431768211456,"numerator":131745469728850809403},{"denominator":340282366920938463463374607431768211456,"numerator":88664992216355285131},{"denominator":340282366920938463463374607431768211456,"numerator":44084475855708762313},{"denominator":340282366920938463463374607431768211456,"numerator":68509235882014471803},{"denominator":170141183460469231731687303715884105728,"numerator":91019691777596525879},{"denominator":340282366920938463463374607431768211456,"numerator":175040804803485277153},{"denominator":340282366920938463463374607431768211456,"numerator":318344369023051072523},{"denominator":170141183460469231731687303715884105728,"numerator":152749953192594142929},{"denominator":340282366920938463463374607431768211456,"numerator":161890811893358014701},{"denominator":42535295865117307932921825928971026432,"numerator":11919003659233725041},{"denominator":85070591730234615865843651857942052864,"numerator":35209955223031840577},{"denominator":340282366920938463463374607431768211456,"numerator":192994828280204133189},{"denominator":340282366920938463463374607431768211456,"numerator":84867428344954663801},{"denominator":340282366920938463463374607431768211456,"numerator":44293346804845172715},{"denominator":170141183460469231731687303715884105728,"numerator":33302813757499795687},{"denominator":42535295865117307932921825928971026432,"numerator":21056454318332272851},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":291},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-6438005148727800335520061631406949815},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6718776592087282698194487473659366107}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-428288761946132973310171056266444591169},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-430481299026439442108614255734883017997}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-10446697507421335756055767910035126441},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-83965113006536880962252847896468533141}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":104535726471956346354298271181565288645},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":103540495829112045954638792685772767167}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":22887327793292185438705799287853379791},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":44127644660253132130357048772209291341}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":109452762133574477770528241115642246843},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":218283236788778448686719430889948120939}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-110780374638137818325638696392526732737},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-222237620585093336833882809197398395515}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":22685710192740338249531973946604146681},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":5586503490416649484140092225988963355}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":75127920685611947872363153684831075},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":5280476661810045988498384114187733}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-44418147867486265320633721507234467163},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-45131208797332690613167268487805163367}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":812582207592665704057377844010730498425},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":404498676995546602798158164239310163605}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-905077927563238297994656611857983523},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-121485442544250551179434758479411107}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1164017680870326435175341221962177316197},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-294404066233828114151633378905401121675}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":443420250127541522002617406946172624149},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":219738050932425721448467442977446775039}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":147384645281796620911250897838711640885},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":144281137469470467908189406897653870137}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-18617301021274581934976111085167965775},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-9354317504919718586179571556113750553}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-44531558954552433750683138190526583939},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-178840978210076489060015737024509046851}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":91706698530893110075589025854532190771},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":182951480933466408877561281370039911707}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":129296935447339917239246467568132229403},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":15797370245430874838033664543807189357}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":27247455740556957095514294657051229},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":7576030440733910959535213809834483}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-125789050314512219623202112703286117869},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-32168079211823929745881776281328879121}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":594657094758140575631083341690131216625},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":294033954380921238964022261750432606061}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-6779139411195047834269866319184806399},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-3389569705597524039695450935390573311}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-431987942877850592534558552122955855547},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-107996985719462648212706563838049862055}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-83330620979381921316389236264467989107},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-166661241958763843040687616850733899157}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":105143486906268410063064440413359636663},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":105143486906268409781032781924777023119}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":23459409750780882229388957177705021287},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":23459409750780882116784945385271466461}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":27400115456168004154259239145827723709},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":219200923649344033037150979467691198757}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-111284967667903181656979011761099807339},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-6955310479243948861964899766541314331}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":22113734726769760466169376127827882325},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":44227469453539520749005576871249377909}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":13060176587827033571424128367936351},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":52240706351308042717000269069475243}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-43930253229264062087455604809323581233},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-43930253229264062229170648346427325617}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":407505991759468526135607719473399854519},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":815011983518937051899021487756008310389}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-498513878907712194327181204028427257},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1994055515630849137073537997802750089}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-37097382558740583304070017657090524221},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-593558120939849333190442525997393011097}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":223080293610833917183023506334034297857},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":446160587221667833742203215627807465275}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":149522000641105430343956481811924746915},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":149522000641105430011339691347571966469}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-4681126058081046677492447652655928851},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-2340563029040523363482315665579021651}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-88833441232178403222730550457613844953},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-177666882464356806733910546637046447891}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":182676419547502807766650591857446420835},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":182676419547502807371678239704451068837}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":131320407480010793177755171076722730449},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":65660203740005396501334289062044323833}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":9916451238143355222698995543931221},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":4958225619071654533060992812645281}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-130670770117186931235571328338314001751},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-130670770117186931372989990448848277961}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":299630896643131511337417653300538301847},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1198523586572526045003997272640706221585}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":14133241102510839},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-33048667602841813}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":6031384267055121},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-122296486591374795}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":55700567405023623},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":93880279006798669}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-108169645360907},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5833314671572479}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":302570336064681},"lo":{"denominator":2658455991569831745807614120560689152,"numerator":-15022638943765}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":39792863131426309},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":11754073973681501}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-14852638139044963},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-56061265658236813}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":729190943677497},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-15825249514945}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":444722269275267},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-68578191730597}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-464067350931439},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1506928008030941}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-18985530905804807},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-21325927782500825}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1907229457044261},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-1835093444434853}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":31287573215695049},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":2198084179749975}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-4164723828847203},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-12471585327102773}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":6776371268713685},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-122392207492225}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1926367418641657},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":626778163040671}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":6406238739364953},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-684465304211593}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-306930735170403},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-15369280852520315}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":443084028468755},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":500005961421861}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":103468254981665},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-205723741896579}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":399186822996969},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1090136762069501}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":6115764598348571},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2714309985033617}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":122536926821445493785},{"denominator":340282366920938463463374607431768211456,"numerator":316194492217413795033},{"denominator":340282366920938463463374607431768211456,"numerator":203890111165592312559},{"denominator":340282366920938463463374607431768211456,"numerator":141012966671778200985},{"denominator":10633823966279326983230456482242756608,"numerator":3518835867912659037},{"denominator":340282366920938463463374607431768211456,"numerator":98447447454886423053},{"denominator":340282366920938463463374607431768211456,"numerator":134438780189801626031},{"denominator":170141183460469231731687303715884105728,"numerator":45832548829908404243},{"denominator":85070591730234615865843651857942052864,"numerator":11445997151170759063},{"denominator":340282366920938463463374607431768211456,"numerator":70856246874219306969},{"denominator":340282366920938463463374607431768211456,"numerator":186063816505283600077},{"denominator":21267647932558653966460912964485513216,"numerator":11242251239487206453},{"denominator":170141183460469231731687303715884105728,"numerator":162655497932848137993},{"denominator":340282366920938463463374607431768211456,"numerator":311911509296717886047},{"denominator":170141183460469231731687303715884105728,"numerator":83152381131063524465},{"denominator":340282366920938463463374607431768211456,"numerator":98942754378667107579},{"denominator":340282366920938463463374607431768211456,"numerator":144221177508887590719},{"denominator":42535295865117307932921825928971026432,"numerator":24685118360244097383},{"denominator":42535295865117307932921825928971026432,"numerator":10942753018270573529},{"denominator":340282366920938463463374607431768211456,"numerator":46156370679792710703},{"denominator":340282366920938463463374607431768211456,"numerator":68708386800063106385},{"denominator":170141183460469231731687303715884105728,"numerator":86415449044219642499},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":32,"numerator":147},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-6595588167738334690391052956235207411},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-3437267518285524211545291744712517689}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-860005575728182471395461354529510559113},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-432248960616204336007510998766939143587}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-166551317774817576364623660628866510147},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-167330447609241376077140077148989261213}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":105279185915060560963976502669509892241},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":26075135318228547926016794503771475091}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":23548971099410254085696420350048779747},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":22715352736330335472827970580801780059}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":109651603974511586352260086239275238419},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":218741014855985011456494419007982409295}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-222062568547875209059909853445280200711},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-13917332804095410704311078645669316171}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":11213943990067090616709712846637833489},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":44131740840338730116492612126136102145}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":39596363659938167283550973542454857},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":3160826295932816857356092304219487}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-43830316885715756418425790633218227973},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-5573682931421986199417800108450114437}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":815487003524834200443893550695024939635},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":405874530075867356894797256345434283209}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-945912467548471559427525395455684843},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2033316069127865941944074228139522979}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-587427298507147373001985357026645823013},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1188518673506099882428732787660301172269}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":446583892580511908276973208266916447371},"lo":{"denominator":1329227995784915872903807060280344576,"numerator":1728917275863828119072276333514664509}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":2341373705620242368665227242188957279},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":146748295070482174593985146707578446959}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-9337898730608453741501616930839900633},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-4687072503171826298760084832230085887}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-177580152995903653927479524426616800289},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-178284556484007767773589456504656395635}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":183061200040096191736647673333575492637},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":22826643150562515607255489957336332633}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":65809514925298619036669106089358703663},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":16088326885103697016960586754747148929}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":26308678577513376611036656768829957},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":13358974555157156694643978229560151}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-32022246710546824469380532422922516481},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-65482945667754431785929222553530229515}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":599937650490317813241538167130570735281},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1186645557840426810871418747271206705671}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-6932890612741693380034430176306290849},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6932890612741693632605786217269965413}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-433787493807539532304271552463918309363},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-433787493807539532624817668756098359089}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-5190079740660222571644678026568238831},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-166082551701127122706680020731738618779}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":3308612426970091281582123389300498717},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":26468899415760730180081822929122543355}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":48256173469973597300835946122507808597},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":48256173469973597067855474511304412929}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":109778803865452385995145993320215595367},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":54889401932726192947316455892128049857}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-55741813193050576046928862281426172391},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-222967252772202304462134604369994271517}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":43635948409393885129918124604224656481},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":21817974204696942470206708046420775219}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":56562839780458594379016677032923775},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":28281419890229249650349039643268169}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-21655091190277676781898346937513539183},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-5413772797569419213792958606924525751}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":818021186221761355805810848360089639505},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":818021186221761355425523846576194997041}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-522004492605392061922465895334377243},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2088017970421568617357705287454621919}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1198064649271100378581105481124618653241},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1198064649271100379245906338006017297239}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":449350031341400909249482680928550788893},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":449350031341400908612600900343016452513}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":75991239535755014440168620307096133559},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":75991239535755014269334385518156896357}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-9375240902579694711938263681385066885},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-4687620451289847407294390105819951561}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-177129542500103823006199107489236699601},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-177129542500103823301563345469108538093}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":182348826616706944275323676800621353213},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":45587206654176735967800961178074546029}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":66818755535101884872744491842932458829},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":33409377767550942391223942459315304885}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":18321235579209144530176096365220567},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":286269305925141380601231817655967}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-132958752262463778510636698086306385639},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-33239688065615944663097024738005551149}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":302280241509076872883287048103649739463},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1209120966036307491178509170199165604051}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":4767215648357003},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-31217026105295185}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1120909163728393},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-152154942337502755}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":259357973443078715},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":120828188059447099}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":280145582229853},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2866441150352051}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":632358659459907},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2018809568382571}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":43168166173096097},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":13446929985096961}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-11898222639810799},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-55645988418475381}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1551770223683123},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":1278207386381}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":465042632382891},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-138808622130737}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-311212220435619},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3267284850688223}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-11466990342036267},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-46850799626125699}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":-16986161195631},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-14644389044253611}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":15238365346728287},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":6565049370379603}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-454219155423463},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-22573553440703715}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2839194948848249},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2050561209521969}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4026278212417635},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":614266520570375}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3726133647278599},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-588716012117}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-4971662961067535},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-16050379658739633}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3896074777504857},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1214870930912415}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":54460998411131},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-104406464976961}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":620589737509165},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1362250074808745}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1382180533393391},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-418867170185769}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":170141183460469231731687303715884105728,"numerator":63130267538066237841},{"denominator":170141183460469231731687303715884105728,"numerator":160233898501341920781},{"denominator":85070591730234615865843651857942052864,"numerator":51738974262021418071},{"denominator":42535295865117307932921825928971026432,"numerator":18143415232077678223},{"denominator":170141183460469231731687303715884105728,"numerator":58244455110743888297},{"denominator":85070591730234615865843651857942052864,"numerator":25124555229466374021},{"denominator":340282366920938463463374607431768211456,"numerator":137187703739255458685},{"denominator":340282366920938463463374607431768211456,"numerator":94750807598297415421},{"denominator":340282366920938463463374607431768211456,"numerator":47538787968934871535},{"denominator":10633823966279326983230456482242756608,"numerator":2289755158124364229},{"denominator":340282366920938463463374607431768211456,"numerator":190108117082663231799},{"denominator":340282366920938463463374607431768211456,"numerator":184827142215694689859},{"denominator":340282366920938463463374607431768211456,"numerator":332388472600037783513},{"denominator":340282366920938463463374607431768211456,"numerator":318429830625624528063},{"denominator":5316911983139663491615228241121378304,"numerator":2669224536146650437},{"denominator":170141183460469231731687303715884105728,"numerator":51324405262204456303},{"denominator":170141183460469231731687303715884105728,"numerator":73839187008688126451},{"denominator":340282366920938463463374607431768211456,"numerator":202054376685812748499},{"denominator":340282366920938463463374607431768211456,"numerator":90295266322378552837},{"denominator":85070591730234615865843651857942052864,"numerator":12021408825388955029},{"denominator":340282366920938463463374607431768211456,"numerator":70874709012951750523},{"denominator":340282366920938463463374607431768211456,"numerator":177313395809288403965},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":297},"tube":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-3375722891739828380920248157954913093},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-7028382060633567486134194149636372759}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-215879023431635364949920794517091973197},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-108514251752267339061752804705597852537}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-82981866741583252394115180498032766495},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-20842342862562110078036747357087454363}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":53004857857618518041903798444535717857},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":105047239260827451302946691128852837769}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":24218572969325455462472380060742391065},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":46750116564107414601194905042769032393}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":219654000730639399399634569182879952753},"lo":{"denominator":332306998946228968225951765070086144,"numerator":214014239991623364905802433083225779}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-222514530667151927257392606344300410273},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-223068577353696287823046775924269198769}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":44304313221832887020086416193292140641},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":680248055295300408478277797124244317}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":83454388052124453369871864586575599},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":463581166216332947637237289738359}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-10801437550345062349086804386403070907},"lo":{"denominator":83076749736557242056487941267521536,"numerator":-10744812882249901608489563479754889}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":409255816800141912283302743383634476225},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":814623133509898521602623265399310099543}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-247386133267850235618619700155790173},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2128753561023270808546627550896942271}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":-18527236193793178895985240930737067275},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-299868592793028903303726717991348436191}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":449777322432844551979963610795035002827},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":111439681938439827373390792869000455399}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":4759621009347980776876398688902423171},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":74606229672884384180741786290656603759}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-4679795016611174875734311031547343505},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-9386210862619785786631353385754766151}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-177044174281300072420040369291603005791},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-177736072262474221657673899919764969853}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":91359822794011157697809000851951979675},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":91143692591413619552971952719175914879}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":133935568263153214473322704506178193869},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":65514917029830817530742393029760279291}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":25222387885758136200512418308130403},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":11421928965898520043775066690947361}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-65191914175737486902953795929651051897},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-133253246008594548102544954450397827807}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1210478990215234104868046820891881108083},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1197195208390002927241325100368461983579}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-885572530568971918608272095259782995},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-885572530568971951122210164836213421}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-871247703824860731978179291747923226217},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-217811925956215183156959336520391485277}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-165521038303216563503488923432432264477},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-41380259575804140981056132213464827261}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":26648769609544601359619815265751878437},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":1665548100596537580308080295452824169}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":24804570201484701225141477176391336181},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":12402285100742350552325906537783570327}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":219868416019574555141604416790513770335},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":219868416019574554936366227403384630873}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-223317207831628330071978272630024717595},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-223317207831628330352010297805828641533}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":1344031614346700670511720730394271389},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":10752252914773605315130891036320174627}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":15274396730539805959380572454003127},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":61097586922159125135954033465902917}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-10663382614687770109300789319020095491},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-21326765229375540294361685567235621743}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":821148304115594985506543357582130397841},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":821148304115594985118135349730641798971}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-547031265148004711710034839202839833},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2188125060592019226645830127842867471}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-302266883188064984502000777084677645305},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1209067532752259938687186532945799986681}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":452569701122020424138581741128362285491},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":226284850561010211744219211185761584819}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":19304936853677770805146450919149476685},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":154439494829422166090219425469328060759}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-18760663155884938434041761012414362181},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-4690165788971234661747818189384329927}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-176603802158446528193468901899889569869},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-88301901079223264247951352219684204719}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":182035116386313816214972592711549259147},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":182035116386313815801527301946359304919}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":67974138943508847069496136086621990649},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":135948277887017693952730850012039113819}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":16658302741146235730029112959787739},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":520571960660816736353086519778609}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-135239731492614381906051807932637077339},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-33809932873153595513066702012793041227}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":609881388942387447486014571447525508915},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1219762777884774894608215844145196093455}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":25051666169972127},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-14465492217744963}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-8034127201535191},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-92932633000285747}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":149418550150595593},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":147389359400485005}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":830831135099955},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1388415272826053}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":668502050250089},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1067601770835383}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":46643025193649907},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":1885966478656957}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-3939591425702287},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-27251764284714771}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":818708398728033},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":11973837329643}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":121492543692279},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-281735999779069}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-47421829710741},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-219104459881765}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-26995479489661909},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-102606801649497661}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":7385770325917},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-14483656701072305}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":7325008727226385},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1796008070945257}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4130309726266345},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-19737238209919341}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4413027526066127},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3925965698237553}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1048125878435633},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":69704297867929}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":2144925039679373},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":81830693096959}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-2419645492503047},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-2082819769873137}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2124165724068619},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":176472138242147}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":115183347375829},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-211910643939229}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":211933353888349},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1660848913420099}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4840753343367421},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-4073050329144369}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":130028760953002990677},{"denominator":340282366920938463463374607431768211456,"numerator":324744128661022606889},{"denominator":42535295865117307932921825928971026432,"numerator":26286509855032896149},{"denominator":170141183460469231731687303715884105728,"numerator":74688934415450090691},{"denominator":340282366920938463463374607431768211456,"numerator":120488262248028235099},{"denominator":340282366920938463463374607431768211456,"numerator":102603317046882372605},{"denominator":85070591730234615865843651857942052864,"numerator":34998175103760737371},{"denominator":340282366920938463463374607431768211456,"numerator":97924136144545196189},{"denominator":170141183460469231731687303715884105728,"numerator":24675200137543890351},{"denominator":42535295865117307932921825928971026432,"numerator":9469841683519257821},{"denominator":170141183460469231731687303715884105728,"numerator":97083099132332190779},{"denominator":340282366920938463463374607431768211456,"numerator":189895596171394891999},{"denominator":340282366920938463463374607431768211456,"numerator":339578858294161195217},{"denominator":340282366920938463463374607431768211456,"numerator":325059725604451465083},{"denominator":42535295865117307932921825928971026432,"numerator":21933990180665215565},{"denominator":340282366920938463463374607431768211456,"numerator":106472938437996079213},{"denominator":170141183460469231731687303715884105728,"numerator":75606469371216224437},{"denominator":85070591730234615865843651857942052864,"numerator":51679183437251996903},{"denominator":85070591730234615865843651857942052864,"numerator":23282323200857833427},{"denominator":340282366920938463463374607431768211456,"numerator":50083144033494090681},{"denominator":340282366920938463463374607431768211456,"numerator":73106457701456945385},{"denominator":340282366920938463463374607431768211456,"numerator":181900155947926634107},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":16,"numerator":75},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-6905416042463727978009081300977514973},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-7180161745243381998262567855242018175}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-433552410194087527924500351776870525865},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-871806492657215143444424715095673466135}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-41347230080376828896208222297564612391},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-166159621854418212386885257814016777087}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":26681914224132951452694899747114334795},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":105780924414877489043610368441935682163}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":6223989448998034002745430641729019055},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":12021383864104213851571980493894131147}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":219959039603709883370419797840202553853},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":219513004189481981613582048405099576097}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-222917769940279411134121676936430788275},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-223412598259508341670059396630146545613}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":43717205201538263828675196867795932913},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":10726159320023619210276119107776606037}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":1373723043058003880981435001449097},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":8568694767164071203642972551430403}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-42544645228761983265140766635039960447},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-21697621032043975213238662450996964177}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":821653924365421467114119416979087210679},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":408808774325121782618951058143546639121}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-129512753387828696816123613652940581},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-557585804092087533844208312082097625}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1196684649099004897878409169730835871701},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1210484650819959704905372281469640431549}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":453000964555861800220615629690683018931},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":112236093023837424608483149209457173629}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":154764317830269455612506824569221626165},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":151673385876092314419353431510543671713}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-9369956767079715758238861327471359059},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-18781515963716701036558031777515198209}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-176520001086657506795909421838350070513},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-44299317330955020172770112084771071277}},{"hi":{"denominator":41538374868278621028243970633760768,"numerator":22264439163966481200180516067042421},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":45493923871537179206581920403583293049}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":68122831383544861800424678695307925565},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":133347716437216441338678704309219232079}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":11991367463750680988358599213825263},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":4667854623445719546464490351468705}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-132672670292341021866783024070029646441},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-33883372498392147076329940508443445717}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":305281839646635658945441772759595021135},"lo":{"denominator":1329227995784915872903807060280344576,"numerator":4717917665701619911459776305882922179}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-7234057244652745769142200761113559865},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-7234057244652746036874190697873993937}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-874989480907780491145955495197965371785},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-874989480907780491804176132976312402701}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-164981333825888682630111183695169999509},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-41245333456472170764524588497451649575}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":26825568405886970327084683852748649087},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":26825568405886970250229807268445319149}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":3186085174198150375211862806007108023},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":50977362787170405754179289792955905481}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":220134535649568574740387497785614254905},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":110067267824784287265413310538067216389}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-223621081855551085594965080751389693493},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-27952635231943885735090406042223545869}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":42346887066893999060473757574124734029},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":21173443533446999429048049397204408585}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":32925108548527478176587424322254479},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":65850217097054853911606245512234663}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-41960519043554346230596785731729881445},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-41960519043554346387235097176470983343}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":824391055330949615978866599690985681149},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":412195527665474807791161323380696698501}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2294647635857178533601159238191166737},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1147323817928589461891087622570199067}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-76257881438688421323804980146944100733},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1220126103019014741874675978954580451011}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":227909965508842735933932340246367550043},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":227909965508842735602113079978685272067}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":78446446136208360148930584592580839581},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":78446446136208359968692179854492971045}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-9377370495332769994995132368621349351},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-4688685247666385052707492146897055815}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-176091331801166269420762369258153985977},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-88045665900583134865211777379496300447}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":90868370878794199288752290994191242995},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":90868370878794199077276312187424107909}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":34562957739343952019517058945027488283},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":138251830957375807885972654723265528069}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":14838596890752067185804212883114711},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":14838596890751962883441199628782693}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-137512827355566951994830899918052821949},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-68756413677783476072822088405500228813}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1230451086549538427905574188526784375309},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1230451086549538427532376186431359451101}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":32025774810873817},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-6515447111173833}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-36918213855227423},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-55667748963855411}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":340131107693012521},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":2692152022714243}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1545367023250361},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1324481658910911}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":178628367783099},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-283567359483029}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":25066063109216811},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":8324149098132793}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2722918395568181},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-52530293516186899}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3430542369395849},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":26998924316475}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":507142377693433},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-143341592627609}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-436500494749301},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3724808234116415}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-15564426904080699},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-27988393061499969}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1392861133950073},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-14181506576476161}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":27772079617243599},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-40421159019955}},{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":74337754290541},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-1030771530505557}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":752255000289161},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6085621630770747}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4341910047577105},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":454840944274865}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":9783581558667891},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":695981186437227}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-4512994449005289},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-4298383415869043}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2297103721302299},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1584801633035193}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":122057970812749},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-107417039526355}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":207693743992187},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-495898802359751}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":504552041146489},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-9769254738883607}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":133836951186752432461},{"denominator":170141183460469231731687303715884105728,"numerator":164508721249086709173},{"denominator":170141183460469231731687303715884105728,"numerator":106954834229099324455},{"denominator":340282366920938463463374607431768211456,"numerator":153706331521777212873},{"denominator":340282366920938463463374607431768211456,"numerator":124603766025405413129},{"denominator":340282366920938463463374607431768211456,"numerator":104763696440728827045},{"denominator":170141183460469231731687303715884105728,"numerator":71427090052819513685},{"denominator":340282366920938463463374607431768211456,"numerator":101187141117597576979},{"denominator":340282366920938463463374607431768211456,"numerator":51220387388784662821},{"denominator":170141183460469231731687303715884105728,"numerator":39158864909374121021},{"denominator":170141183460469231731687303715884105728,"numerator":99115782052788611417},{"denominator":85070591730234615865843651857942052864,"numerator":48770680204904850645},{"denominator":170141183460469231731687303715884105728,"numerator":173442110920384888943},{"denominator":340282366920938463463374607431768211456,"numerator":331806256479163638895},{"denominator":340282366920938463463374607431768211456,"numerator":180233857417271904839},{"denominator":170141183460469231731687303715884105728,"numerator":55208954195310555579},{"denominator":340282366920938463463374607431768211456,"numerator":154826396940826410739},{"denominator":85070591730234615865843651857942052864,"numerator":52867409634289974911},{"denominator":85070591730234615865843651857942052864,"numerator":24011571456379356957},{"denominator":42535295865117307932921825928971026432,"numerator":6518869003952103363},{"denominator":170141183460469231731687303715884105728,"numerator":37702771400998551121},{"denominator":340282366920938463463374607431768211456,"numerator":186592098212178434343},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":303},"tube":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-3528671062986554016810801326814554565},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-7329723311759781186067341539097401873}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-870767356731432421609114670764772635831},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-875570827665715525299760878397255284135}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-10301965916167972730796382739760266657},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-82798829354082115308305731494525115527}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":107433354288961241900048957975646347597},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":106501936676980312166346936546126429445}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":51161893137937210003918976143404666031},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":49436612321306312454346364796546099055}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":220219519315706074904489769064254843849},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":54957351135556652068310347299182450259}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-55818372230734056743375105370185302501},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-223710678009857257958278930774553030357}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":43094651092947479611159510193262313163},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":42238256754416898063315044185829281565}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":92589792777421381737654348129318743},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":39108496864461721525299063085284609}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-41847226674723091543923239845380619389},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-42743119768087523815923385966483896781}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":412455789162367424429140212135402934439},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":820730162536801666924785896759620985031}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2171432744969288466350460347293897131},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-584588975299148067811812060861315897}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1207680513080728137366997859353861829227},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1221550709796046143777050347003326093603}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":228127569468031804800317264544322770143},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":113040052007892795146770824789654525015}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":157217103077144410812116065447240899843},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":154130871690786361121119798560779605799}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-4683473751599771156302323693778813875},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-9387843571745926686767995400933548923}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-176009299021922296737865587254763494639},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-2760466532226637132328405311350596971}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":91037313397025186658355907748349269385},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":90839761358342401149659794922114499049}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":34637109509967985324609077464942163221},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":33914842800841805506357560779488867493}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":11291950690528486896263668803061223},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":886889913806435273238748096396375}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-134954618956450859079618115133198330797},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-137805744318086087343955040928562540661}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1231822464236559635599429741397163899267},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":609211406367288295026818260991987432207}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-3690587820260399650553640118211679079},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-922646955065099947066210520356334355}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-54924726561867929521813064475382024169},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-54924726561867929563485974068945804985}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-20558515079872168051364905253755694563},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-164468120638977344846745533908766374691}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":13499691295142838241151179081723739305},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":26999382590285676403233296724016934687}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":26180238335048720089503724148465548113},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":52360476670097439921327481284656588323}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":55089303226821692749488555656188024389},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":110178606453643385391979104012548227911}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-111940113811305023556332635957434470669},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-111940113811305023702131820700418651497}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":41649827406797170408683009332678995765},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":20824913703398585099797819634999195441}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":17706506693752897586896353711221927},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":70826026775011484046070945481885757}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-10307849143414640429546307175324966981},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-10307849143414640470022529110698955089}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":413873514692506153252876080631198254857},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":827747029385012306101071379092322463129}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-601965966463699017017775020446580371},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2407863865854796468867294360856757841}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1231241472799088155204798007553009987337},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1231241472799088155913441398866413650355}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":459100948908176125915492499745345079913},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":229550474454088062619057411039778101047}},{"hi":{"denominator":332306998946228968225951765070086144,"numerator":155607967148012285357751853722806423},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":159342558359564579836086434696093029771}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-18732417086848881211497807157052767835},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-18732417086848881440474981025913953477}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-87796882126016801516096957138177050247},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-87796882126016801674621661276302501447}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":90727552869422234831068225762514377427},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":181455105738844469229493424626613172891}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":140547306680249670427271476337149449957},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":140547306680249670229171331453274888043}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12856650100192145473521068671800089},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":12856650100192036890712093617927587}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-69888586010985875186127922091803261845},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-69888586010985875263902990309710459811}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":310296977819482048077183542978777255941},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1241187911277928191925939487694098825185}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":39942399334534635},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-5634361017894863}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-57832339115050077},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-65478776828744559}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":191069358023669191},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":195068469303872673}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1210358000254407},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4941019659529489}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":383934241069531},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2414293736420557}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":3347276388747187},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":4521954180772525}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1820372728208157},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-12427200895270991}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3566047975227731},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":7911751771835}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":263873297100063},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-292533413067259}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-967091038680843},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3920391012168829}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-35261316183172169},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-15196887605536431}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3056922982937115},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-6848636825098049}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":25813780531318297},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4468673714168775}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":15689875591833423},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12771864285633893}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1447309020928167},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8517408724280223}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4461973735853673},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":151246938383441}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":11056219593899559},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2173372731326045}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-993837739127347},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-2201536247550697}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2463505001825603},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":863628183159053}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":258575576859587},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-54296816204277}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-28483703737955},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-291047318502693}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1549269845327455},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-1446221580459625}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":137679962041510601297},{"denominator":21267647932558653966460912964485513216,"numerator":20830077210275642653},{"denominator":170141183460469231731687303715884105728,"numerator":108909805407994338119},{"denominator":170141183460469231731687303715884105728,"numerator":79067221005515534347},{"denominator":340282366920938463463374607431768211456,"numerator":128838392425027974141},{"denominator":85070591730234615865843651857942052864,"numerator":26745068249269847105},{"denominator":10633823966279326983230456482242756608,"numerator":4555390936514544709},{"denominator":340282366920938463463374607431768211456,"numerator":104541917830856232245},{"denominator":170141183460469231731687303715884105728,"numerator":26575173547338933641},{"denominator":170141183460469231731687303715884105728,"numerator":40475483610380616111},{"denominator":85070591730234615865843651857942052864,"numerator":50574308548176615913},{"denominator":340282366920938463463374607431768211456,"numerator":200389720041218651571},{"denominator":85070591730234615865843651857942052864,"numerator":88576638607394771993},{"denominator":340282366920938463463374607431768211456,"numerator":338674607962955705251},{"denominator":340282366920938463463374607431768211456,"numerator":185120749399157769495},{"denominator":340282366920938463463374607431768211456,"numerator":114486507194501049425},{"denominator":170141183460469231731687303715884105728,"numerator":79260131357347082221},{"denominator":340282366920938463463374607431768211456,"numerator":216314694979695842887},{"denominator":170141183460469231731687303715884105728,"numerator":49524236282559307203},{"denominator":340282366920938463463374607431768211456,"numerator":54291166606106097903},{"denominator":170141183460469231731687303715884105728,"numerator":38886959135242528085},{"denominator":170141183460469231731687303715884105728,"numerator":95695003977168966667},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":32,"numerator":153},"tube":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-3603530720149463046728488100542983857},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1869254870959280712577304900584658417}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-874499344741469742850718966777215110987},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-879400706404577225803084248785694463413}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-82149213289823286669335013141672686971},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-82528606204402236513461861989652436923}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":54063651485220364142837392223161869975},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":53605301848057671206862083560692542803}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":52547009481866685313686680803316574105},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":25401478799435409568228123051512179175}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":55109173498542931344197240857165181597},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":220100962500168224436830805014851149537}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-55895739996721487770443975862862596893},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-111982089336768648106833837125910095615}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":21218437844667503118336327834670095991},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":41536989464924934474683676916208868007}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":48737192299350650964905692737765521},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":44175498404960398657259145770927589}},{"hi":{"denominator":664613997892457936451903530140172288,"numerator":-80300285199842688766667871420629609},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-42054604934802667469313002644041192131}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":828282168701453602209688470453947284519},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":823958709400893617068170888328995936661}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1138522586428733884834975450380918541},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1226534901427287704491016038015939037}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1218731931446718154854678854372570572865},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-77042102948105251132292945747431106621}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":459540058817554852332010891461922918125},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":455406583484366651078916745101417696407}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":159666120055087626764247626642318347233},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":156584755852119952512177329805390868679}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-9355396075796252225308057403809609715},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-9379812097503494314315754070404792707}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-175513695904811914072081670695490906373},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-44038878391856966200893163308151621059}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":90887064127266530856251343263072020305},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":45350065821271607590630410836887937491}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":17605379032292070366709229263263314735},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":137963919701713501769561412325280611917}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":10510057197928571098680159585119237},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":586874485354595322595976745611457}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-137228792311577318314990295162329510883},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-70034571375736827556698170260269682993}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":621283159896447201458804168231057926307},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1229104949522498874711794836183606155871}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-7525794398810347179892269455801385763},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-940724299851293432882809555891195975}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-882661303480537674131922166745905431347},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-220665325870134418701798032193805654923}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-163986123361803654958012379468923373415},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-81993061680901827701136318754068234461}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":54340598665815598825177346340976618609},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":13585149666453899665627397072910639011}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":26879056041469378187133960241300295389},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":26879056041469378053937111431760690037}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":220537754816202108543547506567055772835},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":110268877408101054162501146664066071821}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-112048035326811119481945110271170184899},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-28012008831702779907680230138034838541}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":20459054854367603190270390603721612013},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":20459054854367603082277986114366107167}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":76030343469526571869876958300195619},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":76030343469526461585211480219301005}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-20233218896733879947301431851464032071},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-20233218896733880030963245775755122609}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":415606840941120631177925662217243089917},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":831213681882241261943048325778887331691}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1264029662823507101988572543736633273},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1264029662823507307814984115878631829}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-310603663538727983245888016369857569485},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-310603663538727983426819760346200064397}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":115603218587467474591798089638287513107},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":462412874349869897675822693990228303239}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":80894211537811153466055954488925414085},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":161788423075622306551827010008424460351}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-18693402364415116534714599753948105777},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-18693402364415116772082013626613491319}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-175112692758670882649885080284936228383},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-175112692758670882974486460560941410637}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":90595779627410310393672997657324229121},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":90595779627410310172412426137125727235}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":142833855731195833201415638956954345197},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":71416927865597916498568037829984870873}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5353524468116998352844004225262735},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":5353524468116941846652556799568757}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-142031911129340912463042059430626873249},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-71015955564670456311735813493284798681}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1251975223764745572591984237920095500007},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1251975223764745572199379752769693361585}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":48344233012959611},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-17453191724190379}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-81717999409607407},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-73718536781574021}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":412830385884000825},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":217290650937746975}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3376351373529079},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2094583342844209}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":765664728592669},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2512643692727515}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":14193766895998491},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":9703081183530051}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10623841527159829},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-701330738886231}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":454768988452055},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":3203396077025}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":542391378640631},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-147873106399403}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1043833186951949},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-510480720027031}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-39529027197410909},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-65571579528245127}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4873315632294487},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12657339373702177}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":22436000267113219},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2265129363059129}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":686476436080487},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-237743929706243}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-295608532872735},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-10929756092777055}},{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":34847033658179},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":116344223709357}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":1541272842413531},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3019508756215629}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-3357339606637177},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-8763772882206841}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1290528775258755},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":926000197624161}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":270774479157153},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-53970464108257}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-71899891618439},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-672448984009929}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1927932599623841},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13519174590440437}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":141552204783295516023},{"denominator":340282366920938463463374607431768211456,"numerator":337528402940800249833},{"denominator":340282366920938463463374607431768211456,"numerator":222032359152133420827},{"denominator":42535295865117307932921825928971026432,"numerator":20332996911288056727},{"denominator":340282366920938463463374607431768211456,"numerator":133195209655328945259},{"denominator":340282366920938463463374607431768211456,"numerator":109253922166853347665},{"denominator":170141183460469231731687303715884105728,"numerator":74374027888280614979},{"denominator":340282366920938463463374607431768211456,"numerator":107990598226986004725},{"denominator":340282366920938463463374607431768211456,"numerator":55141913670244727587},{"denominator":85070591730234615865843651857942052864,"numerator":20915073479501114597},{"denominator":170141183460469231731687303715884105728,"numerator":103177846130934942199},{"denominator":340282366920938463463374607431768211456,"numerator":205817646244639000223},{"denominator":85070591730234615865843651857942052864,"numerator":90461934923456328739},{"denominator":340282366920938463463374607431768211456,"numerator":345670044755608286913},{"denominator":85070591730234615865843651857942052864,"numerator":47534320053799917029},{"denominator":340282366920938463463374607431768211456,"numerator":118681534898290423993},{"denominator":340282366920938463463374607431768211456,"numerator":162296034801011044817},{"denominator":5316911983139663491615228241121378304,"numerator":3457085725267493963},{"denominator":42535295865117307932921825928971026432,"numerator":12767265823892426047},{"denominator":340282366920938463463374607431768211456,"numerator":56505948119257898887},{"denominator":85070591730234615865843651857942052864,"numerator":20053395669946644769},{"denominator":340282366920938463463374607431768211456,"numerator":196294519021606037071},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":309},"tube":[{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-229826139185275713048743799014887445},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-3810914159924293826517293024461370931}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-878297971239110753088440698637079268303},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-883274508746871945694124026128387196757}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-163819720868565769907846393231700972629},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-164540165057911964284400994228331781093}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":108809730046189336073193832225355415707},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":26976821487923270001559389848230519895}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":26973325429598999234230433817609342943},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":26092117546765355596934107945129107877}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":110305939363339828715626808572077517259},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":110164458352566002800462692272654792675}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-223847526775101893325822871548309044105},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-112087267625091715597123436507442380441}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":41744128777780061988424025097563197919},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":40801115067951146191013869647744431933}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":6411095859824463299831048151100955},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":12370238778437883285185402193877859}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-40344480971846215189758169484780570095},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-41329942751637711512349221904688987669}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":831763134127916330307440201098033088157},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":827300795524689636744808176402907587509}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1194659341451782714200327868973313479},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1287385256207935912552548488660158333}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-614920014830018335005110181983490255975},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1243854461050551521955996797628252010265}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":462855828980694244244349271821164842471},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":229341870005614833785377719265298551273}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":81055651944492952975433215705860250705},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":39758729991851663678055497593060737243}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-9334804756059663850618254470555706847},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-18739395706263276300390367057450152959}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-43758694929192301695633085763679590405},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-43913968411210189630830580129732081191}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":181490199574657920289511147651214087391},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":90569630608261707007882094294192008789}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":143128598003155176274300112813681414655},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":140260496533260169557490355502227134469}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":19285662447778680173173484186696383},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2130223352084953009259888721492431}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-69747160420558802586607779876526786923},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-142322832649659057163618401859559816731}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1253360889987464747514123069826972819911},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1239835358087979685749474644990554686265}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-7667777181938352735190921631034732543},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-119809018467786766033656183886310643}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-886581547425989541616723273649618128783},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-886581547425989542300436240648356584853}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-163540100033566959184115701491835662597},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-163540100033566959637421573889756799939}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":27338405886480930211314946223206200947},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":109353623545923720510658930073853180323}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":55169893458637882327428250713067582121},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":55169893458637882052070450844105562571}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":220677530665341685530489239052700354215},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":220677530665341685307280712160676371335}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-224270110363017064932692450477158735101},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-56067527590754266309077679611946354289}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":40152034563054055607513712290235670915},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":40152034563054055384439415783438340189}},{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":636472889585412243933972688072381},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":40734264933466326414593155810301123}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-19832971578867670105885237861978008029},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-39665943157735340384666291402060385825}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":104348541146352115675995492679994246989},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":834788329170816924987069473473082378235}},{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":-20746305030394964141377017762044199},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2655527043890555832848781930917800687}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-626823277926672531487631852223244753007},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1253646555853345063714313746580561662507}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":232877858488377607848080873178443390519},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":232877858488377607495268600189921441883}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":20528807471379176285206044510388998943},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":164230459771033409891061869784516077297}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-9318708471794183146144423725646006425},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-9318708471794183269152436496164908193}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-87324834450715262282859148910765775489},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-174649668901430524898038320348424492219}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":11309212433957909526933915497852148423},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":180947398943326551978353407887036523021}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":18138830495746298624503249909175149301},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":145110643965970388785387554146556079659}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":4192225310051212995388548109969059},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":8384450620102308395274421769769811}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-144276204629270349806824725100214144375},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-36069051157317587493070089471946253705}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1262814945691488987058796462345793694055},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1262814945691488986656168143866716236805}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":7189110855255531},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11641988821796073}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-105099195268930791},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-40851708337209321}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":13727372194833307},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":29506406261241455}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4510979153592537},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3288422892265105}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":192408650740999},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2609275109520129}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":29876716506995847},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":10214367866254237}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":9366876572003553},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-4871637940418015}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3676915786383885},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-130126862325}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":69286594422921},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-299660257289509}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-548630146917015},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2105077394810787}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-21770252306394975},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-140642904269012709}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1740077599230793},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11340956653469615}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":9210886194103129},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-14224098562443113}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":7190436148875797},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1842820325442873}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1402654362068725},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13491998512671651}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4402274256629421},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-65899829511911}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":13639061060292543},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3891384830695833}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2514849596830771},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-4301519700916311}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5346220048792281},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1926259207088267}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":141405069480365},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-53213685095845}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-563728192734479},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1534097363842899}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":75196688374947},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-15643994461457605}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":145446959631012654143},{"denominator":340282366920938463463374607431768211456,"numerator":341745626263654856145},{"denominator":170141183460469231731687303715884105728,"numerator":113275661934444100789},{"denominator":340282366920938463463374607431768211456,"numerator":167296527708462882911},{"denominator":10633823966279326983230456482242756608,"numerator":4302412827488273991},{"denominator":340282366920938463463374607431768211456,"numerator":111584601097371249829},{"denominator":170141183460469231731687303715884105728,"numerator":75890140278489832707},{"denominator":85070591730234615865843651857942052864,"numerator":27883827188622643705},{"denominator":170141183460469231731687303715884105728,"numerator":28598377059859997411},{"denominator":340282366920938463463374607431768211456,"numerator":86446351391804291111},{"denominator":170141183460469231731687303715884105728,"numerator":105199341391803843729},{"denominator":340282366920938463463374607431768211456,"numerator":211367111195162875213},{"denominator":42535295865117307932921825928971026432,"numerator":46188587266445094195},{"denominator":85070591730234615865843651857942052864,"numerator":88199242676515368901},{"denominator":170141183460469231731687303715884105728,"numerator":97643949902201845011},{"denominator":170141183460469231731687303715884105728,"numerator":61502872866780537573},{"denominator":340282366920938463463374607431768211456,"numerator":166155137425331672265},{"denominator":85070591730234615865843651857942052864,"numerator":56571818606173877159},{"denominator":170141183460469231731687303715884105728,"numerator":52658756291500852683},{"denominator":170141183460469231731687303715884105728,"numerator":29398751752392706049},{"denominator":170141183460469231731687303715884105728,"numerator":41363282080258979781},{"denominator":170141183460469231731687303715884105728,"numerator":100653018227777250017},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":8,"numerator":39},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-7499327293119824766383022603581207591},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-3881999175012524450737744463379866879}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-55134797031486577437580773296131715077},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-887202262271309590307590310617064086829}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-81688789474708186034241856822646448695},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-164053739407624464661582518181677227487}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":109480961529563780682529793575632660867},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":13574041830371502674550860695252711173}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":55360395430365898859164099658785832271},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":3348755037493205987635959213731977173}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":220746451082629613287760229650331251639},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":220514566342154607773584744603551881025}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-112034302762950785701847267279817854581},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-112171628401554123502825696093829529983}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":41016684490563462800887158278590233063},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":40030936672280898597423389766143398251}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":26976192246985855139675508984834807},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":55030063577031929537176945039596591}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-4942466854985851742868333077249296905},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-40569404788310087408479805899570148055}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":417675886647710574581014896217560901609},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":103844236743430437087061853654926781363}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2508538020793468589301224288167291869},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2703751069328924736060430082203783081}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-38781432276297868021863003096717859625},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1255094045975333339538975760740535951843}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":233101222086617836364904724001675580543},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":461991811036162589336490832188878735083}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":82276316573385508671869146759030690531},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":161481288623272449797170200485239996321}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-4652855997029236919100841390750507437},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-2337813884111586389505788512529946375}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-174574096506211986668971519137664724971},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-175172536786721871452877009852308070773}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":181224198511480735547094479338856538195},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":11306112871554974246850602580987437139}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":145404303162050196572655673330959355255},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":71274125230550451855483615614984155925}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":17374911995220711006423588046453409},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-151062641823330751817581037207749}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-141750348387825148229587918989189486713},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-144565975802982790564129321204540096515}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1264208089182708327261329028909125627481},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":625308008248041521929581583143821374045}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-3903496002791668367984756248693406111},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-7806992005583337034757411983787036197}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-890551254576111295323292799752711551767},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-890551254576111296015369878976687874999}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-163134832507438851652211225791428952635},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-10195927031714928257199439307760100815}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":27503789285825619633558121619935376057},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":55007578571651239095078276311656704395}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":28297720022322699950054690418502514987},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":28297720022322699807765449980630332311}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":220777973467005460488415165586764248761},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":6899311670843920633138360775679450257}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-14025245064764561993625343113350435823},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-224403921036232992207803957299812078481}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":39351925384353690413627258387650992459},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":19675962692176845091633511375077406971}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":21786497036634618739151867001054197},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":43572994073269178161292445502461789}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-4853779774349575684376375163526149355},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-38830238194796605653636274560334796383}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":419234071493381450991548863963410108557},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":419234071493381450777079848418551327883}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-697641877156228002073988063828480133},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1395283754312456221196273272860830433}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1264937980817779222881092841371639558541},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-632468990408889611817854094285685678497}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":469129375068165601085635612549011315857},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":469129375068165600365483054035470868713}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":83334342706038771156190864729814335817},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":41667171353019385477803973674170536751}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-4641047547359467905697433764925446091},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-2320523773679733984714796644217705759}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-87103100225558833332010563682848143693},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-174206200451117667004229325702354626285}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":180723864945573829683714748302418465993},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":180723864945573829220864566091533337091}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":147376853321383545408601173259144866801},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":147376853321383545191419688089254847453}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":735449999374797424760900479122243},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":1470899998749564265349593093206861}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-73254613818324179538527842353467046399},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-36627306909162089811922037682679469337}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":636854473086193251980915768509725991489},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":636854473086193251774482385046731652987}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":4212834901910731},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5220982083582993}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-127063278698142481},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-178507798589138937}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":14389087987275067},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":15619919747572313}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2898065151486997},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1160360819899089}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":389761735949717},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2704132964672799}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":15608056912401685},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":2634647543805043}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":874729331166035},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-31818659847228783}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1840160493453179},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-26544752625117}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":282243285277899},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-304385087871857}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-561590574423015},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4301246167011789}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-47135624954154099},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-149928992249739405}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":1166085824368911},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2437052951173437}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":13797628028598409},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-19950825495084663}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":36042267047446491},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":2228534482010645}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-2583432928793127},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-4048054905338181}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4285527375302135},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-224076603428331}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":14970050263546103},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":4777967709638023}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-360343544527541},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-8315924531095873}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1367285616231093},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":973275219149785}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":9218416072713},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-104238579196509}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-426203251458823},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-432622598586351}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-874729891078329},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-1121551291401593}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":170141183460469231731687303715884105728,"numerator":74678818286471517321},{"denominator":340282366920938463463374607431768211456,"numerator":345923563452748093919},{"denominator":170141183460469231731687303715884105728,"numerator":115692317758275253817},{"denominator":1329227995784915872903807060280344576,"numerator":672007455086885397},{"denominator":340282366920938463463374607431768211456,"numerator":142287498609653896559},{"denominator":170141183460469231731687303715884105728,"numerator":56986566429430668535},{"denominator":42535295865117307932921825928971026432,"numerator":19358666092985035213},{"denominator":170141183460469231731687303715884105728,"numerator":57589125556751005481},{"denominator":340282366920938463463374607431768211456,"numerator":59316576852670432777},{"denominator":340282366920938463463374607431768211456,"numerator":89311047593553717891},{"denominator":85070591730234615865843651857942052864,"numerator":53604404715302747005},{"denominator":10633823966279326983230456482242756608,"numerator":6782461209250126489},{"denominator":340282366920938463463374607431768211456,"numerator":377290799373104057689},{"denominator":340282366920938463463374607431768211456,"numerator":360060486657728510971},{"denominator":340282366920938463463374607431768211456,"numerator":200577404704591379079},{"denominator":340282366920938463463374607431768211456,"numerator":127461952206728851455},{"denominator":21267647932558653966460912964485513216,"numerator":10631187695440763463},{"denominator":340282366920938463463374607431768211456,"numerator":231417495868000523659},{"denominator":42535295865117307932921825928971026432,"numerator":13573622661116462159},{"denominator":85070591730234615865843651857942052864,"numerator":15292023170623428833},{"denominator":340282366920938463463374607431768211456,"numerator":85314928724749005693},{"denominator":170141183460469231731687303715884105728,"numerator":103212424208804332461},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":315},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-7641597130420171221672171071231626459},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-3951698822800993178429837235119715871}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-443035368195819013894627378148269162627},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-445589423367576583031969963814156552495}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-81488393603742723382893331854076254235},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-163602690347576016623158786376493194053}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":110141345277705029805367802596223334267},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":3414565590908097830907019083136406991}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":28393930982914633084856628640143658701},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":3436882448753816349659661451123229533}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":220841852562446977710736717103493263537},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":220659272676774430595785600256027466029}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-112123843123036727750428818754533880309},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-56117981853877387454801441247738562473}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":20127420307370985045369792134951003361},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":19613390048931412629240433336130952103}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":113461668539176008722718125165642917},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":60828049869668929251462656300430711}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-19349917958529837846805956532275543201},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-39773288406699303128116778128341780823}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":419522619797833173955865248760402898523},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":417157669561805716775498013056166373875}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1317497693093061309240270510504507377},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-355038995403806316829713918414023297}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-626115131564132527311006706611932995495},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1266393190379065138154516323251077885675}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":469579787710627887845977045499672970077},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":232665410114273570114410830894429589557}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":83495065041208995139867175095072964581},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":163923829736435123181209371717332398695}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-18535966136736585393204349747923735883},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-18648689255460786665538264708266409281}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-87066574120482268164084772343755434391},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-87353530042963372925122981166430961609}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":180977428814634257834147219669507237203},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":22584641262694650475262688103725233551}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":147669331829904471642542340100993335885},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":144826345314422157356814799907282689461}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":3820581233296296186805350021461179},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3513398352215930623648604497919971}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-71998016500384653935862308240039824115},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-146797749285779727222725700482401354121}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1275109778804725602658273212514170024733},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1261448853123351584878156469328218787529}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-7943310791489445419472178238602225015},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-7943310791489445726102909171918981901}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-894565193200424261197485480361891359369},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-55910324575026516368614309387772033175}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-81387558034381454170016037211118611347},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-162775116068762908813330829679121031845}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":1729158503121802868057769569720561355},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":110666144199795383201932833139224194407}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":58034366309737763155403562005310094767},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":58034366309737762861341508056811464093}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":110420290664352200968055164748980063577},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":110420290664352200851613051076036607707}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-224499152612299170600533777441080522937},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-7015598519134349091144551290337143253}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":38518127635857940858385542271654755527},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":38518127635857940620538986221458643637}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":93068164443215372361892916261476545},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":46534082221607624677375642410528465}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-18979836414593591970364369784821435809},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-18979836414593592062622411893772833863}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":842250145119970809284590254599629699875},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":26320317034999087776489838118558004353}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-183343039094637632239199257211563891},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2933488625514202561513185191295277227}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1276289623678832680191920249750919468373},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1276289623678832680962345691956348362219}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":472533634300217886013165125257338237995},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":236266817150108942639100488460275847209}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":42275790183885174616875237081766758917},"lo":{"denominator":2658455991569831745807614120560689152,"numerator":1321118443246411703558344914322794859}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-577295648261748888129839621034802803},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-4618365186093991171066441095214601069}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-86891874588934103957656050647583281325},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-173783749177868208263580828512318943835}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":45130534674292295747143486099335315239},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":45130534674292295628816791676823530953}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":149631682711419362022790357145019634579},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":18703960338927420224859611662895118073}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3199347296693908120382885408918833},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3199347296693780879808726773111855}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-148730171279656624136344339196303332053},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-148730171279656624312308637937673755567}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":642329519553563405852844558072270636637},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":321164759776781702820592263054991991517}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":19483138166248071},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":845817963041599}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-146544197182637475},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-384857940855459035}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":475533760881102045},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":128700650650015653}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3596500065623417},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-618162594925449}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":197897149161383},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2794507657441537}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":64634260397350575},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":21182503617911261}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":38337924872465625},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-5850679794394399}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":911947731510697},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-33466324116287}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":571932559713531},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-310152393703791}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-559073782179285},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2176929316539623}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-49997594277113841},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-158655953777462261}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":6003521642495175},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1966713811364765}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":4306153665362405},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-26253887754484209}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":5471773165641889},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":5589257307116213}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-7628370681727949},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-19004444518146361}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":511947871572167},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-842937437772123}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":16316615112051003},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":2836650923874449}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-58436729620347},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-15794486013365635}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5520671726994261},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1904523700310681}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":307405610145105},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-101399408495387}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1152484934753663},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3867125070163655}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-78512629082319},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-20436066013654379}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":153277245008288923899},{"denominator":340282366920938463463374607431768211456,"numerator":350052578049394174935},{"denominator":340282366920938463463374607431768211456,"numerator":236540311398651369205},{"denominator":170141183460469231731687303715884105728,"numerator":88438997499392658645},{"denominator":170141183460469231731687303715884105728,"numerator":73514616963061135901},{"denominator":85070591730234615865843651857942052864,"numerator":29105096948638434053},{"denominator":42535295865117307932921825928971026432,"numerator":19751882700353626121},{"denominator":42535295865117307932921825928971026432,"numerator":14865173399623350247},{"denominator":170141183460469231731687303715884105728,"numerator":30751564886621750573},{"denominator":340282366920938463463374607431768211456,"numerator":92256424253417037715},{"denominator":340282366920938463463374607431768211456,"numerator":218403388223136606079},{"denominator":85070591730234615865843651857942052864,"numerator":55708265397172475695},{"denominator":85070591730234615865843651857942052864,"numerator":96298822001292960603},{"denominator":340282366920938463463374607431768211456,"numerator":367465776333037820445},{"denominator":340282366920938463463374607431768211456,"numerator":206010711609956437651},{"denominator":10633823966279326983230456482242756608,"numerator":4126655593552099455},{"denominator":340282366920938463463374607431768211456,"numerator":174129041951944039539},{"denominator":340282366920938463463374607431768211456,"numerator":236645550038746506101},{"denominator":340282366920938463463374607431768211456,"numerator":111954923846916003207},{"denominator":340282366920938463463374607431768211456,"numerator":63620031977104335549},{"denominator":42535295865117307932921825928971026432,"numerator":10997599006327188345},{"denominator":340282366920938463463374607431768211456,"numerator":211651070131345143517},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":32,"numerator":159},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-7781113549479794885212753472765387177},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-4019949055257606696390170759978191035}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-890034836988420605873958562438031183047},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-895199012865327500367300933385811614691}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-162622144188619979444423162624323341563},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-163191797876196504634165236535146227155}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":110791226929855097553624381925304823433},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":27482231791754713454109476169689055803}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":58228664508890605718670321996418449587},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":56413970659729265604070963935240549009}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":220899589959075219156261152955687248635},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":110382230261721076858223016281261865447}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-112193166856283555025695028956159431315},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-112281103474612964258772187363088356229}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":9864729465230130650248649792177452721},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":19194496547626100363660596778572441095}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":29813466153185706497760442418580387},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":66880174041482061672493293484531163}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-4728142098159081635201209299346451049},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-38941916129188155939417008156399956777}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":842840535788321329260804690527869052167},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":837982321564367520697865808404903805549}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1384495222139084625673830240067068271},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2984761087745596820830576032908720885}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-631757068556131567296049962439314817463},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1277752574167424017482029087609705615517}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":472987630262414378358566694425263883073},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":468700680046582402810695982636713505389}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":169423860782801761381160058507325642743},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":83181277407665203207277715903359587319}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-9221487900200538820046304079630660409},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-9288829227443202285393951420954355303}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-173713390612242409256222105907711003751},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-174260957099881584531785683701650946073}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":90375569008321178633339250810918042473},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":180478407305957081437040970626683150973}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":37480721300942260774969786547639378869},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":147093960890007378757146414722551967055}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":6501238419593321742565879842868215},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6602095374524662856199371720876967}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-18278818473055056614984384524193451471},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-149017346306519514491681159128389166515}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":80379235292708636556675065815851348003},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":318083936028903523627301295713388562115}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-8076608810414573166246167355031742699},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2019152202603643370180781504057569469}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-224654501671443557320215986262908082757},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-898618006685774229989357353851485842165}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-162465748284901474608317981878879642257},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-162465748284901475092597902385647418617}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":27826731887643571532734934011499972709},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":27826731887643571441817391767624623561}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":59486282344368489703511373673736815691},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":59486282344368489399696416410756080983}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":220866918723614484637966991419117490583},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":110433459361807242200033484553827253333}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-224557531250626601731410697779839494131},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-224557531250626602053907470379539270161}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":18825504007814450830284557027641224853},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":18825504007814450707516907745276280489}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":24810138349820293653170601056717043},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":49620276699640523547694302952894257}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-37054620664549774183384066290645429701},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-9263655166137443593489123165422813091}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":846131202138873976505462134139430416101},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":846131202138873976060654592885650184515}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-3084605623300902221847754753507995853},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-771151405825225669842288572512811031}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1287702068440457483414131627261490208399},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1287702068440457484200614489888701772631}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":7437002604657925829068638733696241711},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":59496020837263406538790330858242204189}},{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":1340109299237255588635189240571892515},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":85766995151184357461053314139688317881}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-18364976549536548527442021721818228495},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-1147811034346034300063156088221926251}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-173383728613998527723790521838108391575},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-86691864306999264040147450042846544745}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":180343340727300871782920680082751996971},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":180343340727300871298958870889864105633}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":151874348916508953400096743340137871815},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":151874348916508953169257517285412468723}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":163333359439376799812513419898937},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":326666718878621287727879795264413}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-18867280443658372670898086559021638221},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-150938243549266981548640155470143824327}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1295666980440783794476575401541015126219},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1295666980440783794042587320824814368013}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":44611775646847271},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":8989634774306371}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-162384438715625699},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-205028937312257839}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":241969599022254225},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":128349110977460203}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":1091963305008881},"lo":{"denominator":1329227995784915872903807060280344576,"numerator":-421913741495}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":405877531968805},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2888845104766359}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":66241584227926769},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":20644042801972829}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":12441068414384337},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-6887424887692947}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":894843102003969},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-239350824794439}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":288160576601413},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-79311479004549}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-539316025215111},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2183052514271989}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-51705013749371309},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-166606257932774877}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":7528421928906507},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5713108504866507}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":364302644462047},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-33351250155334005}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":13051057852368781},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":4556477924577747}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-5072227441459521},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-22018232575984827}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1917662738378597},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-41497321645745}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":17659568398319931},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":1639022268642501}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1531867699276057},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-14682846857494767}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1372872232762503},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1789636445667665}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":159942231482431},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-12238944596729}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-364857891321399},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4281908691766537}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-4288462974941857},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-23107627329086639}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":170141183460469231731687303715884105728,"numerator":78599181186169786751},{"denominator":170141183460469231731687303715884105728,"numerator":177061433840986155289},{"denominator":340282366920938463463374607431768211456,"numerator":242026339765339094157},{"denominator":340282366920938463463374607431768211456,"numerator":181830662629571751411},{"denominator":340282366920938463463374607431768211456,"numerator":151905628331406015369},{"denominator":85070591730234615865843651857942052864,"numerator":29731803096254628747},{"denominator":340282366920938463463374607431768211456,"numerator":161216616738133426393},{"denominator":170141183460469231731687303715884105728,"numerator":61382869960374269603},{"denominator":340282366920938463463374607431768211456,"numerator":63758200115625929317},{"denominator":340282366920938463463374607431768211456,"numerator":95284569449033854453},{"denominator":42535295865117307932921825928971026432,"numerator":27793290000599801751},{"denominator":170141183460469231731687303715884105728,"numerator":114375157396045142187},{"denominator":340282366920938463463374607431768211456,"numerator":393223298477950266925},{"denominator":340282366920938463463374607431768211456,"numerator":375018126885455335927},{"denominator":170141183460469231731687303715884105728,"numerator":105796430184033135093},{"denominator":340282366920938463463374607431768211456,"numerator":136781656224981585243},{"denominator":340282366920938463463374607431768211456,"numerator":178246637384130473993},{"denominator":5316911983139663491615228241121378304,"numerator":3780824956861961879},{"denominator":340282366920938463463374607431768211456,"numerator":115417762101120010371},{"denominator":340282366920938463463374607431768211456,"numerator":66155690719734010467},{"denominator":42535295865117307932921825928971026432,"numerator":11340790032552764851},{"denominator":340282366920938463463374607431768211456,"numerator":216984630775923306711},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":321},"tube":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-1979437027909955848988040648870600737},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8173374910136043631152316827657368063}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-447021919163804705960666638125827015809},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-224814346763939476170713828788751013393}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-81159224675150776152988268534791599219},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-40706464203814653772981437831129177099}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":55715474365764594872949460793453525719},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":55290582959245813459634967089239535393}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":1865075399205417574846768527946966961},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":28925625017933570345462138081932691257}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":220923635078410772367141860991161852533},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":110405016734060697236781112917972256409}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-112243094140997735537392497886892041647},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-56153957896258116583068202561931306043}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":9657314773096022847574429392098982935},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":37517944527122586071175966800007425167}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":62643523937405982528132070958699321},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":18297933677979364323026374889383485}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-9229003398851284891251148926339612963},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-38075634966274077965271516041013497885}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":846734508731791067877166267977815628145},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":420875941248217612255532329320095694959}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2910830290457700624984750636055273135},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-392176705127839441676140403791188599}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1274858163375724248439223935046337935551},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1289172766406808565966187079893130008213}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":238212814420909688189887163743019078487},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":472101190462262164044692826613383947961}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":171853935212850384389023913617353736135},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":168797519126950732907295286057422269759}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-18332202127344359351628384521595938879},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-1155572259141772829798814315875078885}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-173316230793069701715885917788290577271},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-43458923916267010581108954709275614351}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":180546515222937638338154668362643653507},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":180302749965253084842347430908642983551}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":76082091235318650328698980882706440661},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":74675146924642017629520609392620739387}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":2632519000286932166089862296589513},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2468775449219561685105044216640911}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-37113270437204851138928636109677112181},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-151223977057191600362012489815634026461}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":648541897149828619752999693588200295049},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1283278510752401208146410125869361757225}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-8206764010637875567704360932983328575},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8206764010637875890015429309149179611}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-902704218943456856695865640936966311425},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-112838027367932107176546795873905692571}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-162211517101934212441999737904853051569},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-40552879275483553234485331485730066723}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":55968922815118101977561965009814160673},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":55968922815118101790663434476463467687}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":60950794254081951568931344986387701441},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":30475397127040975627543803125453821165}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":110429308821572193761841465210934750163},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":13803663602696524205040395471378666289}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-224580859660964617176874925989981631071},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-224580859660964617505888161013094459385}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":18375476803034464946183240154683899453},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":36750953606068929638935169041712250333}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":52834351373930500699372755332729643},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":105668702747860869230610250274725161}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-1128608694619853552253520294812668817},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-18057739113917656934455610606970392761}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":850108020213099329693812406773913345619},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":212527005053274832310304597729717281611}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-3244240901193686456622236591361328201},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3244240901193686926225277484457667465}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1299175786278806571317136276297443957419},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1299175786278806572119925936876374086777}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":239716264903219491759837719783698649141},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":119858132451609745688548462056523951413}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":173961322444911654668143263497078219813},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":86980661222455827116736350889284541337}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-1139905928505639373020098636060079645},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-9119247428045115125814320791190921091}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-173007501774171653395546482859588123427},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-173007501774171653760464343475754958947}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":90094264237092514275723657055319378653},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":11261783029636564253539336536969581871}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":9631505466481851512012132090730087021},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":154104087463709623954230424983108070021}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2739324239058780403051378708719491},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2739324239058917958559196747669903}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-19141583768353924490355260881511016995},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-153132670146831396109952478876062037939}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1306734465332080749062916340780640203133},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":653367232666040374309023023151310845159}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":50576529429055553},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":4136357839704787}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-5382967281609427},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-431608486455412855}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":484418743721666677},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":244639848545322449}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5195114431253745},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1099329427838761}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":26448284879285},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-745253227158447}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":8389583162349723},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":9681089674084843}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":15533968073807283},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-759637570238645}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":434781930106305},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-92464375132615}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":288836329554123},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-163212807126507}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-31318961253795},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1084011462425611}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-52059503742105205},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-173492197514971467}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":18401820596811859},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3320352442787655}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-3154349210180061},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-10224621532489227}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":7605299571024697},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":6345315329393691}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-3156708288603593},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-12520053143612921}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3500008170538901},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1907057617819283}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":9487400554239481},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":3702933862709353}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3445451105963813},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-6654126592896301}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":167947142912747},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":797532654558389}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":41558125201179},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-23493365317633}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-441953198334077},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4698518313421675}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-6180321185252123},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-25936658018168861}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":170141183460469231731687303715884105728,"numerator":80556615187166639769},{"denominator":340282366920938463463374607431768211456,"numerator":358124686260417658975},{"denominator":340282366920938463463374607431768211456,"numerator":247850904571445435547},{"denominator":340282366920938463463374607431768211456,"numerator":186893885083633358621},{"denominator":340282366920938463463374607431768211456,"numerator":156919955688727644101},{"denominator":340282366920938463463374607431768211456,"numerator":121494424196930105801},{"denominator":85070591730234615865843651857942052864,"numerator":41118507575067080575},{"denominator":85070591730234615865843651857942052864,"numerator":31678432894339270959},{"denominator":10633823966279326983230456482242756608,"numerator":2065112986908083951},{"denominator":170141183460469231731687303715884105728,"numerator":49198809485211450593},{"denominator":42535295865117307932921825928971026432,"numerator":28279536447579459557},{"denominator":170141183460469231731687303715884105728,"numerator":117395329680014184937},{"denominator":340282366920938463463374607431768211456,"numerator":401375958221005176255},{"denominator":85070591730234615865843651857942052864,"numerator":95680766275756358727},{"denominator":170141183460469231731687303715884105728,"numerator":108664537111344081417},{"denominator":170141183460469231731687303715884105728,"numerator":70825414084908052419},{"denominator":340282366920938463463374607431768211456,"numerator":182453145841391887631},{"denominator":340282366920938463463374607431768211456,"numerator":247400587907416845477},{"denominator":170141183460469231731687303715884105728,"numerator":59489977306327307797},{"denominator":340282366920938463463374607431768211456,"numerator":68777493703057399957},{"denominator":340282366920938463463374607431768211456,"numerator":93553730559226908305},{"denominator":170141183460469231731687303715884105728,"numerator":111212634535296399019},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":16,"numerator":81},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-8051375813240368934205449413862349495},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8303705784982411254612626626533025977}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-898092398886650242076567820962954629597},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-903348476877890114119529059650708388353}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-162070491061186374398624394523224692573},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-162509665754203152947483847948030305461}},{"hi":{"denominator":1329227995784915872903807060280344576,"numerator":437737688972983086894740212902729455},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":111223158569851020825293574889206994045}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":61148712541435580052364080237801991229},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":7412695984753462693675001134315771709}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":220915144141642140316164916041400264805},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":6900059711698265936300248397251265649}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-28065519351266399083956325121311128441},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-28079671372049931969303473569000791939}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":37766228515886645601500012450603087385},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":36614023513309206192191030696419966147}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":131566971977577234403152505331192263},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":39884036858324746814690891860547005}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-35972865306440682832945655132967814467},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-37174815704339673434068808186996440525}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":212680961054207949430683647313150223163},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":211405227143664110080105870483468824915}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1530414681404981318372015785914870975},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1649295983859679243890630594794512713}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1286262940139446737908843253132253415799},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-40645444473423568530053968507049940195}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":479893326015606259484128623674413632209},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":475532037885051807068788649198437716373}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":87140253576791161786985995520512214315},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":21403602720418122578431865132690537131}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-4550850895557860026589104995457139453},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-9191464550729669327986030907372383217}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-43235756288634714502747602686705121497},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-10839543479065600158277490224368983781}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":90182344454521885853089057733179861613},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":180151207091614772473603763829305716235}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":154392461685718717040067804191487611813},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":151594558608818979405834151829290424429}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":7859983213516017366223651537460067},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13337043671911725157738863873579825}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-75331420329564193070948008747110490699},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-153416869560514338394782765074718969545}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":327039888485603685693378520166043423439},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":20223108073724693051479790148237754741}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-4166828114077471858096421871409816821},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8333656228154944046309183630945278921}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-906818240648548240517063826148019283643},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-453409120324274120620716866194843594807}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-162017188211555009086608416449927541479},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-5063037131611094049840897698393406773}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":112559231334879738986033410250420193073},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":112559231334879738601884334802929771685}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":15606876136396809935776818734235444073},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":62427504545587239418952209222014928621}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":110408689307256878174778466435130127709},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":220817378614513756101261427903689437211}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-112285508587779538759184167055297807373},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-56142754293889769463502433651351405105}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":35818370988275811332031152801425879907},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":4477296373534476383811450851948456047}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":112358217865291335799875452569617879},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":56179108932645599418234962814697917}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-8785666043975365014889777923563294355},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-8785666043975365065689499470340698129}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":427088570038031726512666568470960920909},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":53386071254753965785317493731854452049}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1706361906461154391675418733048702225},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3412723812922309265281634495728200123}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-327677783372903847664908160879771336473},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-655355566745807695739490272114671856747}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":482926166094649747128654472536094134855},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":241463083047324873173722459665054148271}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":176385349102571447294328977082477149265},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":176385349102571446847866545725769351947}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-18093782227619378696118478344707804489},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-18093782227619378989450824817205399079}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-43164094709194010572360234623711485293},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-172656378836776042662952758180364443275}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":180058694125354340432037867449705636169},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":90029347062677169963080033619395453251}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":78160076747704254005270943844121500515},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":156320153495408507765250014944463884405}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-6003344658386649698721964343256231},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-3001672329193396337550966323605433}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-155312695328252907094666831766487748875},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-38828173832063226821900112735194512631}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1317863125231840074872125733612760483611},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":329465781307960018604039997847926481739}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":56626702923551261},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":24178414107913621}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-176379421026036473},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-112283222082568677}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":238556876451677971},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":222174414841581913}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12100711747918941},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":289669003918691}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":902978740680795},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3077069707873715}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":33546901999866909},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":8602427549564941}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":37700740959826199},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":8610810548926051}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1672043508591639},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-531653794992179}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":575600687517029},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-21115871538439}},{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":-6939896077321},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4260983941315345}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-50850542757366195},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-44732045093687137}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":21967797179814663},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-801027267886549}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-9111335413437515},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-6086598437030415}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":69420285716026147},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":31987525797196665}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-14827070550611889},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-27970021442895877}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1544913641011651},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2570625855818797}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":2529368046114475},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":4100214695992061}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":349994316228179},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-5881527779810763}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5164247489132725},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":655876849431849}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":172426213196081},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-89652783908053}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-518039943883679},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5108553940974035}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-2041128713051457},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-28878551818542257}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":85070591730234615865843651857942052864,"numerator":41253408112048307047},{"denominator":340282366920938463463374607431768211456,"numerator":362048576387181833867},{"denominator":340282366920938463463374607431768211456,"numerator":254022685280299850613},{"denominator":340282366920938463463374607431768211456,"numerator":192069646043886925987},{"denominator":340282366920938463463374607431768211456,"numerator":162075542833239146579},{"denominator":340282366920938463463374607431768211456,"numerator":124122808008835107135},{"denominator":340282366920938463463374607431768211456,"numerator":167787304911719639663},{"denominator":85070591730234615865843651857942052864,"numerator":32691958780628257009},{"denominator":340282366920938463463374607431768211456,"numerator":68481246036154044995},{"denominator":340282366920938463463374607431768211456,"numerator":101597756754933098419},{"denominator":340282366920938463463374607431768211456,"numerator":230062579797316613339},{"denominator":170141183460469231731687303715884105728,"numerator":120477007051295773615},{"denominator":170141183460469231731687303715884105728,"numerator":204827079814543890449},{"denominator":340282366920938463463374607431768211456,"numerator":390586060223033504415},{"denominator":42535295865117307932921825928971026432,"numerator":27903080525363469583},{"denominator":340282366920938463463374607431768211456,"numerator":146663343009679876245},{"denominator":85070591730234615865843651857942052864,"numerator":46687473146317696303},{"denominator":170141183460469231731687303715884105728,"numerator":126465109311573864319},{"denominator":170141183460469231731687303715884105728,"numerator":61322005062497211899},{"denominator":340282366920938463463374607431768211456,"numerator":71487927905154873183},{"denominator":85070591730234615865843651857942052864,"numerator":24116322847515607791},{"denominator":10633823966279326983230456482242756608,"numerator":7124141065376378441},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":327},"tube":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-4090937214486265900298887996465193637},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-1053846280703246183957952899304568091}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-451087528444892008956777173768348002003},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-453733338713256202868333639670187911321}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-20235379234184645323486729421240138459},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-40562003809607360188653317396064022689}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":112681257874600286970946443377975608759},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":111855244269751305426924693772474498825}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":31313583017962969717043461207034945825},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":60764530722765952568532126432887030677}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":220873699059795379549729648238721944229},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":220760866088913686372540466201995222051}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-112257249652354713698708351997068322133},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-28078416087741755391113601154973497193}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":18435105417762229546805777387985017393},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":35677638540969167081160812308970931539}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":138099458028190303965540079599284423},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":5413411296564574272274440906172817}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-34996112887169024529641590080813398129},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-36239852154576012684385624917513079183}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":854805061945319800081793727382904279133},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":424793063343648527351688343311486873875}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-804827324299018278262751219877956125},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3468625337172206548763319798983605955}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1297728953041783284610516485812176595841},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-656098642706008075838357194232913478033}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":120847537337784921970856772588313838809},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":239496397150736118869917299428259969207}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":176703774027824767841058675462147235253},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":86828302801182876360759352229140018663}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-1128521746749148142477333459065558253},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-4564683350358775895462474518827576259}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-86297275571250420000391122794269862607},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-173053385177690633067095687929781457757}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":180206744207047781845025592676645854879},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":11251536679901265556827675575974883419}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":156606980638812469808827300674919239779},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":38456497055507882492596581859920505691}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4987232323660986875479322377600857},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-16992393259860079687902755331153657}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-152859018672687613321243864750939899053},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-77797766707062719668613042781699506283}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":659648464337852826722214672683598188641},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1305338636071677981415114568384444141149}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-4228583137773043284598242504789087143},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2114291568886521726767875013352665297}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-910954376328541374743221085199816453687},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-227738594082135343868819078896582873607}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-161887491720074288900576574789035338245},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-80943745860037144710973018223479318855}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":113171410909915351718851010324455524805},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":56585705454957675662060384015437344675}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":63916012505158816885120726208591659935},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":63916012505158816550365048212275284055}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":3449140180711685275454465079713411021},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":110372485782773928687703775357235089015}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-224529959542798661636050764463990377137},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-112264979771399330989216087901247766771}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":34853685322932607560953044049206600471},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":34853685322932607291087993042423919515}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":59657383112799357883524337424446731},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":119314766225598573860118249934182491}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-34136618465701099515723675241553814719},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-17068309232850549862750758137327482743}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":858334932172142718739196574263290936611},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":858334932172142718271434164850237747389}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-3590390382255073605311200588072116019},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1795195191127537049907609973545027591}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-330577087404033574881947534796870388855},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1322308349616134300363949144499884179609}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":121612100653569811755238481468671609235},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":243224201307139623111844400364140367049}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":89403152770466195193024100733511929221},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":89403152770466194963732103505134684663}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-17930614534736977654605683559161859411},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-17930614534736977958255684944159433467}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":-2692681481109169680709763963581656271},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-172331614790986859947713726194970080127}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":179954762491860631376750371036525110881},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":179954762491860630859606433048949923995}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":4953806957001200682459635441908115541},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":79260911312019210792939716235261554201}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-9469929342604189794717577676032249},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-9469929342604338374332160786965787}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-157477582743111768882338360366334553943},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-4921174460722242783789629573356204661}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":166131815609276837056227393863515560877},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1329054524874214695982546152357423131653}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":125242789753992953},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":31717783664252441}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-174776551209120395},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-461159560652813997}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":57535678031771141},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":189714096989770951}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":13825204020823841},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3548413136144933}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":970179804177123},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1578625211097869}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":33016161932838213},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":7020456602067963}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":44719747584222273},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":10512908973222195}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3178121417023393},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-719413622929955}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":570449166254283},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-176078334705713}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-45862389428591},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2073743545084857}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-23881731987763523},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-182562836388790753}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":25708160444487599},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1890580158946813}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-3783914034740199},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-28286213718009529}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":77704622105425211},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":38252224403636379}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-16822180123432701},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-3839459961996461}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":649309814738971},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3313722616053931}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":10705824776589207},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":8914588401638687}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":7977148663675935},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-9984955866777659}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4852428139237043},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":58345980069057}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":44644383920717},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-42576058534509}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1182020971733033},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5505184514098373}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-10220955745015323},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-7974691864450987}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":170141183460469231731687303715884105728,"numerator":84445372509435686597},{"denominator":10633823966279326983230456482242756608,"numerator":11433888240266739799},{"denominator":340282366920938463463374607431768211456,"numerator":260549445165329450643},{"denominator":340282366920938463463374607431768211456,"numerator":197359982751348078273},{"denominator":85070591730234615865843651857942052864,"numerator":41843943820761250377},{"denominator":170141183460469231731687303715884105728,"numerator":63406555744131646703},{"denominator":85070591730234615865843651857942052864,"numerator":42789124707660394531},{"denominator":340282366920938463463374607431768211456,"numerator":134930576735871363803},{"denominator":170141183460469231731687303715884105728,"numerator":35476501954769761315},{"denominator":170141183460469231731687303715884105728,"numerator":52443606836060459627},{"denominator":340282366920938463463374607431768211456,"numerator":233813805020319962757},{"denominator":340282366920938463463374607431768211456,"numerator":247240100889366199187},{"denominator":340282366920938463463374607431768211456,"numerator":418058784270552782963},{"denominator":85070591730234615865843651857942052864,"numerator":99653209093587989251},{"denominator":42535295865117307932921825928971026432,"numerator":28660631309823871883},{"denominator":42535295865117307932921825928971026432,"numerator":18977755651445160265},{"denominator":340282366920938463463374607431768211456,"numerator":191138167732296269527},{"denominator":340282366920938463463374607431768211456,"numerator":258562987941522366645},{"denominator":85070591730234615865843651857942052864,"numerator":31603122847259807097},{"denominator":170141183460469231731687303715884105728,"numerator":37144771780951357441},{"denominator":170141183460469231731687303715884105728,"numerator":49731661209623340725},{"denominator":42535295865117307932921825928971026432,"numerator":29203207546186785421},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":32,"numerator":165},"tube":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-1038640467161925073794611380618231113},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8554448645890831848716415824660440731}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-906286236440911971028969780490455341197},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-455803139258637332954955117433535755051}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-10110050318819337510206080535107500725},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-81022837611913371988099443173510745073}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":113292502437030023687925097807494826225},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":112477756767974151370102027558086626119}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":64117372308958346074913409363881819769},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":15559935365192056892072463351590116969}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":220832062337541193017725147381039523343},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":110342612553633413168021502236135049823}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-112236823252704552375255050918005062405},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-224586053416384538890950786400654601751}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":2246350648202774566344054914874440643},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":17354608270779287883383811235681301015}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":72445199468282606284024956472833239},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":93736697902802969855084491367994833}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-33986198481665594305381717448726541299},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-17635580182074944906788792420218035523}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":429487255349571751996691301175026682619},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":853644098895721224628601821394181745227}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-3386598719630084299445801159098720885},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3647849652552329138496162030062300977}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1309256553029761004254219383294801989815},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-661901178824152434154175991669306147515}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":486915411117262034479568992934426574655},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":120620729161923206360968894393545364867}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":179123976608682394740638028988769507427},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":176081057157448008193114158452211195165}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-8945406160007416043398795529418957809},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-9058167219787719878206147739568851707}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-172272255012001056309671621771865909237},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-172699059261751041146650662470089086563}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":90036863935784444303022392425459867339},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":179923390409423406865975613037802005143}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":79403644096720598906443457114485089593},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":39010951298906774439989256472684594703}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":953525753087041598919017783243793},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-20845448584438050761042481997306097}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-77520439325622464391729111816027942597},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-39439761355331177973886075694337816613}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":332624321028018673073362275113685582405},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":658229664900351447326008378403516315799}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-8577174907510701270500523564021793737},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2144293726877675404017418213139492647}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-228776708078043497367258345897702152119},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-457553416156086995104287856949573061863}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-161827108160338562778602089732847481249},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-40456777040084640828440687163525732541}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":28443675716886373950989083045959321269},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":113774702867545495398411600379595871393}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":32707957284550752328604950968625471087},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":65415914569101504311557469525150207947}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":220643236518227404973885699822934570777},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":220643236518227404714699473862086977155}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-7014366200689827724139327372056181341},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-56114929605518621880422908161836161101}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":8464334849880704892768565465597954413},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":16928669699761409646330641408226338071}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":63272040842846398878663117796187329},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":63272040842846325377352245167181571}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-33097801489336478847833578757053933585},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-16548900744668239532186787639768898725}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":862577592035709495480389681528071690457},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":862577592035709495005291952331543373261}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1888791472447039327637042019453113157},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-944395736223519790648940695290336565}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1333967555733791359696460359238675526651},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1333967555733791360549684433702553809423}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":122499612731096560739902838837983380413},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":489998450924386242145952010224043512833}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":181224469949786166858105405067292604751},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":11326529371861635399191198202594676675}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-17748776943185780381993328229401236917},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-17748776943185780696259068423652939523}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-43008601763643655056853511942763116017},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-86017203527287310309332728315104015285}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":179877588925920304302226222739119158525},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":89938794462960151886803718415384710433}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":80354195885083528990279639726366367127},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":80354195885083528859989639725557525541}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-13143407240098822831493999370152951},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-1642925905012372150241982506380463}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-159626616267003659641196324330783603675},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-79813308133501829923149982836028708333}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":670155079592049852761174138551616673271},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1340310159184099705043558065512454031307}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":136982053971614353},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":38276028953462451}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-41399554392596991},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-116476624724161353}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":216006257951761331},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":145945588960072813}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":15542472281425255},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":1180933857711609}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1061978226294553},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3226507010444885}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":15966382109457939},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":9740529390508397}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":51901526959582645},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":16977236782111979}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1493591039260165},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-931019691613681}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":561907341824789},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-369353203513423}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-538949741121225},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1993480268630059}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-2647541060389131},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-92048680363493325}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":29619932117354389},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":4667871010623243}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-10551858207115233},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-32223698797080861}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":85549315340511909},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":22027744707206705}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-4642943145534327},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-16610745890256437}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1024154379669323},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4150090121597949}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":22476766601149531},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":9516133412412677}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5282964275123821},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-3993515639761671}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4434034456741861},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":114851905664885}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":368869496175943},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-161178256288837}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-658131036041919},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5878449600221357}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-12283865182614357},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-2186173939256805}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":170141183460469231731687303715884105728,"numerator":86367610815879506237},{"denominator":85070591730234615865843651857942052864,"numerator":92405252753376407225},{"denominator":85070591730234615865843651857942052864,"numerator":66859323999288999883},{"denominator":340282366920938463463374607431768211456,"numerator":202766956533695417431},{"denominator":170141183460469231731687303715884105728,"numerator":86412035981715998697},{"denominator":340282366920938463463374607431768211456,"numerator":129566050480900135131},{"denominator":340282366920938463463374607431768211456,"numerator":174581654080595950079},{"denominator":340282366920938463463374607431768211456,"numerator":139204530422084503749},{"denominator":340282366920938463463374607431768211456,"numerator":73500845242356336651},{"denominator":340282366920938463463374607431768211456,"numerator":108268274255843862485},{"denominator":21267647932558653966460912964485513216,"numerator":14842374765398986145},{"denominator":340282366920938463463374607431768211456,"numerator":253648363340574194399},{"denominator":340282366920938463463374607431768211456,"numerator":426590365391349175757},{"denominator":340282366920938463463374607431768211456,"numerator":406808925650981955159},{"denominator":42535295865117307932921825928971026432,"numerator":29439474006661212649},{"denominator":340282366920938463463374607431768211456,"numerator":157129770897685383005},{"denominator":340282366920938463463374607431768211456,"numerator":195619224112983414823},{"denominator":340282366920938463463374607431768211456,"numerator":264300116474259983337},{"denominator":340282366920938463463374607431768211456,"numerator":130288012687391800425},{"denominator":170141183460469231731687303715884105728,"numerator":38592477953232106493},{"denominator":170141183460469231731687303715884105728,"numerator":51275098853954439827},{"denominator":340282366920938463463374607431768211456,"numerator":239383758336466910355},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":333},"tube":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-4216502312388579122394506512112774347},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2168655283116610372215932669682137265}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-455210127252189057035436529836394299147},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-915761472746010720794353312744043896665}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-40425937812327008079171918654222464683},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-161949947295739428053161506550551636869}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":56947449701766713823724209862382065943},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":56545511649756671421875514354719972559}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":16404731901113243799518089347692037375},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":15931699929087088619599392292582262097}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":220763299024453138508601532981789784507},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":110290012217700164856721928189749124215}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-56100107580538316728804746406795876791},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-224544351678425928096566974955199453757}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":34980850143654596562346412689485934385},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":8427300484108676637103182121428962701}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":4748305111541093915414604523237071},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":6321245258126136707309090737761711}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-16471792269919323139531953404566659339},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-17134588895398463943108403229802199541}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":863228363746852108633557585271477594145},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":13402987774261415059168027883735896917}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1781516485367620822689092621250195041},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-479575885741695155588542062399299237}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-330211502779632494394846214187615421777},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-333867349023643299265859419730409278669}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":490468308255098595040876753304641110915},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":486001746431965985244001250197682552723}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":2836584353221312681494367840179516625},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":22312800788932776217486146196280296857}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-17706583094059031935394663963459316247},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-17955506917034527516351354186350919331}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-171977660871096628861265561650474279391},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-172370943004307996735096855833138864159}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":179966516838228823597405196229727669521},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":179848973374546901390856946496725338673}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":160992460131273020930141955289306706827},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":158247307345456799436516929690766791293}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1385114762001046018354965598462907},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-12450156125813179013844992783418975}},{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":-1228185093512287026202699532105573277},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-39976649926240758659468435119675467193}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":670881006296415956252774933173311916249},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":663821290897184169295550647501588012693}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-8693561662222829126066227794849037701},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8693561662222829479245560366845780967}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-459634862771290852903970712342301511085},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-459634862771290853277375346618923201443}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-161840653896539688339905143454518213047},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-20230081737067461111198969080257079919}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":114369416937816859816321059043572926737},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":114369416937816859399724290236391563713}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":2091462646440291734381246938601165335},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":33463402343044667571673824454169469181}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":110257042045952498637412661923815848353},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":220514084091904997010004382948956555553}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-224362400560224851914025468275432524871},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-224362400560224852270221914955662460009}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":32829792655763696610752607121791561785},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":32829792655763696323564031854474692719}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":134051968525716178227594740080629023},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":67025984262858012986556276803209949}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-16013346587665312096193632556398138169},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-16013346587665312207938638133329306035}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":866901135951953596116446938731076932989},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":433450567975976797817106401867065307483}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-3974649711845017898442958078527729489},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3974649711845018418825174734639802243}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1345688752979758618195809850559609469267},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1345688752979758619066353691126926689305}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":493575407300753037075009424758148234627},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":61696925912594129530575759530559067021}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":183640162915861776786117924249790892081},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":91820081457930888151128781992817479433}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-2193507987087208977201255001012280053},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-17548063896697672142795283703630179029}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-85882946534070405148155270399396025145},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-171765893068140810696712511848346698461}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":179827957291951364742013106088950309865},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":11239247330746960262606775297907151905}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":162879179981199691874522421081473730113},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":162879179981199691605971924619237954409}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-8513939589390995231380312932373287},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-17027879178782150816984577885952037}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-161759100825225797380116877463128158391},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-161759100825225797591576918438049605005}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1351631450104977371059254176518255456239},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":84476965631561085660546198612294354185}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":148142469959462725},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":44048133175231879}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-18360212925132747},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-462518188713166529}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":24488139176852873},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":88030182163747659}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":17205289654325535},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":5835672426146073}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":148209899473571},"lo":{"denominator":1329227995784915872903807060280344576,"numerator":-12820766692701}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":15109635112036429},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":1049820753313101}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":14766511031141643},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":47074417249575577}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2774194430475189},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-577298837408067}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":137476826760197},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-195635489251761}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-151431824244573},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-236092251285561}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-34332478752419605},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-2860982947342193}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":16825658574444643},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":7533795547481137}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-26892868310280699},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-72203760145948929}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":23201222583066501},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":49176449259478399}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-2498116971406739},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-17714126906602673}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1422052285848119},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1268146858153737}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":5848165482829929},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":2494457691156739}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":13349495283119407},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-361375683482293}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1952828366041541},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-111841084804511}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":379828776997805},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-75904131681313}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1434485056410513},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1554262221750117}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-3583560510784649},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-38058881903707257}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":176537619117606256209},{"denominator":340282366920938463463374607431768211456,"numerator":373246816033965638081},{"denominator":340282366920938463463374607431768211456,"numerator":274691414571436263997},{"denominator":85070591730234615865843651857942052864,"numerator":52073174898744147945},{"denominator":170141183460469231731687303715884105728,"numerator":89211946332857308083},{"denominator":21267647932558653966460912964485513216,"numerator":8273896926288757745},{"denominator":340282366920938463463374607431768211456,"numerator":178062694504615188785},{"denominator":340282366920938463463374607431768211456,"numerator":143592323237605788871},{"denominator":340282366920938463463374607431768211456,"numerator":76126770504094332407},{"denominator":170141183460469231731687303715884105728,"numerator":55871634135372563975},{"denominator":340282366920938463463374607431768211456,"numerator":241042682283534418637},{"denominator":170141183460469231731687303715884105728,"numerator":130089024783627666151},{"denominator":340282366920938463463374607431768211456,"numerator":435249264837740775903},{"denominator":170141183460469231731687303715884105728,"numerator":207589930018150727713},{"denominator":340282366920938463463374607431768211456,"numerator":241922458473056990889},{"denominator":42535295865117307932921825928971026432,"numerator":20323671815988342221},{"denominator":340282366920938463463374607431768211456,"numerator":200194278109193977705},{"denominator":85070591730234615865843651857942052864,"numerator":67535696227027130411},{"denominator":340282366920938463463374607431768211456,"numerator":134273239482209444055},{"denominator":340282366920938463463374607431768211456,"numerator":80176846157490422515},{"denominator":340282366920938463463374607431768211456,"numerator":105728346448073633585},{"denominator":85070591730234615865843651857942052864,"numerator":61311409260210652577},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":4,"numerator":21},"tube":[{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":-133646844800117998767369960603285769},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-4395583235119522707500068066851039435}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-914571328745399017566053473547533624405},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-919926364413148736595852571781260209557}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-161716633436685002269120068393915530301},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-40491039970416911873291264925800018807}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":57244378597458195779258107030514792703},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":113695363497837618047288865281767319219}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":67131425719664564752439787669682008419},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":65225302219038942040348322820310757277}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":110332483753638699525513904723348603721},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":110223828808388729139803357704047048175}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":-3504686582009373625923113286239168081},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-224477471441349440350870786483684771379}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":1062136591466096342387823210226692871},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":16339027826496224551524768138826942613}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":159271600632891863913897598658883853},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":54414909700023836860548302362108291}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-31868752914409578598611794977953785013},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-16617181221053067335840220000913746947}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":433781307269158940408033751136342198691},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":862023700646530785470761335427080675519}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-3748953757172220680057384255602883609},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4035245634390800432224379889613055103}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-666248734248067163911196439131013252847},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-673599170436352323281533842914746729853}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":494047922634226701977480876610844199309},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":489548509623292857720226580381174185941}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":2874318220746559217024898112660114735},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":180920925930009097108999803445097518823}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-2187931993620516390682843344930894157},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-17776034831432630648569771075122833059}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-171711945284437270364902817046626168409},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-172070236140145437313527972383830821427}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":179885960262672636285126473444126052139},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":44950561723787329114030992148270092889}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":20395218788151431142639688763552804397},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":20054474547173043445259378919495900279}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-4893583057635661173404922169730615},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-14580434780566791451281726484619969}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-79679369968063432207623146742666734049},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-162037503244894816674746599740811568311}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1353092524722287952081198521635303297883},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1338889896346523233150486903476690417737}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-8806203578981670635266773188269900215},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8806203578981670995951484098535031391}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-923437093251662133787319020997867966769},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-923437093251662134541150154498189641751}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-161932665981200189941895265224468904769},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-5060395811912505953339089615500458041}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":114955853057080409295978823724337915855},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":114955853057080408868088158290174727029}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":17112068667815113005380772244083555893},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":8556034333907556456645193919291320737}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":220359495796529349549637436074553867863},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":6886234243641542164970432488763451983}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-224240186630808727064517520704852431087},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-56060046657702181856947138026562003099}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":31771520169245720963803014094086164679},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":31771520169245720667605830795347492219}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":35461076291263079238687988140668267},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":70922152582526079644074769483482109}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-30923792057537189999164331131651049595},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-15461896028768595114898490898107754227}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":54456337309497676602039959617804937653},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":871301396951962825143494245760493735169}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-1045486062401634773038592715069004431},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-522743031200817453229735086186808757}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-339367955318857012055462224322371656969},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-678735910637714024554983746431917438517}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":497178253243682726863639144370787704535},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":497178253243682726016130878297089675679}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":93026873383268593195903626474283677141},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":46513436691634296473692370262589909697}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-17328279095925794148166740956952758541},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-8664139547962897242290447383202139049}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-10720446742005786072053672582198894077},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-171527147872092577562601598664627350695}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":89903289000663431925151461146306393317},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":179806578001326863298098982263520484143}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":82516764613910898471251154449693763627},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":82516764613910898332878241534814512855}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-10563597474446347244397507110726781},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-10563597474446430512626325015920769}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-163874363205822336473627210425102422507},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-20484295400727792086453894624019572307}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":681509871676177883626664888350961571329},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1363019743352355766750885371157277830493}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":19767748836655499},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":12203944948483177}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-120025337777746845},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-7031781839544539}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":339509243585019189},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":4727840594836117}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":18735875897461689},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":1709947960720201}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1329593970059407},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3309241687684921}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":55517305844024445},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-336536797789945}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":132032028901304261},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":60021667489370187}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1270605073080927},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1383719989347777}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":532710506258165},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-415984001981163}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-1099383360955},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1758844847774653}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-23422862904480863},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-178998354160804303}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":4708403725703441},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":10415476216674295}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-2014742327664417},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-19876501138258133}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":24767941830385477},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":13316509986620545}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-20934292338448493},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-37192217788247095}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":720718317621357},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6057339261887745}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":24120366284544019},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":160630966213861}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":4063177326560771},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3423959755811101}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3267776678149763},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-194519231600723}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":389727556196887},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-142080075963631}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1533446542405499},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-3254847134454001}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-16337417299764963},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-41053501624510865}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":180287692349682909945},{"denominator":340282366920938463463374607431768211456,"numerator":376750562400184285665},{"denominator":170141183460469231731687303715884105728,"numerator":141158751147585019455},{"denominator":170141183460469231731687303715884105728,"numerator":106969692337527151985},{"denominator":340282366920938463463374607431768211456,"numerator":184178449393172956673},{"denominator":42535295865117307932921825928971026432,"numerator":16907836677118566275},{"denominator":340282366920938463463374607431768211456,"numerator":181599510519991823617},{"denominator":170141183460469231731687303715884105728,"numerator":74048314592150790707},{"denominator":42535295865117307932921825928971026432,"numerator":9854103357442966845},{"denominator":21267647932558653966460912964485513216,"numerator":7207160955156333901},{"denominator":170141183460469231731687303715884105728,"numerator":122247383158282235959},{"denominator":340282366920938463463374607431768211456,"numerator":266828129037814749549},{"denominator":2658455991569831745807614120560689152,"numerator":3469028615027491591},{"denominator":340282366920938463463374607431768211456,"numerator":423731230173161484563},{"denominator":340282366920938463463374607431768211456,"numerator":248510756986378958445},{"denominator":170141183460469231731687303715884105728,"numerator":84101843937968002613},{"denominator":340282366920938463463374607431768211456,"numerator":204864498682499094273},{"denominator":42535295865117307932921825928971026432,"numerator":34511516460001890519},{"denominator":85070591730234615865843651857942052864,"numerator":34592722497019243611},{"denominator":2658455991569831745807614120560689152,"numerator":650530960266321201},{"denominator":10633823966279326983230456482242756608,"numerator":3406257871341719671},{"denominator":170141183460469231731687303715884105728,"numerator":125604922365080141565},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":339},"tube":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-4335091993235732501407259755151777655},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-556497546499069139708225009795945229}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-918733586235181779264062308412943705045},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-462047489654590522351426734465256810371}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-80903996280751600606296387645196861277},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-162056830286080141135323865102549677697}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":115074374306989460436904628332387099313},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":14286386042655265743893587108784795587}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":68654458357192289497755191687160124153},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":66734843167077895770635699466356222657}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":110269484810220697264484287160291851645},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":110145057167538710993768035895043446503}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-224174843046547043586629279286419957851},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-224383240283966831012843319163247544199}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":8241157567897184561298320435735734113},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":31616254113338321900786537730452445337}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":41718510551269864997218171497157425},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":7300750538839022635653371366694823}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":-480659436340011915831845539848225749},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-32167191980838386838392738923924769813}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":108996634092527017133037311142485868513},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":866337587419924424364203282889155105111}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-986177181276358530458226913763615177},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4244118592501271887933409690763892963}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-168026362640139809063950901592523328671},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1358989419707519929353633588735391772803}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":497654313322462988698597078823630303335},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":123280548880140760381873991150613105633}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":186369792866239447768916098182162599253},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":183336870699153146139295504386129303761}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-17281235825666123644993743950375930915},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-17577711460145621975884343920549901659}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-171476177198785536808824762884344462393},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-171798083720291396684255595310905086419}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":89916425519418656139057644080867142099},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":89891956784988918458546734816458898213}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":165314502995767602492601194224944142603},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":162608588535136590396346449974268016215}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-4311203867858380324904106981574361},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-33630765945676652614811626458364105}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-161493324806555565778305595733888770387},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-41037771248314470449104602706814848717}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":682245077208742714494692914285728717865},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":675101352590682682038778108177589776573}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-4457486897052707481869396479196911665},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8914973794105415331800753227497400699}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-463801451742421126091573331250436163149},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-28987590733901320404491361935969470985}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-40526896633242995247495741171668980305},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-40526896633242995392738344063861503923}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":115534300397594141699871195341500802983},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":115534300397594141260440459491515369809}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":8747489319002879735940558881139825371},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":17494978638005759376834298689685964581}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":220181524095724323635279931718629597425},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":220181524095724323358806418266903808823}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-224095329718564678368161794393439340131},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-224095329718564678738616430480339060619}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":7670752905838626075557436701452197987},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":30683011623354503996785608539452201703}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":149927047470873722109013157420950393},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":9370440466929597429117312774477289}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-14894807156586555041363516376058237627},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-29789614313173110320699700882316683037}},{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":6841984540601381825927840764610884211},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":437887010598488436611482283276076245777}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-1099956218210795396378637367660798823},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-137494527276349441648029855731130501}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-684658259150733251950936630483668627939},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-342329129575366626201955182933548007085}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":250402928149079601742901588601742566031},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":250402928149079601310409269779697710507}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":94232812390671913127858672341833723523},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":47116406195335956436281867378204213607}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-2136154434347817100375701860018226251},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-17089235474782537150963601402517460345}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-171319181673316200305813224408099739815},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-171319181673316200725089023139967980961}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":179814086121495943905299716315513002383},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":89907043060747971670490754718966507837}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":20896350646900370215788989188662257467},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":167170805175202961441140505685558454591}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-25444929775693594534322092856302031},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-3180616221961720932135349079851715}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-165971752859872939243161845379247420449},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-82985876429936469733951077756037841135}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1374476305098920094292764874829039904599},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1374476305098920093778190576101505752677}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":82726976852741339},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":26372746212668753}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-42860833122166761},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-423587857464891061}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":136194760135522877},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-15033689562594251}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":20029296429495005},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":3858935859347609}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1470883714636841},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1635809366580725}},{"hi":{"denominator":1329227995784915872903807060280344576,"numerator":186740351986763},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-160637615142369}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":143134406166397811},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":72771569903365527}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":563717673424873},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-384819396494889}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":493834436828633},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-214530886473421}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":259662812447355},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3150320530921633}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-334060307479989},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-42220476302597535}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":20645880332191621},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":13422668393726365}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-37278064954737353},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-85783114308479241}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":25938401442921083},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":14068975000614585}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-21372664381760905},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-4787896302886537}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-92243720081973},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-3520313939510387}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":24272405037033795},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":10471131147778017}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":19068687302568275},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-662328792117915}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1219316804540975},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-93456800560729}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":389552288880969},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-124095823605721}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-3236638379801265},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-3322486976007147}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-18354618913573155},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-43398066125416321}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":170141183460469231731687303715884105728,"numerator":91987312951955858049},{"denominator":340282366920938463463374607431768211456,"numerator":380119526629465093841},{"denominator":21267647932558653966460912964485513216,"numerator":18144933977820270991},{"denominator":340282366920938463463374607431768211456,"numerator":219709212212637316693},{"denominator":42535295865117307932921825928971026432,"numerator":23761408361745434147},{"denominator":85070591730234615865843651857942052864,"numerator":34551928389281008207},{"denominator":340282366920938463463374607431768211456,"numerator":185192136625318344101},{"denominator":170141183460469231731687303715884105728,"numerator":76360086029519227799},{"denominator":170141183460469231731687303715884105728,"numerator":40810553314204884573},{"denominator":85070591730234615865843651857942052864,"numerator":29746157268357104849},{"denominator":5316911983139663491615228241121378304,"numerator":3872194213614606695},{"denominator":340282366920938463463374607431768211456,"numerator":273597268410241161931},{"denominator":170141183460469231731687303715884105728,"numerator":226474741429375257643},{"denominator":340282366920938463463374607431768211456,"numerator":432468579969160242527},{"denominator":340282366920938463463374607431768211456,"numerator":255286472332404630613},{"denominator":340282366920938463463374607431768211456,"numerator":173975519069106355767},{"denominator":340282366920938463463374607431768211456,"numerator":209630998728989492683},{"denominator":170141183460469231731687303715884105728,"numerator":141074618965371325129},{"denominator":340282366920938463463374607431768211456,"numerator":142583736940660775765},{"denominator":340282366920938463463374607431768211456,"numerator":86461123525835012499},{"denominator":340282366920938463463374607431768211456,"numerator":112368450898628024395},{"denominator":340282366920938463463374607431768211456,"numerator":257274627640161154377},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":32,"numerator":171},"tube":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-1097904997934055395590555031724007213},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-9012875938564717870147767399547227259}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-922902346602683600629694256453951314933},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-116031226636558616525742737461761822217}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-161898325949016544830678037744520775773},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-81120863135426497971425155172489405087}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":115652038345573396890818860236178878145},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":114878499136136743532229191162949459621}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":70187615468639214673808744104643933221},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":68255014582662811317534085248848718909}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":220386413881135523251212530942509979071},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":110058616517536893117730792230986061273}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-112019429743434992102984578804714380219},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-224262556313468587785768485072452735453}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":3988762687428678791002537265608945099},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":7631072049398084171461865004010213805}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":174759306830396567534721786451813351},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":125092185160750548615925129368191395}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-14812227698073884040567227599262139673},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-7767040699422892617134315693407057243}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":219110923483939070603954126854056711611},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":435365015310215109389951441554982624983}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-4150650951012881597601623548552225313},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2231791968474728271564547233383446935}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1355986222433317416518864071475577681041},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-685421105427211866774356163707821946919}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":501285843971114111329795516142728759637},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":496721854273968127647945918292127193511}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":94390921277625379385150687426043330037},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":185750625012235677797488159272498496917}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-4259934225932359770982482550051950507},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-17360339339503167306875446629206470501}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-171271360429101680842374108174732447873},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-85777784349545783043535660037253573035}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":89918281587880216776402539896688304435},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":179791416549212321675867777564190865049}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":83725043146324914086828822304265370261},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":164765022887285348720434131543192917891}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-6287678532536747415349304809600687},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-38313383778841716630237195502716467}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-163610770598171971591557463128989361833},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-83123348337337810206127466945548356507}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1375956155588926958249207052631255066713},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1361582364214958967695516295193611109185}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-4509870009321793474991713248460962245},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-9019740018643587325271753770601411721}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-58235066653585450715141840507892753747},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-58235066653585450763080916831273124569}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-162369746713145313409645458583278943883},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-81184873356572657003693100522729580499}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":29026259110466841923062661930254329461},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":116105036441867367241029147510262472815}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":35760656452799823957278392165646452405},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":17880328226399911880555045710748328945}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":219982292219172216716790634528900028731},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":54995573054793054108574739031906403609}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-27991269179097481855377054895729488919},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-223930153432779855220765200011754546175}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":14782385124816290373481459718228023407},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":14782385124816290216013950586963773409}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":158306231572885146313318908867353595},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":158306231572884977324953702187269325}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-14312346385757912741053124162974721191},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-28624692771515825727621247160931186937}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":440157232404504309831345668706279318199},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":880314464809008619160525159103614541029}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-4628653945599454445948241397361968493},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-289290871599965937933990847826835331}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-172652809841075536666872011219410817995},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-345305619682151073564751520469725371699}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":126114242799727140430225678918258281071},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":252228485599454280419029567134982295545}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":190876240268676592706332344807333022427},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":95438120134338296090901959044757015253}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-16830755175523487879220930582790822863},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-4207688793880872059760811200225665279}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-85571468704584323985942973790500468979},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-171142937409168648400888810511826593887}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":179851039570394086301795915542488518073},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":179851039570394085725146252591406623213}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":169290397925889045254902622400074485069},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":10580649870368065310066854853795302363}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-29984360229554723149798326115267115},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-29984360229554902668705519789428663}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-84025321343389233905837889818391965943},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-168050642686778468043350052213509530161}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":693001159299262389137999682302187700149},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1386002318598524777749099018408439782917}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":170695250416071411},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":27485423259897581}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-43043712817721783},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-392031515916505659}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":24966404528926741},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-37103357290226251}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":21102213509391077},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":8364490871926885}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1639110669793103},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3211992946883775}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":38141938596320847},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-19205878258279425}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":153984131692024975},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":21093172769265957}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1974832305016079},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1704962802978515}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":56378259384745},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-55795434793115}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":140170648304073},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2727949240633091}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2597514008622639},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-38584887401622333}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":5591091684456727},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":16265170862741917}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-20763022699247609},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-11439945337226485}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":3353816322664047},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":57929016288466499}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-21249581104168577},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-38928870981129389}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-939901759267087},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-251312328315639}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":3008971875603103},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":1300117387977765}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":5516814459832627},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1076909261071981}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1527754296626427},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1170417046548383}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":387681274992649},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-107062004503703}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-208960081294275},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6678315392079387}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-20165171572109783},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-45334611540486613}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":170141183460469231731687303715884105728,"numerator":93793150717445802745},{"denominator":340282366920938463463374607431768211456,"numerator":383338116685493574637},{"denominator":340282366920938463463374607431768211456,"numerator":298696298898393949091},{"denominator":170141183460469231731687303715884105728,"numerator":112802190622029345209},{"denominator":340282366920938463463374607431768211456,"numerator":196165875192341456075},{"denominator":340282366920938463463374607431768211456,"numerator":141217165292209907011},{"denominator":340282366920938463463374607431768211456,"numerator":188839574702651836837},{"denominator":85070591730234615865843651857942052864,"numerator":39366417308427563175},{"denominator":170141183460469231731687303715884105728,"numerator":42246866954281665347},{"denominator":340282366920938463463374607431768211456,"numerator":122755855101573947585},{"denominator":340282366920938463463374607431768211456,"numerator":251003321865660180379},{"denominator":340282366920938463463374607431768211456,"numerator":280483574302627242451},{"denominator":170141183460469231731687303715884105728,"numerator":230994999651578906543},{"denominator":170141183460469231731687303715884105728,"numerator":220698547074257937547},{"denominator":170141183460469231731687303715884105728,"numerator":131127686856985507777},{"denominator":340282366920938463463374607431768211456,"numerator":179907606062682502445},{"denominator":85070591730234615865843651857942052864,"numerator":53623649011865581653},{"denominator":85070591730234615865843651857942052864,"numerator":72078718688970588539},{"denominator":340282366920938463463374607431768211456,"numerator":146914538075479962033},{"denominator":340282366920938463463374607431768211456,"numerator":89759206225197332597},{"denominator":340282366920938463463374607431768211456,"numerator":115835468811317113643},{"denominator":340282366920938463463374607431768211456,"numerator":263437588377983620275},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":345},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-8892439948850495728031989165812089541},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-9117778401399688085100024892606171879}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-927070228323854258329921161627073250497},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-466198489966867098431088084083020376477}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-20257784728576993093441171091265570613},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-162515364872176307172065326096614872507}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":116222025106732924469851190739595845811},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":115457886541023165348283711330726066303}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":35865242794981270253747235638064351953},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":34892703329459324142548748561793701321}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":110104944345768009037904581452679803743},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":3436347542709673026101825831829418163}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-27985224990001981462991533529607699779},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-112059527625868385315679557709197347973}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":3853162310685244576195073079465158013},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":29402429864207433536252208535619798103}},{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":1429169547592075529269849590141523},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":66838056950781663900049255397566243}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-14228020827414820110640653308223081737},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-29937789052989051442857300489527102495}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":880977031146131608618401463830477029295},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":875195908980404124845693799943558292299}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-4367138345454753237819645502532708543},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-146687613104344897336521343269197515}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-341955806107901489500193306134792600529},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1382756163130211417011773586621815684177}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":252470373139765416918472526604052429535},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":500346424078006799152360037798536232835}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":191192709166654184028100180146635883331},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":47040653851299557595088180910625261261}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-16778782576767221108696683420844742813},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-17123730241228683377882148089261457355}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-171098431216718146973290970573113710887},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-85671854750913547793199959056977186349}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":89938136769066558016083841659619752067},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":179807176408536257486405267651229710783}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":84783946418147200084733376854940219103},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":83452231050874178568996572274815602897}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-4188972205877917142130454743359523},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-43211818598138131262422551466603273}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-41427605972985083275277473276202753045},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-10520232098204149657601838353134489957}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":346872924690433865485772206346170108317},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":686515075123748081991045385190630768775}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-9120362903255251065313805239123017953},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-9120362903255251447654768853805163387}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-935905446714849861238725898113291874631},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-233976361678712465503064363931323322465}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-20340418798474130673115637631045156101},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-20340418798474130750024464435519783363}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":29167081526293303831104146563972248399},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":14583540763146651857643629811846196255}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":36536028594204333316963238700295240223},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":73072057188408666229109758330619423501}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":219763993703471787550347624498794008593},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":219763993703471787261707730243968420537}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-55936762408731888612775371416277782849},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-111873524817463777418127919583442050107}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":28417311748812957444963321934391239777},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":28417311748812957120287806107795573697}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":41746994023788635229213344233798813},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":10436748505947147875635971589930993}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-13714787947429478948146405599341140187},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-6857393973714739537389386876215199191}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":884917991207095635693582836850440414751},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":884917991207095635185365345675007393961}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-4868797087583661043515397362094114801},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4868797087583661618515711330801179957}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1393189213722612920807151847797594243283},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1393189213722612921749519784614663028671}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":508130241351472387893337700788412594325},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":63516280168934048374030044008772891093}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":96643037752894500020825637380560526487},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":193286075505788999502786015674581200291}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-8276334761954767780716545066879851861},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-16552669523909535933445805036244154591}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-170999288317074296899396155721802193417},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-170999288317074297338322260338857979749}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":179917917407272551120390833092819914647},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":44979479351818137632797377507014971595}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":42847930682806855527113471354387867451},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":171391722731227421805717631629681808353}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-34748439626907118882216492465416093},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-34748439626907305213036058503587333}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-170110429802166049766305444006037382461},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-42527607450541512501279148423669545845}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1397598880757211177296444223838295157761},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":349399720189302794189256580577315355885}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":86922600712400957},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":1708912966006945}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":8435462930985119},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-352405966514219027}},{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":926143744931601},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-61234831619319577}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":21897312854323845},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":8758648463893215}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1843505680561453},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3120858764940337}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":13542486581413439},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-14931258805752073}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":40943879288097933},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":94314559759026799}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1710763414071673},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-937496238567407}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":50950477818753},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-472009803235749}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":226257614087623},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1143081643527197}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":12568048483759877},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-136320678025669041}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":23985728846598749},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":9415523983521123}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-22385634128838787},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-96320278171263917}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":109300962755275905},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":58033123956225311}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-20506520825294281},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-4862372178996697}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-112690050320895},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-9079803523604603}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":23650497158088005},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":10029414792024933}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":25107140887896517},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":4916589022926029}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":69327621805821},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3283501109484425}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":386149262787995},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-23373543324871}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-210386609235197},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6650162351783231}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-21658394592031265},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-1470521188334939}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":191110901814084782879},{"denominator":340282366920938463463374607431768211456,"numerator":386585358091278105541},{"denominator":340282366920938463463374607431768211456,"numerator":307453564354984247429},{"denominator":170141183460469231731687303715884105728,"numerator":115813602274182248231},{"denominator":340282366920938463463374607431768211456,"numerator":202405877352762777577},{"denominator":340282366920938463463374607431768211456,"numerator":144291473382025628515},{"denominator":340282366920938463463374607431768211456,"numerator":192542446272189801941},{"denominator":85070591730234615865843651857942052864,"numerator":40583991258838057449},{"denominator":340282366920938463463374607431768211456,"numerator":87452899108935256795},{"denominator":340282366920938463463374607431768211456,"numerator":126630772556217555751},{"denominator":85070591730234615865843651857942052864,"numerator":63507004300054978999},{"denominator":340282366920938463463374607431768211456,"numerator":287485586779490454951},{"denominator":170141183460469231731687303715884105728,"numerator":235579096951788799761},{"denominator":340282366920938463463374607431768211456,"numerator":450523040439715207493},{"denominator":340282366920938463463374607431768211456,"numerator":269423433314966586693},{"denominator":85070591730234615865843651857942052864,"numerator":46500679767470747573},{"denominator":340282366920938463463374607431768211456,"numerator":219456241767344861629},{"denominator":340282366920938463463374607431768211456,"numerator":294590566256447528889},{"denominator":85070591730234615865843651857942052864,"numerator":37841551958223216307},{"denominator":42535295865117307932921825928971026432,"numerator":11645646245162630235},{"denominator":340282366920938463463374607431768211456,"numerator":119403932856018390419},{"denominator":170141183460469231731687303715884105728,"numerator":134848125811399761859},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":16,"numerator":87},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-8997652554847095830636813595081788049},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-9218527192812007024102940414459896905}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-931230980571324224739319993889548756735},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-936531839431754091768814534057878533351}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-162312945207411578745062614400986401259},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-40720240066187231347722763506222142985}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":116784597705643630561620990721454489445},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":29007382408695278940240846727281860643}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":73282656168627989452954018382829894459},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":71325608098596498418805311983120000865}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":220012056751656498521365732796319422525},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":13732150714175855029725922020071796259}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-223704765919352359005794400697170676427},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-223955196489827354800206400179933115653}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":29710705968481237735626184547950709395},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":3531418597499333481124191954003417393}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":23925453321031813712865060462221455},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":71284816875625091450515012157194027}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-6814378128930596456218779841567709491},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-28776601688826207939037483826896031885}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":885575876588576743177792086826244545501},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":879729863500167716491939944667875289915}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-4594532965799859981421463472719156123},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2467871381897902313344620260062012133}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-172465194670868439531143175933103418619},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-697365385491757643553726114085198021739}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":508617648087587276536479950316344272757},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":62999334220854143497834880419226088647}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":96801439557961515345613474795597695953},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":47643320099190080309078117475136712711}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-16498205428066859463877145642691651811},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-16867705147463113658506144951706468323}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-42739563948421098471814098839916076433},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-171163457588666898902403523550847209855}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":179947243871503801467849641373871031995},"lo":{"denominator":2658455991569831745807614120560689152,"numerator":1405002735965657166478830627032267313}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":171667340527590156044144409997372979449},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":5282071662261459352661640154204347719}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-21167125406748962538474180020237997},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-48328854795924103715566213858086825}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-83895827309873202516079943530256321883},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-170381535290067032827318810624202269407}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1399097867645597911496322620460655847679},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":692273628796647214777481531190262151441}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-9216694297507204321293013908233342653},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-4608347148753602355244535107555847297}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-235007469015556216176530832272438821443},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-14687966813472263523229674553983801171}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-163172457571123461892381003166212146165},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-163172457571123462525943005810375197867}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":117224420909447666307158474222396667079},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":14653052613680958228948106029323618343}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":9328966757181414866161330060561923749},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":74631734057451318511655721734055129611}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":219528891640504265067196032264612160585},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":27441111455063033096534539862208752205}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-223548475767839379114449545621246281401},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-223548475767839379507121907455000256615}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":13620581596411949379642265526400925235},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":6810290798205974606153267624650196309}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":87989241856852289054518705009351229},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":87989241856852198553236788672163201}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-26204826733367678100050756150299254963},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-13102413366683839180638921577521082815}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":889579669010247633637352176312729969533},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":13899682328285119267553583473947410927}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-5120622282600837120065345375225230413},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2560311141300418854650324401654111235}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-351304027684759941298876143721429601213},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1405216110739039766156473802648521006323}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":127956050164695293219692995644679788605},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":127956050164695292989752647084317116575}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":97847825270441395558371195413363268263},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":195695650540882790563130033961116528611}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-8127409502877597979525754402893980183},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-8127409502877598171793120578537158177}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-42722258879671349932389151330554742277},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-170889035518685400178604113352180812389}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":180015118231217415222109757820375034261},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":45003779557804353655032851023836714523}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":173474220668102368269838735481329151881},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":173474220668102367957951444861926735727}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-19869886490866045182779684673083377},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-1241867905679133866566505192349343}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-172150536285903234696236940271878492259},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-172150536285903234942393318779766766629}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":22019796854070886160101063389899190799},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1409266998660536713694346356256550226475}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":174545625958799507},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":51658247712893473}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":8585300920739953},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-152356643948974851}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":30362725211006327},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-43489281462379393}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":22376778943658555},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":8821547566658765}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":521808057079895},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2997774514203721}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":3650889866893723},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-42211607403136761}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":85879634176063485},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":101533212520784185}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":366623637617941},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2058115314367257}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":364514700169877},"lo":{"denominator":2658455991569831745807614120560689152,"numerator":-3941343067439}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":161573180683939},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-915612525843819}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":24641080644038343},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-57267160278712697}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":50895331918013141},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":21007728045435937}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-46758116215586319},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-24985408486003217}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":109493650467210213},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":28192409214911367}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-19085714534705821},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-19080512993731053}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-665213341073217},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-633114433616367}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":5748266800874511},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":2334952000813287}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":14039773413720611},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":7491074823714809}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-437401358600763},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4293532923399815}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":24036348513015},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-84744332517253}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-3294697192498151},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6548662403901595}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-22756678859775361},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-12117529642715313}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":194536584464316222953},{"denominator":170141183460469231731687303715884105728,"numerator":195050611667486029961},{"denominator":340282366920938463463374607431768211456,"numerator":316591862833626505115},{"denominator":21267647932558653966460912964485513216,"numerator":14861252211138460017},{"denominator":340282366920938463463374607431768211456,"numerator":208814916871848868539},{"denominator":340282366920938463463374607431768211456,"numerator":147431449100035715645},{"denominator":170141183460469231731687303715884105728,"numerator":98150533944480658107},{"denominator":170141183460469231731687303715884105728,"numerator":83666983986084056553},{"denominator":340282366920938463463374607431768211456,"numerator":90500847413030786993},{"denominator":170141183460469231731687303715884105728,"numerator":65305990798561437879},{"denominator":170141183460469231731687303715884105728,"numerator":128439754374562542031},{"denominator":170141183460469231731687303715884105728,"numerator":147301353956052603713},{"denominator":85070591730234615865843651857942052864,"numerator":120114505530634271865},{"denominator":340282366920938463463374607431768211456,"numerator":459854142704706650319},{"denominator":170141183460469231731687303715884105728,"numerator":138398320388539312907},{"denominator":340282366920938463463374607431768211456,"numerator":192263631686856393491},{"denominator":42535295865117307932921825928971026432,"numerator":28064615923172599899},{"denominator":340282366920938463463374607431768211456,"numerator":300978882626512224877},{"denominator":170141183460469231731687303715884105728,"numerator":77970858621959404275},{"denominator":85070591730234615865843651857942052864,"numerator":24170512433862535841},{"denominator":170141183460469231731687303715884105728,"numerator":61538281135669217731},{"denominator":42535295865117307932921825928971026432,"numerator":34505999203580431173},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":351},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-9098739633425518996919139811091955125},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-9314972331722839680865791892379327853}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-233844616264751211338929503252106404487},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-470324140808727502092898430929032464611}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-81327275054435588468676226375025758755},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-40835638224522465353269733383531393733}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":3666875179915117314225001743075295243},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":116593695032716488284032258552251444119}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":74843713882752096473945416036870605383},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":72875206444592729535239129452255597119}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":219795104771999194307949620307010204889},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":219483994086725126731929664423871497485}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-223510258158388258578965828172836074965},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-55943339949746869160655349047084116187}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":28566830009779226984611275390502424323},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":13535823700058265794065871514206917211}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":100087785542995238323821833193442047},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":151778659505811934319987563475440991}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-26029432229227659611976805007968747177},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-27585147413262435764844296915518052891}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":890235372655070773104286208168284212907},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":884327171046209508749929694042529607905}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-2416600117185028635738898129208611809},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-648646095813261873981725637020359987}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1391680748002776112433894732840636504009},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-703382702600572098083232940105595320595}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":32019691740498770082857313228859444299},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":126916315157409543016574625190029358975}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":196012876346256746542637620074187530477},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":192983097634625916498358059385844579653}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-16197847207716664552842942972030482221},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-8296047112854371932311950532746351069}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-170851627962322827730999113884370341501},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-21376961877894724245169770718100454327}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":11253033170016482934898185659755605189},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":22487925602117524699354501771187304517}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":173747873202555240654832023040793703747},"lo":{"denominator":2658455991569831745807614120560689152,"numerator":1336952564331353278995090530431424587}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-6452957127888204208079091168101063},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-13416735209285417948910267047875971}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-84926928417295363759733028827920946499},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-43104896627585987496964979739693383019}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1410775655662947932740589826334778142157},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1396134794656573759425519266062090315299}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-2327143853218293664383636808935556605},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-9308575412873175053363314604861917519}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-944128167216538291084001241248594606619},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-944128167216538291872163749030253619091}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-163720967753727110271509151298179580821},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-40930241938431777731030823286723777481}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":117773558211549017684935768760491735975},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":117773558211549017196791166684226688207}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":38099964841970000434383631746451253261},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":76199929683940000437968679869922915943}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":219279317612369251117388609441313450631},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":219279317612369250816055704428735009467}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-223336951775863075671959253907430808015},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-223336951775863076072262911864550585447}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":26036861910125411480657589446439255243},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":13018430955062705567864388064529187311}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":5790126310841828075125937638839319},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":185284041946938311123411192462833727}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-24951021855518350192813320351033054375},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-24951021855518350462220690916349746395}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":447147185284817167520544650939977600471},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":894294370569634334521837701989328442245}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-2692249443422955161120710658903677159},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-673062360855738865742686345318250677}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1417302433622188709533444982690593602181},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-708651216811094355256645085503803241613}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":515537275700905703070190840465529796721},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":515537275700905702131337903412529951959}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":198105521856889701294166114503460480213},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":24763190232111212590673038249629424735}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-15937053246129735348659248768499480975},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-15937053246129735746053112538338918599}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-170812905628235015488908496640196201223},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-170812905628235015948277481910719819357}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":180142958698695378457884126225713305963},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":180142958698695377842896984940098957075}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":175537359277706077013077531690785383961},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":175537359277706076691785402072850599923}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-44960591573605522756329940300122841},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-22480295786802861691353217017977703}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-87085204953789331771132491505456384169},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-174170409907578663795980512246434125369}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":710503793033820955991286272310923008005},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1421007586067641911417566649919969548821}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":2696122309585201},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":45880365477118089}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":135850363138537431},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-62431768369409683}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-7861340422927491},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-454477020583735659}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":5637215632562405},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":4287558404570849}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1182642712700707},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2851204861757739}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":222045655707983},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-28144918790665995}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":11103124944741293},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":105854868379256567}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1242268102062839},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1121849379646149}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":322760885381265},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-543602435046857}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":864241422449193},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1362744985935757}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":77860750957400573},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-89262575777477829}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":53405607744597775},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":22737578894660597}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-47464185171270327},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-102238934616504843}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":26942224087457863},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":52956768701865677}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-2123012487936311},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-36681292751515981}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-3494664559477911},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11162089497599553}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":11035253778156553},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":1034618531763729}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":1934826183474393},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":4946304306734451}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-728448960377007},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5369138863179575}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":23953252956577},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-40068272117967}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-3114631790852671},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6368796530059823}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-23348534679545807},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-12376164843684649}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":197851047953391678161},{"denominator":170141183460469231731687303715884105728,"numerator":196944232586260709077},{"denominator":340282366920938463463374607431768211456,"numerator":326111277775757606685},{"denominator":170141183460469231731687303715884105728,"numerator":122032657082635984961},{"denominator":10633823966279326983230456482242756608,"numerator":6731146361448319241},{"denominator":85070591730234615865843651857942052864,"numerator":37659465874046784655},{"denominator":340282366920938463463374607431768211456,"numerator":200115931413191586655},{"denominator":340282366920938463463374607431768211456,"numerator":172462663675259762741},{"denominator":340282366920938463463374607431768211456,"numerator":93639876224329798179},{"denominator":340282366920938463463374607431768211456,"numerator":134702139668742928937},{"denominator":170141183460469231731687303715884105728,"numerator":129771119140972970073},{"denominator":340282366920938463463374607431768211456,"numerator":301834700707944356959},{"denominator":340282366920938463463374607431768211456,"numerator":489895206783783823263},{"denominator":340282366920938463463374607431768211456,"numerator":469399062462675939493},{"denominator":340282366920938463463374607431768211456,"numerator":284381055656788528419},{"denominator":170141183460469231731687303715884105728,"numerator":99346549086225328995},{"denominator":340282366920938463463374607431768211456,"numerator":229677595855610707429},{"denominator":170141183460469231731687303715884105728,"numerator":153741519168823056875},{"denominator":170141183460469231731687303715884105728,"numerator":80322054344248089619},{"denominator":340282366920938463463374607431768211456,"numerator":100312956552572145699},{"denominator":340282366920938463463374607431768211456,"numerator":126856137535391074939},{"denominator":340282366920938463463374607431768211456,"numerator":282489869288590637199},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":32,"numerator":177},"tube":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-4597777223823174946195850841766774475},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-9406952946254894181404821731508230425}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-939506509296939899618831367690792524185},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-59046261059361846905734436217587305281}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-163091172788038614571938365249787498957},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-163904020618887087776364742215010715481}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":14736060576486664511134158149475604839},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":117150636053620371358530579439006819241}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":76413244952484140105175929615853612121},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":74433788402447671667931253947297158715}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":219561294624007382879614760525405198309},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":109618632394488102377713740058249038313}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-55825185804455164980934179559428994813},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-223576001606730348349720262056812204717}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":13697098190908505163221852376991764843},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":25863864491885894654851969941189993083}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":13078507448059834276248949985632253},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":161309182980581750482477214803717303}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-24772378409931476169929813591183789571},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-26363987658193923049205402239806791365}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":894950465312023580876261273162516437309},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":888982913865605861150892460884978144491}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-5083508059003477103254983242704982239},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1363662573744269317839650592221052105}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-350925049842687776048648161296361449421},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1418859313053637714203711939989148613805}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":258015708426463627295224888078724009407},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":255678366096382470277758672500900743813}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":198423260974549847348774807784636935661},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":48848145678729946063403486934097363747}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-7938779406242702916789555466250649035},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-16296736805007395289142589204140569003}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-85389633349855154564241804946863186885},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-170901232054127076961950836203011667297}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":90090219715562364613102168785394337737},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":5624898412781421586719130906887696701}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":43952240317168303549385956023480139829},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":173214805045816718375774513591813726933}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-15346186729883045536364295467766521},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-29614082034612327901202653253298687}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-171896449461211109007077568413614028461},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-174437317708132365898671284797235410883}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1422525962445985316158418735293661881983},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":703896890231076767821391379170712062623}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-2348958725210825304796779418181998645},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-4697917450421650810700405925963396405}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-948194128130282088270448776191339134929},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-118524266016285261133343401210159659639}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-20546575403352435452067156712418949207},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-164372603226819484288964635104436980211}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":29578990122142999172194557564704197247},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":118315960488571996187792784057092968135}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":77776230059467976788862661957681306239},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":38888115029733988172273740298157119225}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":219017670292171846585099005620128488421},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":219017670292171846277217587247884545793}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-111557528303959748376071968267966300317},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-55778764151979874290048926986416127011}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":1550309647299525999307767007122247231},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":24804954356792415633470572989645372925}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":194911023085075846422439847127197581},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":194911023085075652676892649807870321}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-23668750255847035167663132054141587481},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-11834375127923517722737076884006086035}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":899056771193650920681461554041516927873},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":449528385596825460078644457167480991827}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-5660796535481106507836942920304374787},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5660796535481107126230660953800504139}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-714723661510783096253112329408689293527},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-714723661510783096752616012480512973477}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":519267788273674689388270820088289619397},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":519267788273674688429881247728298854893}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":200516280897385080431156443999304393751},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":200516280897385079846770509802755048449}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-7799615496208847734546595948775106061},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-7799615496208847939844381547825392743}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-85385774197687043060546722624683994417},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-85385774197687043295492918725373352601}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":90150836085725649334542019856053512729},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":180301672171451298040849784654071064499}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":88790316581518720280334518256220969425},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":177580633163037440229712038798824938995}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-50412727204809451123517916873421049},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-50412727204809659246137583854913639}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-88084762413337949393504254331544562151},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-44042381206668974762125704357522500763}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1432821459883656326728885751453465272125},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":716410729941828163075410853591698709321}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":167626618008431965},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":4615362202006765}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":13141235573790707},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-189402801493623889}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-157880244423623891},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-282147667450735071}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":5587068134436717},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":1997368905335377}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":670840329794173},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2673227024431395}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-13940966212099785},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-9019915880094443}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":90646349084990073},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":106955022582760163}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":132324655963589},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1214086034704277}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":8825318019139},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-147549509584199}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2212841185004839},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-221310091297297}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":27823025280750829},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-60445508605232149}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":6932381301026307},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":23888946961309797}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-46609039617292683},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-103212050736354613}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":104146953050258303},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":11859542909930937}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-7048347265192123},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-4308774201563071}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-535179698495317},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12158850417860521}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":20863793835711499},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":424199543568775}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":8438812322017319},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":752881859307693}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2495552170603189},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6514068841366101}},{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":2988873816467},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-80170989264827}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-351458874081685},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-763108866540217}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-23324332230526771},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-25049368555778841}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":201041495229403210191},{"denominator":170141183460469231731687303715884105728,"numerator":198974692729815966745},{"denominator":340282366920938463463374607431768211456,"numerator":336010483157303770151},{"denominator":170141183460469231731687303715884105728,"numerator":125242771851201853873},{"denominator":170141183460469231731687303715884105728,"numerator":111077456193255864925},{"denominator":170141183460469231731687303715884105728,"numerator":76955800002853821717},{"denominator":340282366920938463463374607431768211456,"numerator":203988716867072343713},{"denominator":340282366920938463463374607431768211456,"numerator":177725106177496732751},{"denominator":340282366920938463463374607431768211456,"numerator":96872337294552189007},{"denominator":21267647932558653966460912964485513216,"numerator":8681497613510012205},{"denominator":42535295865117307932921825928971026432,"numerator":32750056381051669297},{"denominator":170141183460469231731687303715884105728,"numerator":154590536982512307173},{"denominator":42535295865117307932921825928971026432,"numerator":62434422695783018623},{"denominator":170141183460469231731687303715884105728,"numerator":239583215894645057487},{"denominator":340282366920938463463374607431768211456,"numerator":292182780348733612489},{"denominator":340282366920938463463374607431768211456,"numerator":205293846892635337689},{"denominator":170141183460469231731687303715884105728,"numerator":117469578900060026317},{"denominator":340282366920938463463374607431768211456,"numerator":314106272959248407385},{"denominator":340282366920938463463374607431768211456,"numerator":165476489598473118471},{"denominator":42535295865117307932921825928971026432,"numerator":13007634807508982499},{"denominator":170141183460469231731687303715884105728,"numerator":65372753891765302623},{"denominator":340282366920938463463374607431768211456,"numerator":289018634932593411285},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":357},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-9287939865312107695710326711759250435},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-9494295340922777313952529752565754729}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-471804460104243830102480754627395380695},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-948801390288993968995358826993805958123}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-20453341882479220328382963079648197573},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-82284530999383619535759084524051163701}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":7401890915491164060920841974307722429},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":117700591940847949665908688117146674183}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":77990835443944264572672710294521073293},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":76000940155050637756334898467298314509}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":109656478406031664667656897531566838189},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":218976564815122547156061941043954674465}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-111539374440668741764765236387658693975},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-111682820493182959844061036003845095671}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":26193341254603643418325324195788939869},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":1539284238113832752602998681332209323}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":218651946594192881318012714593437375},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":10697954582125216467925829383406189}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-2935867617738416149329737734509231351},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-25113697512586241714174334387382985411}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":899715902903349876144460066689959702051},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":446845989044055192726328719500238970269}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-5345825853658987067862933294287381719},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2866278092764109805823905665231926077}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1415779190829109109576154980983220161969},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1431011618759905109149054995857931308533}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":519765001821358917024948278673385446301},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":515067528354188678254270083694765646415}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":50208656950033418421032844909641021887},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":197802287863195925952190186459196292855}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-15537200269643769811086561305414125341},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-3995370338657044101373460174361064339}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-21342726724683245762762878800923005631},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-85410402360271344076703988383268744671}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":180343191976609965025160337193971814007},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":90060355278352434077989417222666361177}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":177850102299563319235688757038896706707},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":175280387830833049742462806832287337441}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-4476340404541489938713220063596127},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-65014225196104383615008041604279589}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-173918877024508227569182352578407211273},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-176434205855212587300008654704439526365}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1434349590314305395120696430214449319565},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1419525141151345968783885562976246990343}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-9478286859759789503294275755078380003},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-9478286859759789911993500967443466357}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-952221576923370351779076126644996920383},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-952221576923370352584291098312843232801}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-82565446260070466861270437195020330573},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-165130892520140934415539800782718023947}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":118851834682597191301253680464097211483},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":29712958670649297696788091241500263731}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":79360221295080953425953584294217541261},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":79360221295080952967761303039813240111}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":27343301711297209065365580229340907089},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":54686603422594418052063523978138490497}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-111442712149053324757442651070198963293},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-111442712149053324965582482281812586163}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":11772997487903893305611881276250516235},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":5886498743951946561242837783858696369}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":204865883164656269213462371666557491},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":102432941582328034405644618458150615}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-22358612241768873507958556104556277553},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-22358612241768873794402161008506394633}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":225965337282535051205380820023640563079},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":903861349130140204292743287790962565751}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-5949883946714724529290363384574236157},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1487470986678681290652238632299618543}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-180206224642194325083263265948046402579},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-360412449284388650421144218088178829381}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":523013958289690315808464235037761521893},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":523013958289690314830074526505790187045}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":202928552455962426307463700652211506815},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":25366069056995303213378320149125512423}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-7620610051183070059637745126232097537},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-15241220102366140543422178100380505471}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-85382767196716838976217237791450917305},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-170765534393433678433056011483943650927}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":180491407505986397683584142516021498867},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":180491407505986397041854259888635128937}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":179603564541807539703798476559330170707},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":179603564541807539362908863282449561315}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-14024396556404572668429240510640767},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-56097586225618506533551857692245407}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-178147382264539289234822593068645034069},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-89073691132269644752160777236222348563}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":722354668311622838906139051639053293871},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1444709336623245677220986221974587764575}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":4989324390738255},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":24143048759379803}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":72579355780610573},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-62563117890395277}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-252362123900266493},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-168484300605252513}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":21793393599291655},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":3522399727428747}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":47618135738965},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-307691428146257}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-29928561327601017},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-45136792573055897}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":91251973440813027},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":104507242838795675}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":459785385190077},"lo":{"denominator":1329227995784915872903807060280344576,"numerator":-10193262250887}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":247154325124555},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-322727079302565}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2740404680010351},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-207167860567233}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":150655902428329065},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-13860576479960347}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":1780721648758523},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":24329634775413841}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-5512214998394837},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-102725796282049885}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":98546119169873221},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":2490553419652279}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-10455665123967943},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-31518612642734093}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-4982444688182675},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-3276388125312855}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":19350812924458901},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":2390097480863547}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":18204291142145967},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":6939606233664013}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-881134249948767},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-3850311289430717}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":382057846601865},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-86615619721201}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2350481033908931},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5744443319472287}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-702894089255589},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-50177467223263575}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":170141183460469231731687303715884105728,"numerator":102140927470155210499},{"denominator":340282366920938463463374607431768211456,"numerator":402399764004471539785},{"denominator":85070591730234615865843651857942052864,"numerator":86572168914269577405},{"denominator":170141183460469231731687303715884105728,"numerator":128521641725987930599},{"denominator":170141183460469231731687303715884105728,"numerator":114546693040572959333},{"denominator":340282366920938463463374607431768211456,"numerator":157305100449177391973},{"denominator":5316911983139663491615228241121378304,"numerator":3251575513431128245},{"denominator":340282366920938463463374607431768211456,"numerator":183124441185579819883},{"denominator":340282366920938463463374607431768211456,"numerator":100200640263133263287},{"denominator":170141183460469231731687303715884105728,"numerator":71610112540887243065},{"denominator":170141183460469231731687303715884105728,"numerator":132150403812052859201},{"denominator":340282366920938463463374607431768211456,"numerator":316642968843319689559},{"denominator":340282366920938463463374607431768211456,"numerator":509206058346024602851},{"denominator":340282366920938463463374607431768211456,"numerator":489165505633757949045},{"denominator":2658455991569831745807614120560689152,"numerator":2345375298873783755},{"denominator":340282366920938463463374607431768211456,"numerator":212069282370051620825},{"denominator":170141183460469231731687303715884105728,"numerator":120151741320769771127},{"denominator":170141183460469231731687303715884105728,"numerator":160426838314392351505},{"denominator":42535295865117307932921825928971026432,"numerator":21305339824456346439},{"denominator":85070591730234615865843651857942052864,"numerator":26982420777772919909},{"denominator":170141183460469231731687303715884105728,"numerator":67373891860378524925},{"denominator":340282366920938463463374607431768211456,"numerator":295632098223575869219},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":8,"numerator":45},"tube":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-4687863223006657285145400124722606399},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-9576810994313181059253972283249775061}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-947679498426880349814601680390679299821},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-952825795460897734373072636198254395343}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-20533122951077219046029621766105057141},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-82670589895317532425619883817464283427}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":7435345039022626557620060030431551641},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":118243787140150881884000764209444622171}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":79576071566095226564265812050819323281},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":2424257739682585197504197887893402103}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":219052489078062264085291322021210612821},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":109352150609579044541684080104706312187}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-111423430305085930297487849335618103671},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-111572428081612395055943410165801784925}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":6241202517075986177162195317634126069},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":23366252953188657511403691903754274029}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":114184909978517301850069426338603515},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":181359076351328914693703010314574009}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-22173720863395140574341520448173391283},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-23834864632786134875600002158996842775}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":452263117839710128953908873533144600567},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":449224526458727163536948410782461521103}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-2810261728693601190027123679057600971},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6023254238326243657881200780983674837}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1427916878437022452982754650039258019537},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1443221324282459848217454735621440439155}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":523514027849894184108930900587459368181},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":518795983876316966687764619388500658355}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":25405950584720818939472517364495059855},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":100106400238671347052884719828475930561}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-3794160181458697855212786409684456865},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-15646185466482463041781831946310364773}},{"hi":{"denominator":1329227995784915872903807060280344576,"numerator":-666944657038253887841052227991969109},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-85396533302154242116862305986322155033}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":180536925770160460041348471849605204915},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":90137766441352917798174965138449010251}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":44967705396161915466159467979015400417},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":44331541945714631678680069829810125909}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-41168402320962178440765485661845675},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-4439150780931078270829491065463815}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-175920610353017238042275065579211947625},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-89204877544801922744804747109480229419}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":180780905093263897529770336051639633389},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":357832426613623668924168177256162051771}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-9555728786252222650525797439982941743},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-9555728786252223065823073036369102279}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":-14940693083648048510803775030673872717},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-956204357353475105506366101149306277853}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-41499788519179849169445481980598085733},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-82999577038359698696052121831377507425}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":29845342901727734765453081255048852889},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":119381371606910938534314796415962197433}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":80951489913666922713442723671599811179},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":10118936239208365280125638979497092659}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":109234037513564398750436725128022630923},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":218468075027128797179061780337012758711}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-222650739621495351765594926148427536137},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-111325369810747676095300148841521233551}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":22260545047070473230483128291964640303},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":11130272523535236426575828019966178305}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":107577579947455781325238384420846831},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":215155159894911355395022285091493385}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-10510609150633012521321512170596611693},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-10510609150633012668976932866197838761}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":908702386370175305413451595310824490957},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":908702386370175304880277253963840025603}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":-97689494116708915260740469884701939},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-3126063811734685612584116216588056291}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1453908752806434910196667083581151971967},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1453908752806434911234920944139477777973}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":526773907042965316094118456517159243947},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":263386953521482657547622986280571251945}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":51335748232831780934328443145204995423},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":51335748232831780780091475493775807499}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-14862897538146651312749873561869191563},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-14862897538146651750805422325125747807}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-85397676382340987936549580678832467389},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-170795352764681976364662482207868510831}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":180712227995662003901887463194937098931},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":45178056998915500811599805275297978537}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":181605703751439646758249171316491809321},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":90802851875719823203574954606768201899}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-62016123413522027946672118136301937},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-62016123413522251791393524124478167}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-90051755572553823392317351160346927253},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-180103511145107647062371365603862208109}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":364167957219830529133365365820592697157},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":364167957219830528982193174062733662367}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":74274482189221527},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":3726634339588279}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":373155334396410739},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-29347201296475885}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-343582424259196333},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-778975767781536553}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":651536179259965},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":2856453799452019}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1728274497566927},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-555151893235093}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-11610531928230781},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-55050793059626429}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":90679606891257331},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":24617844983417257}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":102971733872839},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2786559020791303}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":217356814951969},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-88583822707049}},{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":25820486557505},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":40759305228017}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":24408629430675975},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":1993600013050903}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":57882030853969657},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":23982724450277923}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-19953538162667021},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-3145229928404133}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":90932220297268315},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":30323166647657941}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-1534011518349179},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-13917722205409637}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-5567840828329363},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13971949243653293}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":8782774749624057},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":141852682476359}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":9703869468018297},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":7645263787416787}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-1124481060577151},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-4446676162976613}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":381318197225805},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-99693260887049}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-433333598116521},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5293220177977079}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-20787938664130209},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-49697240225868019}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":207578089950343447019},{"denominator":340282366920938463463374607431768211456,"numerator":407246324724594530727},{"denominator":42535295865117307932921825928971026432,"numerator":44617932649802520731},{"denominator":340282366920938463463374607431768211456,"numerator":263741196177047899639},{"denominator":21267647932558653966460912964485513216,"numerator":14763497958720468615},{"denominator":85070591730234615865843651857942052864,"numerator":40218501307578271675},{"denominator":340282366920938463463374607431768211456,"numerator":212461241850383042665},{"denominator":170141183460469231731687303715884105728,"numerator":94331965479785127419},{"denominator":340282366920938463463374607431768211456,"numerator":103627264228176795957},{"denominator":85070591730234615865843651857942052864,"numerator":36913447141028540189},{"denominator":170141183460469231731687303715884105728,"numerator":133246761677897815291},{"denominator":340282366920938463463374607431768211456,"numerator":324223471527075748375},{"denominator":340282366920938463463374607431768211456,"numerator":519096560138471103895},{"denominator":340282366920938463463374607431768211456,"numerator":499405937451183564841},{"denominator":42535295865117307932921825928971026432,"numerator":38557885700461208071},{"denominator":85070591730234615865843651857942052864,"numerator":54755893081855154039},{"denominator":42535295865117307932921825928971026432,"numerator":30721751558976496855},{"denominator":42535295865117307932921825928971026432,"numerator":40966544821465496573},{"denominator":170141183460469231731687303715884105728,"numerator":87773716668717940225},{"denominator":340282366920938463463374607431768211456,"numerator":111922120197265031687},{"denominator":340282366920938463463374607431768211456,"numerator":138866551698691421303},{"denominator":170141183460469231731687303715884105728,"numerator":151164964432468600337},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":363},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-9457010946770137224368589952500134601},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-4827242779940657969448552323416145563}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-237928013302489768387707191347137785075},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-956807290344071855833302375753985685575}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-165009473395993459098126724599615026889},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-166223664637468205342268220304848113907}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":7468404443486680439556607771965486643},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":29695107659171806134406053419709430761}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":40584269980490682771635161680505250821},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":79159296998869796014926967204233182657}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":109391186517046697660977503923671083845},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":218422779596936167331651349920216313469}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-55651908719004292879105310179547459547},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-222916289789449925310580934124120571181}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":23709156393725592852510098509475446795},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":22077542214547530439646741138754559101}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":238416594152389859141776485443200079},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":95945406507845107285496257752779231}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-20833205147740558687462696447407640959},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-11264050959441565514253273102037753385}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":454687908058564160344314989073362340403},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":903248630576030413582089210840430857905}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-1476992487694189368304991733004303409},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-3163554955078214016961964629282091647}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1440112295656939025010090318263590625837},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-181935913807886847696281051159046664779}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":527276601728544868914349937730494381071},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":522540331240928697709599480569820470425}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":205662850757277089134751560568706840559},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":202624741533594129770612672129145655303}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-14795758441998351951667777916261219281},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-15290715842407005942506000587396343443}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-85379508020633363713645899566271292063},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-170824199562936232678718561437111833407}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":180761692635135621524786569045120012691},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":90230687912484908271875334869011556729}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":90935336315244181120200758747322499187},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":179351663643065225709854123681203039913}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-11691617599922817182646471337775795},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-19316393965143182102926535299618261}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-177901147254540047658379488695549991685},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-5636359292329139481962829069608661249}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1458219510857197407230777147828688578049},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":721604103076403298054393614984342545119}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-300873109044464190778864109126458645},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-4813969744711427263466500826989851305}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-960136354746422338525503441018695483071},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-960136354746422339350942041749022461179}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-83490240146039003960639557139873828545},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-10436280018254875541104370261827447039}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":59952372707677947081926006858741440263},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":14988093176919486702834058070649174741}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":41274811568065587007631760429853822697},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":10318702892016396691025556805920309773}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":218185242211855393188787677505720652913},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":13636577638240962053716817922413506129}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-222413733326003965957525793073548602807},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-222413733326003966391773037900378665309}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":10474585765329955633125648117836857909},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":10474585765329955438776825706751528605}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":56446367361120830823748366899320453},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":14111591840280194311531510259491489}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-19657187953276523024669261205163622749},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-4914296988319130832271969378922139151}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":57098373146084126512120572644192301431},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":913573970337346023656592597651787472035}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-6567890453672869002691998033330312597},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-3283945226836434833289485831515118591}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1466222966933066446636872531181775649031},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-183277870866633305961906013062178494107}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":530545660835964365431182255482936699673},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":265272830417982182205662521983607779641}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":103880144225664123463663092907725324253},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":103880144225664123146697730931778846725}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-3616037341835098507315242414136064083},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-14464149367340394481591642649477674639}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-42715352258686409737142011499268874917},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-170861409034745639451293879543195506371}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":90482055238099006185763202510706581333},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":180964110476198011702002206348544011249}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":183586629702884269366263469429179958289},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":183586629702884269004667981365834914381}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-68168815798814724707922904675532067},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-17042203949703739198016664888219001}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-182037468701274970075733461274867338009},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-182037468701274970361948619521430984975}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":734354720906083857201429185286053067555},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":91794340113260482111537705843067751809}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":66960915745305471},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13010728246643063}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":57094044887646821},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":897861006027357}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-426472379604153651},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-438059647310923763}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":19489958982735041},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1999712327786129}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":975972028348559},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-973567510659647}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-63688025480551911},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-65693686231440821}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":177408895648560061},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":88497801096555481}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":767685426108535},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2948676409814687}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":190853599421859},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-777099566309017}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3894403682539411},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":243233056473091}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":30607070105857795},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":23579435005649677}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":7260310386459307},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":1427084909536771}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-34133424724971331},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-48567307774481753}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":81613816039399479},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":9505315016047655}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1202058663349145},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-23551781693916041}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-1505854529719335},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-3679692745332157}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":3854130781322557},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-752327206414959}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":10246870240410761},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":16320969836801481}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-5417533927033903},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-10079335393157731}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":379120128524945},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-117964634867567}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-959658922278475},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4724052788504833}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-18158705234533783},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-12120239493410979}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":170141183460469231731687303715884105728,"numerator":105465604400548942991},{"denominator":340282366920938463463374607431768211456,"numerator":412494515629637011197},{"denominator":340282366920938463463374607431768211456,"numerator":367970581497236900829},{"denominator":170141183460469231731687303715884105728,"numerator":135291014654490579953},{"denominator":340282366920938463463374607431768211456,"numerator":243526607694605226839},{"denominator":170141183460469231731687303715884105728,"numerator":82312722850030556279},{"denominator":10633823966279326983230456482242756608,"numerator":6783723964566844655},{"denominator":85070591730234615865843651857942052864,"numerator":48586741057541841923},{"denominator":340282366920938463463374607431768211456,"numerator":107154760675139843555},{"denominator":42535295865117307932921825928971026432,"numerator":19025950523309708789},{"denominator":340282366920938463463374607431768211456,"numerator":268569433482226893927},{"denominator":10633823966279326983230456482242756608,"numerator":10372683195393138101},{"denominator":21267647932558653966460912964485513216,"numerator":33072267878900884739},{"denominator":170141183460469231731687303715884105728,"numerator":254948652082428459055},{"denominator":340282366920938463463374607431768211456,"numerator":316954187114431194079},{"denominator":340282366920938463463374607431768211456,"numerator":226160988820035483509},{"denominator":340282366920938463463374607431768211456,"numerator":251354832347894150757},{"denominator":170141183460469231731687303715884105728,"numerator":167374883040436077463},{"denominator":340282366920938463463374607431768211456,"numerator":180795413130939460039},{"denominator":10633823966279326983230456482242756608,"numerator":3626306979220530491},{"denominator":340282366920938463463374607431768211456,"numerator":143105696926348710303},{"denominator":10633823966279326983230456482242756608,"numerator":9659761794223171813},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":32,"numerator":183},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-9528480367832505760480352538206938433},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-9727440543201820021951464842795360289}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-955700417903425539932073584674215651107},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-960739812403921187525753755364314423361}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-41465887822375379655413115107121510007},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-167219579161680299182947133168525813509}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":120017277889488893945656143900390580929},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":29827678838322791427708106057228003829}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":41383913993909519016839946015150572595},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":80749674572094464930707913792271445775}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":54626288633836270519622443251340200781},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":218134359453182236302326547711228645897}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-222363673557298028299281241471477205513},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-222682635850850610400746859728663413451}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":1401683798950382845887593388209096681},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":20762983421849602497017837216559736519}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":248799208680010865589508336448693555},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":202768776575513764002844480146590747}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-9732941846567351432226355452354836401},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-21194033257725061168342883179807817553}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":914258800096245101764953571784659469115},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":908085007067278660781979885072746392373}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-3104266184923135822545224081676411993},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1661121226519315240264966264252642383}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1452364354395260416460725185578938007295},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-733904169253502676910072081701027199229}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":531050735619632056169689086505214944673},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":526298703867780121642530070767465204297}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":52020263648305985414015690185432919405},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":205038763857783032171955139645586374087}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-7197220397616274449532005558077068307},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-14914948287359329845443357148236288557}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-170784271204505168814115547114217387913},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-85447543403136619701975843674834800503}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":181017457938378532297102662835252671091},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":180678313557582388907432171775293690537}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":183849237610502188078252174972708878147},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":90678211105771904221847050831312883571}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-26302748024584965904027946857365245},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-83732100770621499324796278630475323}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-89930006580464578438897084701295334101},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-182294993002714055946199496384599275687}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":735133444951559100634366573728692721975},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1455161266543344773113221534761437532797}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-4847338494096203577182186995716150235},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-9694676988192407583201219584343064591}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-120501439037603201133686869732283327407},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-964011512300825609906261937377236626661}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-84038861024268091261192824352537871801},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-21009715256067022910197655489955057511}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":60211056568035663370770834986311463111},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":60211056568035663093194323511580312213}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":42077104580933858893094205355975376499},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":42077104580933858642061846509040777539}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":217900560912748536883827133471855268549},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":217900560912748536546622035002812608329}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-111088588472353876357404216830826239367},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-27772147118088469144853920080220929351}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":2451555738241000232841459092724758439},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":19612445905928001462373714161249219667}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":236763501999647208445076295574936525},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":59190875499911746718137376316280359}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-18267148582650887083002235175074281077},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-18267148582650887396775239283741968241}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":459234998262689266037742943828898951415},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":459234998262689265767119447830386341689}},{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":-53886954775149512457342475472886925},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6897530211219138274083307006843102669}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-184823887284694365798098418954562563583},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-369647774569388731865910552918006084479}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":534327154965280901459451821055359316893},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":534327154965280900418088722368795565551}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":210181152870129545783195138694320805349},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":210181152870129545131796796925470999457}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-14044870771614306038705576294025381799},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-7022435385807153252843159637528238021}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-85482011504464105416605092743042241073},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-21370502876116026418415949473193461053}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":181246944604965204025008947940255076107},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":90623472302482601670577964619351937887}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":185545950280028009782456837609363460301},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":185545950280028009410068730736249463607}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-2329863641737473638477398503606297},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-74555636535599397016416293735432619}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-91974420521814764057447481072997050151},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-183948841043629528409837392523884201823}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1480822569675446586533321668799883408041},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1480822569675446585901330643998224016321}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":115764908224200013},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-37027036169150827}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":539538934380144477},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":71261030748359977}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-498671483340655979},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-481525720148665543}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":17728199660504519},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":59922927493375}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4387597299995331},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-823634999003681}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-81387432998726081},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-154260459687629323}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":85132433068630929},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":74469930583735013}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":379244654082993},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-96620774459327}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":168041507127969},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-851544124853567}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2250661930716921},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":28677536150463}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":74863200468821687},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":44772411183568293}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":28744398273218373},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":20822210613792413}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-1676410197730923},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-92130105492533043}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":2206887013446767},"lo":{"denominator":2658455991569831745807614120560689152,"numerator":47280380719167}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2139250917080363},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-18697103712644071}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-6326657484129045},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-957167088742453}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12863738197783899},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4350069822738585}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":21444418036151217},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":16959828842076061}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-3134726410205307},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-702486443483205}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":375148063332663},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-70779071954523}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-2796359665211},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2012049369593683}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-14473943542043331},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-23207033536358311}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":21267647932558653966460912964485513216,"numerator":13396376676516169165},{"denominator":85070591730234615865843651857942052864,"numerator":104537337701917277863},{"denominator":340282366920938463463374607431768211456,"numerator":379365607628804020689},{"denominator":170141183460469231731687303715884105728,"numerator":138784303070870396319},{"denominator":340282366920938463463374607431768211456,"numerator":251029341413285597613},{"denominator":42535295865117307932921825928971026432,"numerator":21070764090147109811},{"denominator":170141183460469231731687303715884105728,"numerator":110981783011140357307},{"denominator":340282366920938463463374607431768211456,"numerator":200177054113228991697},{"denominator":42535295865117307932921825928971026432,"numerator":13848219200292364597},{"denominator":85070591730234615865843651857942052864,"numerator":39221177558245383517},{"denominator":85070591730234615865843651857942052864,"numerator":67629635502189633661},{"denominator":340282366920938463463374607431768211456,"numerator":339753401780190465967},{"denominator":340282366920938463463374607431768211456,"numerator":539394776246597495487},{"denominator":170141183460469231731687303715884105728,"numerator":260324632547716377043},{"denominator":340282366920938463463374607431768211456,"numerator":325687683081651500547},{"denominator":340282366920938463463374607431768211456,"numerator":233485877482547672019},{"denominator":42535295865117307932921825928971026432,"numerator":32131262280715167737},{"denominator":340282366920938463463374607431768211456,"numerator":341913544847160486979},{"denominator":340282366920938463463374607431768211456,"numerator":186191568271419338013},{"denominator":170141183460469231731687303715884105728,"numerator":60146155708853197351},{"denominator":21267647932558653966460912964485513216,"numerator":9216825370995945143},{"denominator":170141183460469231731687303715884105728,"numerator":157989771169532179607},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":369},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-9594475390122054818586058554760459007},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2448730979272192659237998719022282733}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-959638465874843366369258720733173252175},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-964617354590633087931705921389372305583}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-83415170019706396046475887076284676419},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-42082935641516237594056293306332284951}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":120534095648139886885830930560733572551},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":119834817611713227704543745876908572353}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":21093381000366765069019520667824796777},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":41173483742213593055887025533516796621}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":218223383935738354702297930687470070793},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":217841966696908739567195401068999147547}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-222117876674522258910593976067396214447},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-111223303143639855833729800285300760789}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":10559364807218572935628940373579093215},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":19423148776664799821192037831336735867}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":259524682684608129859169662732826383},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":53499832179934897742080312561784035}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-9036317217491423066620518729309584653},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-19833249455309154128626415544143294699}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":57448071812284009752436631108847570199},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":912952283819657342280771097397476704623}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-6522574318288993047195736135458790525},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-3487867836063876301079176457575377843}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-366167961597480403947365100417712807395},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-185022881477671240532947711822634021067}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":534834351095817857490929951393701897471},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":530069139695980642958035609564381159977}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":26312866516114212787566639302096610569},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":207455550264929862292602389113308977155}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-13972584288332049479103993820440924243},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-7259383854726216407600690826297726539}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-21355716368252343173276609442223732721},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-85501255916643840504882288965811492607}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":181304099898632908624401550588313977191},"lo":{"denominator":664613997892457936451903530140172288,"numerator":353371745847080557377521812217470243}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":92903063879910240043324252044495688611},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":183340018807669134440003478596703834559}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-58685530493127772505605509479672477},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-90425882268416508826051938406043895}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-181796761738896506246770406333800082383},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-184203831362681144536400953545449383087}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":741194877910583689339928139538190805895},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1467189406922278862129575183735048380233}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-4877838207210326487749914614837837551},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-9755676414420653411281449025255032827}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-967823847674235526295026993126972131553},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-967823847674235527143944248397715363435}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-84646736938440505270736088777744897043},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-169293473876881011324196084788734925839}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":60466807135229274282660039899669585767},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":120933614270458547995896243399259818927}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":85764837444075741174900591740058134385},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":85764837444075740657437776070905743607}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":217616731200200493380344713498904151587},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":217616731200200493034859862831744040065}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-221943877196604524857933808145609305511},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-13871492324787782832017778738316470845}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":18250943009014181772466007614685469113},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":4562735752253545340036570666574072101}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":124048008004480030039634075886185167},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":248096016008959831032296252398783303}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-16851734261578396564319430774332473879},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-16851734261578396887699707156980933251}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":923384172145084599713159820977379165259},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":923384172145084599168274528419602823231}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-7241397960722562557162568694372068575},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-7241397960722563252619399328810505565}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-745505844800057442113675236819017872683},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-372752922400028721331765333908088749803}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":134529059514885710774908841515112207321},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":538116238059542842036226153513955211319}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":13287895352732132695476436894288137535},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":212606325643714122458259599338130247797}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-3401241515923959878332723361733976267},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-6802483031847919997672761035584699723}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-85551713381837742089726892010379128375},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-171103426763675484705200374080199037289}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":181560532324004327102948678850240635693},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":181560532324004326404458255002821764467}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":187483302681560273145015875159255432751},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":93741651340780136380764317048426888569}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-81176028923776516976534473746067481},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-40588014461888383165730268366509311}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-185837243688225562682188633842655555093},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-92918621844112781493057659357018938627}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":746505746198395424647514460876234186217},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":746505746198395424324566162583879035251}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":23613470383838695},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-64553005705972683}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":154797198366791631},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":131664198496202235}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-139434779908346529},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-129445203749694421}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":1949925609494325},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-275001572033311}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2455242247195527},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1321167688405479}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-49566465208199791},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-44522632871382911}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":159932308235801725},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":55827778656278611}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":401382605515489},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3221310244259697}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":150813347182729},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-465746105095401}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2557412250878035},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1323642496835761}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":358066280409439579},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":33605192101730841}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":14014722517972263},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":8950737775713809}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-9026906365494321},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-85698980342610387}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":29046805621318883},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2077391890422049}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10191958380918667},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13337073403348837}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-3221241885657821},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-7868281936412301}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":9904864041066393},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8502391329300281}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":11129802727231723},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":8581760033182219}},{"hi":{"denominator":664613997892457936451903530140172288,"numerator":-13713998346131},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-3092763459303677}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":369613419741553},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-21374331701981}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":279623510494679},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3189787771682811}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-4853889368592153},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-43425970678345303}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":170141183460469231731687303715884105728,"numerator":108905653227084507565},{"denominator":340282366920938463463374607431768211456,"numerator":424214865337886133795},{"denominator":170141183460469231731687303715884105728,"numerator":195561521180720240625},{"denominator":85070591730234615865843651857942052864,"numerator":71175960874007416423},{"denominator":170141183460469231731687303715884105728,"numerator":129364146004242398561},{"denominator":340282366920938463463374607431768211456,"numerator":172702946533045489729},{"denominator":340282366920938463463374607431768211456,"numerator":227123273568937352447},{"denominator":42535295865117307932921825928971026432,"numerator":25769731304558368127},{"denominator":340282366920938463463374607431768211456,"numerator":114522944796908106749},{"denominator":340282366920938463463374607431768211456,"numerator":161688242600321769531},{"denominator":170141183460469231731687303715884105728,"numerator":136165411761443456453},{"denominator":340282366920938463463374607431768211456,"numerator":347709336609958987777},{"denominator":170141183460469231731687303715884105728,"numerator":274910804206676908025},{"denominator":340282366920938463463374607431768211456,"numerator":531671404683844646001},{"denominator":340282366920938463463374607431768211456,"numerator":334669930969347842629},{"denominator":85070591730234615865843651857942052864,"numerator":60250666818016498177},{"denominator":85070591730234615865843651857942052864,"numerator":65716022850508801733},{"denominator":340282366920938463463374607431768211456,"numerator":349231534078288154385},{"denominator":85070591730234615865843651857942052864,"numerator":47935236446964707497},{"denominator":340282366920938463463374607431768211456,"numerator":124677192727456796869},{"denominator":85070591730234615865843651857942052864,"numerator":37990297073696082579},{"denominator":340282366920938463463374607431768211456,"numerator":322931439196384570467},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":16,"numerator":93},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-9654732143537636566281315694343502893},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-9856669817588783618285669390144982637}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-963520126832993509385216936622180938405},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-968433981511314506227997146784014491359}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-83956361367032420816166445224734446723},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-84781357939389125266430235403257069725}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":121045061437423755695099779571582691713},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":60176448329071639231599260470055572055}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":10748152203230357336752707911204186239},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":20987690944245397615200424019226633481}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":108969853226367443180343026605625072435},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":6798382845402230987253026813010144913}},{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":-1733382948216369871884304701663330321},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-222210972452820243109680289644865702505}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":19785093929793821383025688953104522157},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":4514653422783906545021382259765807815}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":135300054322800605210988820123461279},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":225588894355857063778596845440928403}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-8327046218237335298450520087917823911},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-18446377043337133707872372762289698905}},{"hi":{"denominator":664613997892457936451903530140172288,"numerator":1804884048396099246914031057201062691},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":57365273142187378478627812868901107503}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-3425227239991732555791775805741806507},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-7321211792340189941146401902919491315}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1477033444951477439265288327597645096705},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-746304989106126155230139282893587980371}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":134656320882624005237508793220890536797},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":266924792562350721290602891589187236265}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":212929224560106005098671769215421542245},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":104937905785621635901072010991125844265}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":-211407727618448201067555828815776195},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-14102068127618042243171069100597593277}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-5341991443638094892116217772308523999},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-10696668395094423712664445889810415887}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":181621409079618856530435864943530951667},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":181205337441114797431235936138276061169}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":46935245928037451362867834141445983535},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":46325514419114730240255999127713540177}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-65006081536907052989131662287914573},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-97346299070523933405408219850280391}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-45927743865902916957719886587264658707},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-93044815631895135335516851059695017007}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":373647092957499887981007637887730226525},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":369823259025679619641368774617563777821}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-4905323973260007219995830877331640929},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-4905323973260007441418591727133744679}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-971567469751936958044295948057911452455},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-971567469751936958906189534373516172387}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-170630059877765640033835132499616620235},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-42657514969441410210198539056122201261}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":121439370457765017385080275490443846181},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":60719685228882508400541108919639459369}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":21845274740124837539930923897605798429},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":87381098960499349626461931710286079023}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":217336503750189106462763693977662271897},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":108668251875094553054295626321397630737}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-221716669987689680653766652438619800557},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-221716669987689681119014906702120628179}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":8432619935698774776307042273910291745},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":16865239871397549128023539223058161959}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":129894915517065070531867292538300909},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":16236864439633119020271664423141133}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-1926448069927657933370142975318173163},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-15411584559421263800208060778709130551}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":464155010419509742203411131725273731505},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":116038752604877435482323749022914017225}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-7599836370319467642986427452719087581},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-7599836370319468354619954214448940719}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1503483170166076371429430366417073388091},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-187935396270759546568799131757239954081}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":270955338380222326616981578271014162069},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":541910676760444652147948828352513083945}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":215036569589910416636195175246291385825},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":26879571198738801993544580685424385233}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-3286087178268305647996598308874733759},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13144348713073223089427766447166073871}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-10704985171681226153090194700977469589},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-85639881373449809493532677904299925235}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":45476146879035387747344579860233565385},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":181904587516141550275925792756127405965}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":189398353702275392749043830633573926783},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":94699176851137696177070266005258533847}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-44014440346968578960334282219814803},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-88028880693937416321574792684416567}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-46925580509989522878327265718938784133},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-187702322039958091826485464741824158863}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1505276372231825652704362859123886359887},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1505276372231825652044391144719171238407}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":34993704156349403},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-47725192328574161}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":346245644466520721},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":93467631194592301}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-601823150501430993},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-545038627979244083}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":6573901935958219},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3347687149379065}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5453108815058377},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-968128564004573}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":-1815771478279589},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-101519660670748429}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":4581910456130207},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":4146669012873341}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":449882217751315},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3349346719157279}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":70478815704875},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-253632165805681}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":357937789393179},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":843430848910733}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":421067961497834023},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":90346293193770131}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":53691656511451417},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":13998983041935873}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-493137958913279},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-77739271222734203}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":1379086603206031},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-23796444216222419}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":8199929992123159},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-7553510026814881}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-396289433766321},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-1993024180426537}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3298001338587755},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-6628680249411793}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":22873283975938801},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":8409941702082129}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-3808783724178883},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13414227052241835}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":90942771815375},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-205683613563147}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":609499019678649},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2232561898975693}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-3697787778133171},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-19739586909242335}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":221340041953317180185},{"denominator":340282366920938463463374607431768211456,"numerator":430694015144530431545},{"denominator":340282366920938463463374607431768211456,"numerator":403235384809707563817},{"denominator":340282366920938463463374607431768211456,"numerator":291990781080071815969},{"denominator":340282366920938463463374607431768211456,"numerator":266627671321379025871},{"denominator":170141183460469231731687303715884105728,"numerator":88521402847033851815},{"denominator":170141183460469231731687303715884105728,"numerator":116283701620251911931},{"denominator":170141183460469231731687303715884105728,"numerator":106146574053401940405},{"denominator":340282366920938463463374607431768211456,"numerator":118369116234005855607},{"denominator":85070591730234615865843651857942052864,"numerator":41655359604153909481},{"denominator":85070591730234615865843651857942052864,"numerator":68498986986515628931},{"denominator":85070591730234615865843651857942052864,"numerator":88949229261032542199},{"denominator":10633823966279326983230456482242756608,"numerator":17513950602765095669},{"denominator":170141183460469231731687303715884105728,"numerator":271486600243499106195},{"denominator":85070591730234615865843651857942052864,"numerator":85976822049110655345},{"denominator":340282366920938463463374607431768211456,"numerator":248715884824581993837},{"denominator":170141183460469231731687303715884105728,"numerator":134400596807446084487},{"denominator":340282366920938463463374607431768211456,"numerator":356711800000129571115},{"denominator":340282366920938463463374607431768211456,"numerator":197448750981726487509},{"denominator":85070591730234615865843651857942052864,"numerator":32300042096692995289},{"denominator":85070591730234615865843651857942052864,"numerator":39146466413511416505},{"denominator":170141183460469231731687303715884105728,"numerator":164983983254668692495},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":375},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-9708961825635837551363691695054810191},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-619524212607047235698508843545342413}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-967339614010928774376543125017323042893},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-243045487660999073390345450978697668485}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-169113327866012183888963855223048072013},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-170914787974700450414047076348442037185}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":60775147209709722923974171599044165583},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":120865094253907337123446009843942955839}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":43801250011439618392396676616131268775},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":42780326356548787210532466959876202387}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":217656821861752688160338170944093611199},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":108627957623115370180201799345611135317}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-110816898862615865777239081521838518615},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-55494582617800375599121289924610598709}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":4606652068440674318112132125666429505},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":16669955626277542272623321821886484507}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":282032644636421465740318194183767753},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":237543955050423731752441379619011487}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-15210898113964549550082191193818547707},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-8517024694545523295939715698611891131}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":929046834110649969943362735435496499927},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":461377493741122001207743474808972693157}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-1798131258688291154085565638806169339},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1920313573611786006136330436918833497}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-744723853531096068152276141445299738811},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1505087532441419615532534188165938899503}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":271210643415534424575575514509011955781},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":134409474826787765866975291775625137391}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":215360696084720025660786701492176318845},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":212300284483602355435756587743344767063}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-6533443224596563080356695703927350675},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13664752687529474865860203500318060963}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-42769625096677379779770205561403677355},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-171327764156369169722810437798026927163}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":45492272019249583526592921796197852359},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":181515137240338325548690095627155886631}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":47413368943901250277975832500058237931},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":187242172337777525167042556529920173789}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-71566087792277077073753379389414471},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-26123046977402598246038623809845543}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-92801133075877598001049735422273456369},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-46988010379114715700747774656652520183}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1506862883105886811840460800369468742637},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1491472448984669074961206938789898745203}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-9859274800238371115343590314991208367},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-9859274800238371565371521588348900593}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-487618297747126834201285992187013709261},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-487618297747126834639130626192258667799}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-172089520533634252123833537130165480929},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-172089520533634252955710603586918068615}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":30484871301306368595016159094264548415},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":60969742602612736890591455837104988027}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":22250646620047496658271969374409510983},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":89002586480189986083617824257678845349}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":217062675595798487446419705286961515769},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":108531337797899243541569617368562969889}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-221498414028151936097387081315995127961},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-221498414028151936574115718125560904271}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":15455914562112675632634980889147957535},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":3863978640528168798864212002013785465}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":271851819132970707806366773772784991},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":271851819132970463150902466132339097}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-6973671671466602634023276536808533067},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-6973671671466602805713024475808433795}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":933240888518766890499196437549319616267},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":933240888518766889947932447073030109767}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-7973177937944174182675890700394538617},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-7973177937944174910755249534665375007}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1516003858610618387870467095816403247481},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-758001929305309194506547638830408346573}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":545708160735078776986400619728121040233},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":545708160735078775877204606132754480807}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":217472668540107854834945550458270226419},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":217472668540107854128109413320751515403}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-6331470690324420153658325953968718617},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-6331470690324420410293361907277502475}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-85746541000635290979778425749806745689},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-85746541000635291254654935884438524451}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":182278735862909768064216716235674750797},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":182278735862909767335461716646089479565}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":95645399975465274298259430280458697949},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":191290799950930548189872136354883509177}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-95112498673171929924943378373309911},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-2972265583536631176737493251377163}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-189543751828043346345331644569835506273},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-189543751828043346668031860626944939405}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":379404312627908311612410562227599415137},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1517617250511633245775426694764103684685}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":41234126473661209},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-64124419002210533}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":94181353047893069},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":240159213041495947}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-314440384542454575},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1119689892098565365}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5136723358250937},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-3173788793979727}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2982774865112179},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-553265445657261}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-132582969760248411},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-227051705021383911}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":63204230796448321},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":7478182586213301}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":254959777692785},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3331683377573161}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":123046619330633},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-269561328744683}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3116105669445223},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1012678652007881}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":484299171836496847},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":114335933658187335}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":6227230018948703},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":9207752047069685}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":820910880103097},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-16828486560243427}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":14087145588134247},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-19977666471543849}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":5681777205783877},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-610103422463835}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-6036853333068061},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-15818220477948085}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1304525456243689},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-18490501477198249}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":22966718713536221},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":4031221263229577}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-8087384499860277},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-7072665831446751}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":345601375701731},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-119977899224901}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":494006185382031},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-529223541572069}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3576616623383363},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-33972176928232913}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":224929224154439804975},{"denominator":340282366920938463463374607431768211456,"numerator":437587988199574134235},{"denominator":170141183460469231731687303715884105728,"numerator":207846564333434732867},{"denominator":170141183460469231731687303715884105728,"numerator":149716275919635939069},{"denominator":340282366920938463463374607431768211456,"numerator":274731767212391658481},{"denominator":85070591730234615865843651857942052864,"numerator":45398250226821805061},{"denominator":85070591730234615865843651857942052864,"numerator":59576213316319886621},{"denominator":170141183460469231731687303715884105728,"numerator":109293445339651117843},{"denominator":42535295865117307932921825928971026432,"numerator":15290891438481633533},{"denominator":340282366920938463463374607431768211456,"numerator":171687644511982463385},{"denominator":340282366920938463463374607431768211456,"numerator":275504181585884692161},{"denominator":340282366920938463463374607431768211456,"numerator":364019374373083158225},{"denominator":340282366920938463463374607431768211456,"numerator":571278792127326029783},{"denominator":21267647932558653966460912964485513216,"numerator":34660246374101475101},{"denominator":170141183460469231731687303715884105728,"numerator":176703047455462661959},{"denominator":340282366920938463463374607431768211456,"numerator":256630145269736343845},{"denominator":85070591730234615865843651857942052864,"numerator":68716490089609233987},{"denominator":85070591730234615865843651857942052864,"numerator":91090648879651389637},{"denominator":340282366920938463463374607431768211456,"numerator":203320333129435426747},{"denominator":340282366920938463463374607431768211456,"numerator":133865035424248303885},{"denominator":85070591730234615865843651857942052864,"numerator":40336900695067904093},{"denominator":340282366920938463463374607431768211456,"numerator":337089002676371179793},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":32,"numerator":189},"tube":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-4878424345792182678876525839925624661},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-9961758838682424250911339475887616577}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-60693279450028375876094261555341508557},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-975842456715283454285385814410914036783}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-170434515141544894603292313978833877757},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-86194981251876174454360248493819023489}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":122049895591549028119500705236136838475},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":15171441791473626942935020429967070741}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":89224964157637161327868671606044619239},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":43588112524853129718708369072099606413}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":13586038978691689051362841151759712895},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":216975424570287841231387816122247317649}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-27677014349316722699219544827140362707},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-221750065009151447732932523400345181743}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":266310148923124884948907868233655627},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":1907219116781945224446239446830431163}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":293829505079593710951324960264541819},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":124935520518772882808093701630488647}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-6871848017922345810263235955887393229},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-974806594155332960983014847738470657}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":466994791766533900949268794708567515615},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":927678958317458559631929147801884787913}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-3774564990741376013722037753635392117},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-4028096934924954091433796381365281075}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1501913075835386123239795973280181108397},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-189701752392786075642017487806260081223}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":546220038502896964173600942549096195147},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":541431858789061061922876370975223487639}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":217798131545827294950595156133647045807},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":53682432343146579570360313791702236591}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-6291441977299743313474378940583063099},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13206733686236971585258767643279763119}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-171250207532143180945033183277635262947},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-5360804989990861124660390639332953505}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":91173375703894461824370261534003309973},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":181855458194847397678946378032693798239}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":95771652072316043789920210697564816507},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":189160025875346870662396099612335309819}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-4897743331925327789063707456853589},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-55930909115367457534830754902252969}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-46867568862651849410745637826995097009},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-189790741344114336346247664786704617441}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":94950832097232756535429395850010214699},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1503727823195836935097449012376947299259}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-9901211305050571499080810924501402379},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-4950605652525285978203688765077353169}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-978825566753935540303771753125759851501},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-489412783376967770596968436477679548141}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-173673600538716111703746231949320908075},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-173673600538716112561003489342915190491}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":30608510920808799034715211046765060373},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":30608510920808798881195069811557299171}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":90628894826902826918807878121867717473},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":45314447413451413176355838911509470469}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":216798085417640923350216992173560254919},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":216798085417640922977396846149990302597}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-221291984085542440667924537471387405211},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-110645992042771220578364695339256535311}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":14023545036262556724855522358063881849},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":3505886259065639068691253739501401473}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":142144447353784272073248985760427805},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":284288894707568291345439336756617465}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-12459657568879655508196744794770074323},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12459657568879655861981505231582617195}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":469084975187705685426108227971509869089},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":469084975187705685148834947810464411163}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-8361743137713344406264065913294089083},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8361743137713345151064588314032843927}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-95535747885022214035405261157444273429},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-764285983080177712865602952636883930627}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":549506308005018641463584056415775565327},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":549506308005018640330616927775899338351}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":27489428111348300283996605887152778519},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":219915424890786401545605949365438287047}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-12160675962356376859057049458625662329},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12160675962356377388566921754208966539}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-10733958907806563645845235376820431025},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-171743342524905018895672829150109729089}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":182682514912229584756392062717114978025},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":91341257456114792005989504842565789059}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":193160368001952628388001832458048828091},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":96580184000976313984636794720317734931}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-102424583955606259646344343111841873},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-102424583955606536998292426507385993}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-23920154936257240710265467420522102027},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-95680619745028963007315341482425571811}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1530034044504728544967182660331837955145},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":765017022252364272139275779311207001117}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":4293055582633683},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-80381402525250239}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":391426438528331585},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":143544011406490425}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-637208724973835097},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-275404778983996605}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3504259289901343},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-9016176663334527}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1587047954460401},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-38248561056683}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-146600293434119681},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-123546023231621629}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":101789531701458083},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-19001416414795129}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1131930615932471},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-806028039997447}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":102562769847641},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1119491905888863}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":6599267502630237},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1172452382534847}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":271343601481501617},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":275713319125397427}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":22094399627511759},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3942792034189375}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":6695432282565127},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-3406515194612905}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5276610451850071},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-53853727141722345}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":14006557591482257},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":2760160929294463}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-5491279605943299},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-475051895795801}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1986313637761839},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-23973620412544193}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":703775742877533},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":3867804551027941}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-2102009780596045},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-14565772325416193}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":158478544917009},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-68139685591233}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2783735054253265},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":147267136391895}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5965988276693901},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-26761275024225907}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":228578608844718768057},{"denominator":170141183460469231731687303715884105728,"numerator":222417338743838890615},{"denominator":170141183460469231731687303715884105728,"numerator":214198211750658032773},{"denominator":340282366920938463463374607431768211456,"numerator":307032270122793953797},{"denominator":340282366920938463463374607431768211456,"numerator":283044906929234939123},{"denominator":340282366920938463463374607431768211456,"numerator":186359827135270414371},{"denominator":340282366920938463463374607431768211456,"numerator":244342031129504706099},{"denominator":21267647932558653966460912964485513216,"numerator":14065192229915073553},{"denominator":85070591730234615865843651857942052864,"numerator":31599979572511062705},{"denominator":85070591730234615865843651857942052864,"numerator":44222563259259372791},{"denominator":170141183460469231731687303715884105728,"numerator":138569896609563327511},{"denominator":170141183460469231731687303715884105728,"numerator":186190069098379480175},{"denominator":340282366920938463463374607431768211456,"numerator":582326915823490274827},{"denominator":85070591730234615865843651857942052864,"numerator":141612840211478850561},{"denominator":170141183460469231731687303715884105728,"numerator":181586101234614891379},{"denominator":170141183460469231731687303715884105728,"numerator":132375040478630945469},{"denominator":340282366920938463463374607431768211456,"numerator":281063537907104025167},{"denominator":340282366920938463463374607431768211456,"numerator":372191741301321674779},{"denominator":340282366920938463463374607431768211456,"numerator":209361042642105163107},{"denominator":42535295865117307932921825928971026432,"numerator":17334459910472709073},{"denominator":85070591730234615865843651857942052864,"numerator":41562708833104825583},{"denominator":5316911983139663491615228241121378304,"numerator":5379628191076924525},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":381},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-9798343764837833161386454429658201201},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-10001776669807080439551143394868919619}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-974771542435233118148685419002968717617},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-244855518256359655171887767628633117777}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-171878362164785937148482676481639539693},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-86994972926634543450995640383937848247}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":122543947590504269031765126049320674357},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":121872322717972274308895998721528425625}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":5678262816262563995449579334324862859},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":88797073304633204100998330114285265799}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":54275429058737305508974659228455609911},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":54177827460860469035277330711059114113}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-221210629319891279723885040396249850293},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-221530390106847565113030238117598049775}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":488668617756434863418327557167072371},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":1727822963409189457733934328298248507}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":305997949931367085383164021831325065},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":65644180431950662768835778130393897}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":-191455214281766605375458034780237095},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-7067794428627721853901732082736486521}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":117364439244184692470472296458187244815},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":116576296822697102218271473567580276161}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-7920603373868586112262103818715472491},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8446349014624466816399970436482878195}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1514427883334937180995021556455625408691},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-382546909022937312437369236966095135259}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":550019145028975037237679834395035688257},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":545229162480201413503818469414831762695}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":220242333976159600777872404255844636197},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":108582463968051052250178984819591514571}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-3019505088637125528004777981631777299},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-6363966302885550338547118245447010881}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-171458910437216781856211004651409571227},"lo":{"denominator":2658455991569831745807614120560689152,"numerator":-1342192391232459241325542741675199353}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":182753925610017667427014403685784841331},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":182225937002120000658622528952898522085}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":193410199045314627631517948025679185715},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":47763827790666412618533428147892573625}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-21349305687452351486427819769815447},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-119452867364632362903426057858253891}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-94657337639841365540823397696731434051},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-191605440763288883718495284958165994259}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":765819781353974748990912746044494433471},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1516059215823153662196937939261447191595}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-2484020274029224212510261767653419613},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-9936081096116897314780804943074966297}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-491164433476003917167845068047532363269},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-122791108369000979405128133611016811939}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-43845934442409796294602330889933083867},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-87691868884819593030755831314831256549}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":61461556292282376410483104664787507535},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":122923112584564752191365034781013791007}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":46129810569870255421594155981782730009},"lo":{"denominator":2658455991569831745807614120560689152,"numerator":720778290154222736406557035257269527}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":108272804183441008924861004224057160595},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":108272804183441008733459418820925598819}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-221100263897845878433729621868507957355},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-110550131948922939467611249711848984807}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":3142176998115772387487248216083960169},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":12568707992463089086612924604838082133}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":9284625086228238968755857740005597},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":148554001379651692908985378949008909}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-5474588035560253722294343282396648799},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2737294017780126952264615334427658467}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":235772554777114307945938337531768252477},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":943090219108457231225524527706376662847}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-8765838494277716649505459146004029505},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8765838494277717411310849598070536985}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-770592800103191799146476452428936505933},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1541185600206383599480212038103025590871}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":276651335287460790540404604315864905357},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":276651335287460789961733666718619755583}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":55591414265975576533131401334009616713},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":55591414265975576346520874630675587927}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-11637493641519555925406960686384578163},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11637493641519556471577121107906107553}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-172030407784118646598093267643617742909},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-86015203892059323586457982841338509039}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":22889421795369403369906463510999723979},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":183115374362955226198808877638120792201}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":195006814478490262745051611523461060999},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":195006814478490262313892617841624314171}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-54981103853419191806340312221994103},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-109962207706838670885444874389783757}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-96577261250480762886770584958029093411},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-193154522500961526116146845347103425901}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1542526544415610876566480980920411521149},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1542526544415610875863254215300803052843}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-6619796367388833},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-191990124147801417}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":400712066631796039},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":162029315454391791}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-312383683305921455},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1063984819917664007}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":230840944014111},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11727220364855929}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":6639214279049163},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":480894346175351}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-39373617143220341},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-262913022036461055}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":74249704905271531},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-11959447400544419}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":650897268410565},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3058526753498507}},{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":670629922287},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-143717724069133}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":6877073211178067},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1305442559636531}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":296609948233790515},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":80062950718225645}},{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":291214219039833},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2081005487412365}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":24100798872154517},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-40755365618693751}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-7258721696470579},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-8466658298994257}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":33155508022812845},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":12177632416723589}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-4720997002109587},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-1774378926325575}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-3527873577365551},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-29716232328228513}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":43617374266016507},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":3597139784146169}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-8541093690943787},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-14787564947340833}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":283253547867201},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-308834861150235}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":7275899548878169},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1773478352777267}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":663025186306127},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-8998885217232173}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":232287123466891520879},{"denominator":170141183460469231731687303715884105728,"numerator":226214391822678740119},{"denominator":170141183460469231731687303715884105728,"numerator":220665780404156089133},{"denominator":170141183460469231731687303715884105728,"numerator":157396438468273035589},{"denominator":170141183460469231731687303715884105728,"numerator":145785713282675521687},{"denominator":170141183460469231731687303715884105728,"numerator":95674438063199885965},{"denominator":340282366920938463463374607431768211456,"numerator":250685395030341281525},{"denominator":85070591730234615865843651857942052864,"numerator":57916463492275929863},{"denominator":170141183460469231731687303715884105728,"numerator":65295245276839888871},{"denominator":21267647932558653966460912964485513216,"numerator":11389547143275794727},{"denominator":340282366920938463463374607431768211456,"numerator":278977927163550834305},{"denominator":340282366920938463463374607431768211456,"numerator":380883017013270998245},{"denominator":42535295865117307932921825928971026432,"numerator":74199642317541358171},{"denominator":340282366920938463463374607431768211456,"numerator":578640700324897408035},{"denominator":340282366920938463463374607431768211456,"numerator":373210564468865012943},{"denominator":85070591730234615865843651857942052864,"numerator":68270085798389129297},{"denominator":170141183460469231731687303715884105728,"numerator":143700009388471444439},{"denominator":340282366920938463463374607431768211456,"numerator":380206800817373783899},{"denominator":170141183460469231731687303715884105728,"numerator":107788186802645087445},{"denominator":340282366920938463463374607431768211456,"numerator":143636086080768389057},{"denominator":664613997892457936451903530140172288,"numerator":334570481454930799},{"denominator":340282366920938463463374607431768211456,"numerator":351593775521606103947},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":1,"numerator":6},"tube":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-4917018044289302867171508188611389923},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-10023384456160340224289530009300354717}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-122296394007581401086524290973745411057},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-982915298993494524807968578948905663349}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-173446652124537668528487579636045318829},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-87858068133161050140537050284888977865}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":30758128640024741013082345128921893969},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":61183773459569610621970744985976729745}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":11560477510622972307300874204365669499},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":90422792020449387229856642488471199759}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":216835686874200445791679582170666528577},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":216459672308605221377053684398627047549}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-221020227707501469848226550828567938235},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-27665272404832263079431491085494250327}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":3551956270192021520220363594009621643},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":12365024635712792520622136395315694895}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":79636318059615060426429000644195835},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":275667594658318556850870757804193143}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-10739860390141407360666415033989831067},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12650746144295016806572071053428844049}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":943814767505069514791880026002448474259},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":937542748472116020909424325334201832605}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-4153633737642565449184869188366339025},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8852024099567265977313011543323532825}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-381747588438096237387686149913073533245},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-192850809729011212463517548265176662033}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":553816147547694560644128147556873816279},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":274513718472360657925668951555727572871}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":111347061026632505462608723332733447299},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":109803340380811055807269002488327373351}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-5776119110885677038016826533844243047},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12228280155754713312181729630380492761}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-171704579036208827041011255483633919807},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-172092213923170739966136358739540430185}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":91595024779774012923978028714422736885},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":182626122173638646030203781913716339095}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":97626960405781900368909079824035263981},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":48231937755776735526525492571090580975}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-92663157200263503505085582815635659},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-63631198153503816026278135790385421}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-191135168221368148382574398706623195159},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-193395880908265921378067803083136150175}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":96508837671469699918209129710566845305},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":382116640063993617891504708573779090053}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-2490868863247597792832745111251693247},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-4981737726495195821799166722774274641}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-492870568749220975270562089935169232719},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-985741137498441951462339753612790983181}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-177221053512482992488557087486685396133},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-88610526756241496698989616481453376625}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":123406740046163504357564565186436342279},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":30851685011540875928028568480071780143}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":5868397820728070652000033099510039163},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":93894365131649129831363004393251672969}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":6759629700558567894293205937427186591},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":216308150417874172224140652790499258425}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-220926138774439813374142009192237457133},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-220926138774439813888949844913931015997}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":11091977741848295425440211649783917429},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":11091977741848294948516737140139350289}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":77579026375525046196379114699135609},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":310316105502099914980352771773391249}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-588534271516448621253312448702293453},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-9416548344263178315494905645558962037}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":118499319301521552772966299953436230283},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":947994554412172421621407600276490388191}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-2296438648557619374181464984179327735},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-4592877297115239137914418812638907403}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1553842768220836023823176769396841045041},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1553842768220836025033433129550823549431}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":139273685085201915760090247924410005701},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":278547370170403830929013201103929254505}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":224824196886039811607962162506513790287},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":224824196886039810840888909796958169641}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-11093344949483831448130356940997057131},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-5546672474741916005695449558982717331}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-43088511348262123462976266111386333973},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-172354045393048494439692134299402099171}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":2868385571444573595916448403468320839},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":91788338286226354680895965853702928431}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":49207481516135155870145822469206643431},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":49207481516135155759158231342446883891}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-58860893868176508713840780500843411},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-117721787736353314928977946667706231}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-194923369643523918188964928250539302503},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-194923369643523918541970695964270487023}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1555094410542849436753423613895680176573},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1555094410542849436035410993018020043785}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-3979011255984831},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-55750144985585355}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":807200046257176491},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":351930724051702787}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-591324474514472015},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-502105445456535323}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":305671449657303},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-7227495739065877}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1725595002813211},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":252619714051131}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-165296696970958605},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-275275389441236793}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":21650715045074059},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-19708860766333137}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":753546515904089},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1409618530462441}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":73905363749683},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1171150866242569}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":7076947605668269},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2779576986894149}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":159666294632603381},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":361119646672092291}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":29270687269119203},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2204308316899241}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":2212873163682965},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-25864998678137341}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-25334043193643045},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-20378752719574235}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":1190819135369251},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":18732307517915009}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-932604718803013},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-6425941065407881}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-12367269526949455},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-8905431006674933}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":10366236223134087},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":12811328762004477}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-1058427815286567},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-3687354836902095}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":122241934899423},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-348375346650889}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":9064721760332599},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3340692599607385}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":7826890839249235},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8221968206753171}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":85070591730234615865843651857942052864,"numerator":59013502075086899021},{"denominator":340282366920938463463374607431768211456,"numerator":460380152210123522019},{"denominator":170141183460469231731687303715884105728,"numerator":227252314764955689621},{"denominator":85070591730234615865843651857942052864,"numerator":80679441325402679081},{"denominator":340282366920938463463374607431768211456,"numerator":300315816648876952659},{"denominator":340282366920938463463374607431768211456,"numerator":196565979257350217149},{"denominator":170141183460469231731687303715884105728,"numerator":128671424712134519549},{"denominator":340282366920938463463374607431768211456,"numerator":238459574089775917039},{"denominator":340282366920938463463374607431768211456,"numerator":134901959315396579467},{"denominator":170141183460469231731687303715884105728,"numerator":93859402273925873167},{"denominator":340282366920938463463374607431768211456,"numerator":281022626909570566419},{"denominator":340282366920938463463374607431768211456,"numerator":389532444884011893849},{"denominator":340282366920938463463374607431768211456,"numerator":605097544592342719803},{"denominator":340282366920938463463374607431768211456,"numerator":591139204261048429949},{"denominator":340282366920938463463374607431768211456,"numerator":383526939402370859811},{"denominator":170141183460469231731687303715884105728,"numerator":140812855178428193455},{"denominator":85070591730234615865843651857942052864,"numerator":73470476924919626625},{"denominator":10633823966279326983230456482242756608,"numerator":12138001757788064765},{"denominator":340282366920938463463374607431768211456,"numerator":221972041255106861157},{"denominator":85070591730234615865843651857942052864,"numerator":37187587940806196209},{"denominator":85070591730234615865843651857942052864,"numerator":44125005460571307413},{"denominator":170141183460469231731687303715884105728,"numerator":179493272836524095669},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":387},"tube":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-2468238648188769601843128864258000947},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-10038897622978485710075982354810392653}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-490943492304523962257812208746987641369},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-986305808038647022716281601305846465183}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-87570431303636826224452552310831599747},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-177569614230928979743947291803331303677}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":123515642081532437626881891061882055971},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":122857275973790564920752050505470288727}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":47059704584029799758005200634545003061},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":5753311126592677104752656955980498145}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":54145351671812665818891959660030860569},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":108111711741782104508554769459527743485}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-220847796994493897168996110596576411747},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-221128315775996099131469876204380726661}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12755714449608807697476001323767998427},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":2721412469537906555551479732117419119}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":331478784019536565806401337148595339},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":289150272834126153109837279311906897}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-1150565727304531192709220287313995499},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11143026099196536505434539253068625583}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":948701101628146188494748491084391655611},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":117808348464672585052229121996949329407}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-8709430840473933141474918076251938469},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-9273507378511768221780326574749593273}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-384899651734142943395269618874578818997},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1555468539634690020699822766894869379211}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":557608527808438861093453199045098538469},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":552824241993419659793468903680919257515}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":225154327475296966743756005779867122539},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":222055804795969565235230997472014793221}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-11005489491701444584594451345641525479},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11707716324832680014575195770271422845}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-171987088883917112065541100277150771481},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-172420277885932457391062771742797230209}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":183654475010066373778921288806902929885},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":22881934286381748447349548407990024119}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":12317141243120606514527414557087368581},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":194777098321663657656276393700424665429}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-100158110810887660373404667825331737},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-135286826237781547659068984980033101}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-192931487856992693026796280455696429711},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-48790458574170255123561293215072686317}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1556718475689912316871014147658463649615},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1540949663162910715751280889238949291473}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-9982951817133704137369777675117795081},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-9982951817133704617282750792131153087}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-61816074615202043415974449608314607771},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-989057193843232695593420358024218658739}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-89593172026824723648434636653030649461},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-44796586013412362058275018407209078213}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":30971238907911642450997230759206302713},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":123884955631646569142353951964148893315}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":95532729346352027083420569948516165889},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":47766364673176013232424766131836975689}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":216088642251067966206878717215163409627},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":216088642251067965802729486745247064375}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-220772487916911638255513869339384480037},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-220772487916911638784279638388224860813}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":4796962545627069280638680807095656933},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":4796962545627069035207818103514558419}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":323920167296261074876948541477253551},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":323920167296260796200638415254320069}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-3931211663022036369460871314327432545},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-3931211663022036562815265723340557727}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":952875673751051938312315915608552180975},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":14888682402360186527273006204731419505}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-1202720505610072334611564626378573287},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-601360252805036217099727393567819925}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-783270691003215894845342992665326788389},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-391635345501607947731104139044502726341}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":70109994406958024476605664344387387003},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":560879955255664194604884679587803214581}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":227291886897042718583127083555384517535},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":227291886897042717794854787668577936131}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-2632047458448703816317725106047664717},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-10528189833794815846061902509975980361}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-172713925974985472277078028325710010737},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-172713925974985472878133862535175463049}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":184065697292355427146436556224342128659},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":92032848646177713176376288071388415891}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":49657379861035939974358344723525426333},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":198629519444143759440319300632360796923}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-125699065976293016013560328887586247},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-62849532988146662029757670206297491}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-196667581216599444757783746551556577857},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-98333790608299722560750296057804582497}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":783868585310216751890661337336430195529},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":391934292655108375762080795117565489133}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-99433688877352887},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-126939471125149695}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":801489524886209653},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":183286012445606569}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-535912137482112635},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-925225465345571899}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2999370027477941},"lo":{"denominator":83076749736557242056487941267521536,"numerator":-4189296473835}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1790014801182819},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1493401303391973}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-169028792874046543},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-283662954239689225}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10800398277834575},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-27815716328469291}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":438907066803651},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2534772003414507}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":70529760362055},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-148028794441649}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":7185805635571299},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2829617682276037}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":84762101447784011},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":394031423385130769}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":1295165261735367},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-16353718947160941}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":47194785947356031},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-10774779738531105}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-42699695575460373},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-94927514336520739}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":10689271418298223},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":24849027806759807}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1232279637387303},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11309213412299367}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-4439171232871841},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-10420358213894289}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":38819307995898095},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":10701518362681015}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-8164183716723253},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-14472319175344505}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":101985759150409},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-391017788927415}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10914500153027989},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":4958937490399747}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":42279496815408049},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2158023791544287}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":239879263931820205751},{"denominator":340282366920938463463374607431768211456,"numerator":468697123395594968943},{"denominator":85070591730234615865843651857942052864,"numerator":116980185874363944333},{"denominator":170141183460469231731687303715884105728,"numerator":165405202771086741829},{"denominator":340282366920938463463374607431768211456,"numerator":309282685513470437603},{"denominator":85070591730234615865843651857942052864,"numerator":50504324538568837821},{"denominator":170141183460469231731687303715884105728,"numerator":132160926446312167259},{"denominator":170141183460469231731687303715884105728,"numerator":122714358751722891979},{"denominator":85070591730234615865843651857942052864,"numerator":34834381920763379779},{"denominator":170141183460469231731687303715884105728,"numerator":96676108157518238775},{"denominator":340282366920938463463374607431768211456,"numerator":283279726558772095667},{"denominator":340282366920938463463374607431768211456,"numerator":398333022461460802845},{"denominator":85070591730234615865843651857942052864,"numerator":154209075160208930181},{"denominator":170141183460469231731687303715884105728,"numerator":301977101837133705269},{"denominator":340282366920938463463374607431768211456,"numerator":394127193914470074159},{"denominator":340282366920938463463374607431768211456,"numerator":290391078715823898365},{"denominator":340282366920938463463374607431768211456,"numerator":300515954730770681259},{"denominator":170141183460469231731687303715884105728,"numerator":198413965572983019949},{"denominator":170141183460469231731687303715884105728,"numerator":114276942531570571789},{"denominator":170141183460469231731687303715884105728,"numerator":77011340005554445125},{"denominator":340282366920938463463374607431768211456,"numerator":181855445000694979447},{"denominator":340282366920938463463374607431768211456,"numerator":366479686364787285381},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":32,"numerator":195},"tube":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-1238085482554558269595285939205804383},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-10049053919851113854692243069973191565}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-985312552605932549994680438696308120419},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-61849900095689159716194865514849269691}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-176962155653155122612788777876157808721},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-44887783561608455342617967945602606821}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":123993357164098234197876843686092177293},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":15417695045799122262823137407191052401}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":47879287541560376882179830132540354249},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":93687230692596727172141153496490307293}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":216341778370220135578809041655512950121},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":108002749423380252982272263638053206793}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-220696217130455252177546723868376815341},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-220951685623771431856883525274439622243}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":11281638608066553430507021202045536563},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":9385029945883973379838927878452600777}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":172402900217659087875359643135865921},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":151515685210813374433603783412209699}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-7647779047756763568338490491399072991},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-4806539133048612199256142675734100163}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":476783662567239581169422467107043600619},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":473687678832624725215290614797321856951}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-2281846583248409149600208340191933727},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-4855534472681022790825548460620119835}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1552250662268196564464246494614716130811},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-392042930448647789513387310059235504389}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":561393714382250908213591619181530222443},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":278308538279212539464815133372112867339}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":113811896134104225253961222515536833601},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":112256565366232758772275925041082487425}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-5218867765244079805098469221418650853},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11166190440483351167079117215093366719}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-43076554952851484000139706825344646611},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-21598059453478939314252649568002853171}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":184146467361184957992226461102026402603},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":183513366484815792847299205974778767829}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":24858879596379837390929712766443720591},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":196603135986040836804321283263033592817}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-107877808346934786458778864735359559},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-143521915918571777259402539714380291}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-48675849761187083766600450689757519361},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-196903105032504166292033055475099072475}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1569370290801997105141023884901373228853},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1553508201625166361690342893675533772605}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-4997016260395909319225562833109340851},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-9994032520791819126131777843201459823}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-496136020521994333940544250945356175803},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-992272041043988668836289353812862008943}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-11330004608240122474071682739721759987},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-90640036865920980274346404866764544045}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":31089442593030844735468713775103938169},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":124357770372123378263712262010998084141}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":24293579853569053937727183343011791317},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":12146789926784526889243709020131724215}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":215890032670885121673575897389459651767},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":215890032670885121258037783376836273771}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-55160544123888038400491847575624339039},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-55160544123888038536337657994407017029}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":8075116243180914942489087460038286195},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":4037558121590457218664459271921408371}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":168963568938704570815018641396633833},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":337927137877408853827780958766876627}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-3143724090325117606479421891096385005},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1571862045162558902809285274124387003}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":239431541111949465580061726587573423321},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":478863082223898930874220647001224598199}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-10074119391890381190821548114381433671},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-10074119391890382005437636588934121271}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1579279262265958883281503897204247338167},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-197409907783244860567400478904512637617}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":564655705727660199367114643712808620063},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":564655705727660198132878285007046797119}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":229769577599568135561714295530459873387},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":114884788799784067375831309940624479893}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-9941997732931596110152088292322713603},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2485499433232899177230964032405762503}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-21638702777522026517763051431646038765},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-173109622220176212756747477060971296615}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":184581626636541925229174207434508845707},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":46145406659135481104560992641165508463}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":200405441165929384922059710193207266759},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":50101360291482346112849378550961614251}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-133889087008613213824206955130975189},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-133889087008613532739581180261185237}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-198386989177744417515100411750667294465},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-24798373647218052236231151632278814235}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":790227108683376119483640448609457638725},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1580454217366752238219082327106651562581}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-133128357829686921},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-71054930406455967}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":785072063594704797},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":365513672362154107}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-14300161277803565},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-829130423818682751}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-1529470513548117},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-19835481908860867}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":926703015879565},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":475863086522035}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-167624966751461849},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-287387168991573101}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-2749578473539709},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-144632877007472563}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1024865049502917},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2237034706096061}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":39561069309829},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-297246850372013}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1797556314039869},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2771412653587053}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":709925274122342993},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":417388106092410213}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":11761585525383731},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-6176275958075967}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":14878473405470213},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":1013471808511091}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-29403555995109327},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-1687084880455073}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":47106254514774999},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":30331052162321139}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-228071423066711},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-9577869868466387}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-11573228288542975},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-23927569104329099}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":8949759929177783},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":7989086796626983}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-951109078320607},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13968154141617931}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":161417580615875},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-437362119817315}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12807359638916293},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":3301262401525141}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":54082337351476431},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":13077951322023069}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":170141183460469231731687303715884105728,"numerator":121882390203296660293},{"denominator":170141183460469231731687303715884105728,"numerator":238695323382729276661},{"denominator":340282366920938463463374607431768211456,"numerator":481587180317525979813},{"denominator":340282366920938463463374607431768211456,"numerator":339074437744781500067},{"denominator":340282366920938463463374607431768211456,"numerator":318476775519606211583},{"denominator":340282366920938463463374607431768211456,"numerator":207709175905191633371},{"denominator":170141183460469231731687303715884105728,"numerator":135815151356477889267},{"denominator":170141183460469231731687303715884105728,"numerator":126288970537847591889},{"denominator":10633823966279326983230456482242756608,"numerator":4496890440851348177},{"denominator":340282366920938463463374607431768211456,"numerator":199136939250851102789},{"denominator":85070591730234615865843651857942052864,"numerator":71439134397476820513},{"denominator":10633823966279326983230456482242756608,"numerator":12727806590393671875},{"denominator":85070591730234615865843651857942052864,"numerator":157205559253183240785},{"denominator":170141183460469231731687303715884105728,"numerator":308546798096350729231},{"denominator":170141183460469231731687303715884105728,"numerator":202508725111714614935},{"denominator":21267647932558653966460912964485513216,"numerator":18711346945410129277},{"denominator":340282366920938463463374607431768211456,"numerator":307309178463085707123},{"denominator":85070591730234615865843651857942052864,"numerator":101362803364615840963},{"denominator":340282366920938463463374607431768211456,"numerator":235327918353922878339},{"denominator":85070591730234615865843651857942052864,"numerator":39864346930678722107},{"denominator":340282366920938463463374607431768211456,"numerator":187371298236363676701},{"denominator":340282366920938463463374607431768211456,"numerator":374078782863117130753},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":393},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-9925290737828281374186043423829886621},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-10053828813665028582722334561255481457}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-494321132388018668923004375190352158331},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-992791555447990905941833181704975137843}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-44727842290929175306669342258039271663},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-90830559031522080964298204786087976897}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":62232834146968670907894568520399311369},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":123820432002503149956416708933518561651}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":48700461848311419757574301560517847427},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":95325152196321936125927413035186729263}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":216119730146365547708161039622251531049},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":215808851193389732695337817750393572387}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-110284176509537754010548432788950360499},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-220795169572226764424633280055930126965}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":9786168923111435394504889338477220981},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":3931865302269233531114807147320702695}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":179266811111875151977685445765957061},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":317317486766796184487098098716447681}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-6070267204607845025893975872864660645},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8061551783981431803379037865885527717}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":958406113599544425403934365676244980713},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":476130590217276386225043866841824458163}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-2390352272148093279508212726328347085},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-10164958651474428706629509763442112343}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-782472221434544848603550564111109554011},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1580913834242510622042949697107540540023}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":565169089102455775975152645205353585147},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":560403384828242907785966016497072811679}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":57525841508958345562289740800321366629},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":113489750163032988649966050626970591069}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-4924473604638964322595663820888015583},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-10603661236518914423936411073000780889}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-172661654761622547985524818410497014537},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-86592183447625895450528457681801860489}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":184665206658512180465282617001462199567},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":91999542570280115725680174568182381261}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":3135064091343094916339907007236497049},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":99202838477526639986524386425636050141}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-57908631912898183850770609568769209},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-9497671256897817788284135245400269}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-98225349067950574013837554715063903305},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-24827441117860514416095184805674032941}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1582096222153968341326204609825178412173},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1566141720450040743239669688075379766399}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-9996203759814762754870841334363085345},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-4998101879907381625222819924093822137}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-995380888737989597174029262051500986433},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-497690444368994799073693862902405657071}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-5734449048025111188949818551191630593},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-183502369536803559037782846676216774677}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":7801573553913207699605289920392840273},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":124825176862611322498643760824451122777}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":49409372153991954884831867915533843681},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":98818744307983909113852390066058922719}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":107857640783790613485174529100408106469},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":26964410195947653317865919973881741667}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-220538047521000610568459342205617790485},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-55134511880250152781784136941747129275}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1634027928777393503014992505176711603},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":1634027928777393373057874219924083851}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":176171966934188368849510236576102319},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":44042991733547055063653106472425051}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-4692267085249896768345694314018237749},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4692267085249897178504308141914906145}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":962538497097908195111680988302640467091},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":481269248548954097267228703014268909617}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-10543051008422272802331138715806489167},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-5271525504211136817591853553076006365}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-49751691983629346441358643585158262843},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1592054143476139087405660293240587363931}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":142104835306015963931614020737752751413},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":568419341224063854465276839786768961413}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":116129062330823032209461622979300043509},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":58064531165411515896624716417337061963}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-2333686914083205482213285817746611245},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-9334747656332822546066446170113822375}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-173540608154646330236312016892223217331},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-86770304077323165432437631840809520109}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":185123570284209385571334876546232241281},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":46280892571052346185679232164505422021}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":50539391857905195682899408879105899119},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":50539391857905195561747629715337974295}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-142286177785520887207221078349546255},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-71143088892760608662820751987619825}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-200081457216757042751973642774067167273},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-200081457216757043138085442233627175609}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1593244806266042143094035268975273310863},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1593244806266042142330413893048140197103}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-163995341843782083},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-156741659352562579}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":759046079859751619},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":173456864907565515}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-355344443164391559},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-718067577744027767}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-279457684635773},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-22472780082289835}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":7673707289239587},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2207159250419587}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-80234650047884995},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-286011876071780883}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-27211036445258001},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-44737955619469649}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2391476480297317},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1919359074110995}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":101414940788213},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1184914851891181}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":443778219475501},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2582609449559881}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":733111887132782349},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":429823898385316221}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2496215084975381},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-33879352070725725}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":72510945955338457},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":18252556146363167}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-9143949320853163},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-60388120953868467}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":12798928794536617},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":17493950010636331}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":930775844212867},"lo":{"denominator":2658455991569831745807614120560689152,"numerator":-59837735852817}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-28398779486292565},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-27013100947982093}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":8111547796556953},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":4550564341329583}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-3385087790272221},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-6614591351628675}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":118084512624533},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-243912160838501}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":3676115611533525},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":1028360281061395}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":66580366959176503},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":12200926583632715}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":170141183460469231731687303715884105728,"numerator":123856327634240803963},{"denominator":340282366920938463463374607431768211456,"numerator":486473165701632853559},{"denominator":170141183460469231731687303715884105728,"numerator":247756482475876239873},{"denominator":340282366920938463463374607431768211456,"numerator":347513673883830188245},{"denominator":340282366920938463463374607431768211456,"numerator":327902939608484972321},{"denominator":170141183460469231731687303715884105728,"numerator":106824038958446567177},{"denominator":170141183460469231731687303715884105728,"numerator":139638168952945841005},{"denominator":340282366920938463463374607431768211456,"numerator":259912081152728051347},{"denominator":340282366920938463463374607431768211456,"numerator":148594254645790062417},{"denominator":170141183460469231731687303715884105728,"numerator":102538523996458655065},{"denominator":21267647932558653966460912964485513216,"numerator":18028759196417349429},{"denominator":85070591730234615865843651857942052864,"numerator":104102024102898727807},{"denominator":340282366920938463463374607431768211456,"numerator":641064720062856988831},{"denominator":10633823966279326983230456482242756608,"numerator":19705181539326580197},{"denominator":340282366920938463463374607431768211456,"numerator":416204086237047482679},{"denominator":340282366920938463463374607431768211456,"numerator":308602356446547001975},{"denominator":21267647932558653966460912964485513216,"numerator":19641800605218317227},{"denominator":340282366920938463463374607431768211456,"numerator":414295026130682827483},{"denominator":340282366920938463463374607431768211456,"numerator":242300328823974493193},{"denominator":340282366920938463463374607431768211456,"numerator":165058907258395695929},{"denominator":340282366920938463463374607431768211456,"numerator":193052660939681182697},{"denominator":170141183460469231731687303715884105728,"numerator":190894799353335300671},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":16,"numerator":99},"tube":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-2483556708785344211174784163539268057},"lo":{"denominator":664613997892457936451903530140172288,"numerator":-19634332145743970886472718471324127}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-61991943601679868554067117926935181817},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-497940265898992803512610017614717039429}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-180989009759971550745115911628967534163},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-45974912369668909786356507873937633725}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":124932565538023463864144339868800929859},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":31073476060644731077027174390059907111}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":24761516055659543610635086822995285563},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":48483173884451332038719798451085196633}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":215918209241389024804945865755640734571},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":53909110884087498372811546073213290521}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":-3444797599373016670945803889303631411},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-110330817699758248584054159614437307023}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":8269872292937397958749509473018267899},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":3161155897686283898072645771120853209}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":186334758195143551253908477982059817},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":332015188723771926827047395040199161}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-2236317139852196096090091275052226717},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1622273542411054553338645294830396729}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":963210022253396569737067345416526837947},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":478558423456921224874852532911607881693}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-5005877217930514476282120699008172419},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-10635403996154551335137306362643977609}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-394419445033366418954206474520851832043},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-199211575182299718807950735886598021571}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":568931993707940560656258789788742284167},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":564180562618740157852502673120300270163}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":232593903164959334140074934108155376413},"lo":{"denominator":2658455991569831745807614120560689152,"numerator":1792623153498890636611589637591415769}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-9239104983467157807539905030176932167},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-5010048463658267182316592136948712417}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-86526489409838588679553212074102490643},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-173619412824667525189086294998815014067}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":46302447207091470845181330561617091629},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":184511830837450373422412709022347635161}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":202393335186113536943323005601971067701},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":200184564052575589730072459359718916309}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-3874086261699925202538675560823575},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-40150917289062534241093243409990233}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-24771651640722529144673638911198294263},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-100155486822711038367251056850686251079}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":199361938308410513550016598693227482403},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":197356203711114420469315145546134340431}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-2497228710648391376487312353390396349},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-9988914842593566009707168115830791295}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-998379165409844273009491405196974758761},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-998379165409844274001820353793744984151}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-185853017327404092241068266532293842445},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-92926508663702046630424462066840121355}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":125287149410891460311497536787925041193},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":125287149410891459599219722691212238675}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":100465616597567538910878043464896737797},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":100465616597567538235740193317820593617}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":53891838109193402650660266738841162631},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":215567352436773610162827870023702414695}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-220462913553917162364055233447548976225},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-220462913553917162938719029797542798183}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4977465280715668147766264191930772985},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":2488732640357833806444813157692650509}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":367177418576281606366386865475851517},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":367177418576281299520468960179806329}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-769380005515114802932432763854828673},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1538760011030229817043965279015330441}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":967305040314677996706756602501380402319},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":967305040314677996123386439067117924079}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-11028764969519875678429164262084925699},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11028764969519876529854690912921385283}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1604863679047912892259405104910426549673},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1604863679047912893566607339388585098991}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":572168177051970899845405403269951561921},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":286084088525985449278298941816859888661}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":234758386084871875255714493463243563411},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":234758386084871874400310674543265649045}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-4353214134091133804728565545203160019},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8706428268182268245584064662174103041}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-174006258634256855818267213381520338743},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-174006258634256856461099172597546451201}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":92845275459841303482080946465206338467},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":185690550919682606117395880566671334745}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":101942901903723053923261347266263163373},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":203885803807446107347561152158012696033}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-75441964345067573547886417102767031},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-150883928690135488759970919985226993}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-100875440378419127667596683860105439749},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-201750880756838255733009660089126245745}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1606108053607432305467213763597460538845},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":803054026803716152343965635025964651427}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-23832436078281213},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-341354391991386457}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":180865349916896725},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":155702834011252835}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-116223782686705591},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-595151493541217277}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-11351623638940543},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-24948211299444245}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":7916510411918477},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2378224169205085}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-146708729252332093},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-278950070478752309}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-42750729482510551},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-106376392074160789}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2772641648762937},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1586673598090495}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":138588667867947},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-585055433319383}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1726247484992535},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2255589828450869}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":93379613362198413},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":26802625650745985}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-6862507192705435},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-43814666351421065}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":42822769381069043},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":31174020120791185}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-84916348180538363},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-33170311591369317}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":54797526791154063},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":9630478812433657}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3089784849428123},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2784349336982955}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-33415206549957771},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-60168341359353677}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":28906383398138565},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":272818867182133}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-5676849427151553},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12263898010781969}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":75171890094621},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-270495298977183}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":16581760855095045},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":9792909100877635}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":19954423455582769},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":35954980854163007}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":85070591730234615865843651857942052864,"numerator":62950902974863008643},{"denominator":340282366920938463463374607431768211456,"numerator":495958446432562572079},{"denominator":85070591730234615865843651857942052864,"numerator":127427244209152324271},{"denominator":340282366920938463463374607431768211456,"numerator":356132108754526149407},{"denominator":340282366920938463463374607431768211456,"numerator":337566155930416715393},{"denominator":170141183460469231731687303715884105728,"numerator":109920238897608953903},{"denominator":85070591730234615865843651857942052864,"numerator":71817068128101315185},{"denominator":340282366920938463463374607431768211456,"numerator":267436139280649309267},{"denominator":340282366920938463463374607431768211456,"numerator":153422304602880769237},{"denominator":340282366920938463463374607431768211456,"numerator":211176775051249913459},{"denominator":340282366920938463463374607431768211456,"numerator":291525984268888413347},{"denominator":42535295865117307932921825928971026432,"numerator":53211785905729858997},{"denominator":340282366920938463463374607431768211456,"numerator":653573881479758601207},{"denominator":170141183460469231731687303715884105728,"numerator":322189938684511711423},{"denominator":340282366920938463463374607431768211456,"numerator":427693771654218247465},{"denominator":85070591730234615865843651857942052864,"numerator":79514784386030548621},{"denominator":340282366920938463463374607431768211456,"numerator":321402603040608358275},{"denominator":42535295865117307932921825928971026432,"numerator":52921103226129847993},{"denominator":85070591730234615865843651857942052864,"numerator":62369369415741250037},{"denominator":340282366920938463463374607431768211456,"numerator":170831790961645821971},{"denominator":170141183460469231731687303715884105728,"numerator":99452375879290287209},{"denominator":42535295865117307932921825928971026432,"numerator":48702414427035191745},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":399},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-9930912374659024271292655991312263355},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-1255676995736797485419258057084516685}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-497497115506865654568373965572410647501},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-998860808256314189509561238012594953753}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-183195247178224375695507971135507815603},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-46566617691004049801092548490682048445}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":62697010350092429779264332439341122399},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":124761971991769818380878771240756191935}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":100693609477880789668144073193955714379},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":12326303244471643075977497573161253573}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":53935043725264086172384224929041664047},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":107745620783152583748829243380842739623}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-220395107333326622560182084967247589227},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-220553929764075498745687043877962315259}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":6733310063590132102473710579679403597},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":4761326578784551198336307188977087303}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":387220695158111028326705007373605175},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":347130991293515385141213836143677141}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2855519920303338582404879009925023393},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4896350103577292578070911623138588179}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":241992875045707270633489084493025347005},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":961934830088472540312290857790472616529}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-10478650042284345447813696626379209563},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11122659703663618992988115321628750049}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1590448416651108381271255742612704086581},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1606505684901415429793464261537284074979}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":572679736659827143726663418249197989605},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":567945963953423488991789441935496485441}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":117548129999009506154769855807444845801},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":231942776290937958172827660319952170151}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-4304086562792055721453104248357892259},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-9415478159749346001973139489271743865}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-43369919613097918052793882163494640353},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-87044487737469126231270204418700932525}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":185779227148569520630603172244676741843},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":185050719521502702977396234681835209271}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":102059323122867598153288885157918530923},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":201939669785608069573703046233184294933}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-33082957863836107256969543373738623},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-10589896867258927694812131057924939}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-199870803736111894637589141469928998699},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-100988669271281687890717076156143714443}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1607767267049339601513079469078909414089},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":795815599756171212321725525511303850077}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-9971577746328515357319352834984504613},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-9971577746328515869709695253457231083}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1001262531850379071809158144784316049581},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-500631265925189536410648033184196741017}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-188331459727346272293164595034871760887},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-2942679058239785520967286157781328361}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":62871822117655198699797096377351487731},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":125743644235310396669712567047816615607}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":102114552706400874044678040106093001067},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":102114552706400873349729269730150611457}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":6732787639850736171947125451459118371},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":215449204475223557049582028909230406813}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-220419548298645062236681754812346674255},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-220419548298645062828040916146607154035}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3399722935485577748168418832402128425},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3399722935485577197853397287492491797}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":382434380092406315284697036067614887},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":191217190046202999253439180266917899}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1443841578344573523805263429887210509},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-721920789172286979345539946937562641}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":972018076797187537074952576125318379917},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":972018076797187536484437223147031174353}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-11531440926447281802519522759044793421},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2882860231611820668217851060830689129}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1617705446752885249479482625545569889403},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-202213180844110656351532483916350818155}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":575899501285202757287175760518404966021},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":287949750642601377985017943109938100039}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":59317804837823708542906121641325366415},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":237271219351294833292620789191071200221}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-1007129746644087851287907990005423167},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-4028518986576351732914333533812148191}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-174505849077723706322847503772953745043},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-43626462269430926745078497787099838623}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":5821297184665987303632967251708580919},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":186281509909311592850861110291017509545}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":205590084857776542163503614234664148879},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":6424690151805516926555159311683606593}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-159675176085384311355548325810363021},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-159675176085384664917607102265215395}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-203395186880227327969526357503545465535},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-101697593440113664189699688349224806637}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":404760733701702063139571921461902788123},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":404760733701702062940771446187135318073}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-211738843739275831},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-366689543669233711}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":84757962062815489},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":129869679126262905}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-46133633231679939},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-461453992793453021}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-13336953070674133},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-27194237381563205}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":8136703399479927},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1210638140208107}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-126050443695182367},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-133124134358103807}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-14249573188804265},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-122584966610786971}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3195114099561503},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1252321279072753}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":193052441527023},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1145181596951769}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":6593261065818763},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1778266112079581}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":750224064491226963},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":103061015097562895}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-15991232828471197},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-54202285123513905}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":24663963321980573},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":42612567056050291}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-23496641448955803},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-143442555220706361}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":28913727429769121},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":2556971547735995}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2746085129275461},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-845344347915079}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-9480260272826347},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-33022007481032757}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":12615145617999453},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4000143879022973}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-4340170220266011},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2775222427961449}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":35196426381691},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-595534954683161}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":18370441851186603},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":5612119520871969}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":46646067556908441},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":23591960218300945}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":170141183460469231731687303715884105728,"numerator":128058847929635692147},{"denominator":340282366920938463463374607431768211456,"numerator":505859798622913717175},{"denominator":42535295865117307932921825928971026432,"numerator":65523283271050197567},{"denominator":340282366920938463463374607431768211456,"numerator":364933884211287735391},{"denominator":85070591730234615865843651857942052864,"numerator":86867881868602915737},{"denominator":340282366920938463463374607431768211456,"numerator":226292893856220177905},{"denominator":170141183460469231731687303715884105728,"numerator":147806996996637334989},{"denominator":340282366920938463463374607431768211456,"numerator":275155287054765501185},{"denominator":85070591730234615865843651857942052864,"numerator":39597060055186912537},{"denominator":340282366920938463463374607431768211456,"numerator":217440500734517087795},{"denominator":170141183460469231731687303715884105728,"numerator":147544343243546557545},{"denominator":340282366920938463463374607431768211456,"numerator":435156835215991460193},{"denominator":340282366920938463463374607431768211456,"numerator":666360601249502391917},{"denominator":85070591730234615865843651857942052864,"numerator":164636302288637985349},{"denominator":170141183460469231731687303715884105728,"numerator":219746695366033625779},{"denominator":340282366920938463463374607431768211456,"numerator":327758264799965349903},{"denominator":340282366920938463463374607431768211456,"numerator":328719182200787424661},{"denominator":340282366920938463463374607431768211456,"numerator":432682305664271028991},{"denominator":170141183460469231731687303715884105728,"numerator":128432938885324289529},{"denominator":5316911983139663491615228241121378304,"numerator":2762198656602138965},{"denominator":42535295865117307932921825928971026432,"numerator":25616617062005919067},{"denominator":340282366920938463463374607431768211456,"numerator":397577896442196332603},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":32,"numerator":201},"tube":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-4957367976628175320341250626974607475},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2507803614630912294793670115509470357}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-998007062525090514856679021855844598679},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-500864045686314048192401426534061471971}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-185529910277977480245537293785463570459},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-47190245193060900050211754763685758691}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":62924993762809388062091662874342115577},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":31306152960647106107444830526789302779}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":102343176137298277871567411153677767089},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":100256998870930789387314946647278323725}},{"hi":{"denominator":1329227995784915872903807060280344576,"numerator":842142933453844701113864803332794735},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":215376205690077914660066164873910691353}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-6886069874551986190904743704669584231},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-55121125410098271860108431516760697245}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5177036967178960010915661360643541517},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":795330025636510344855422968134777939}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":50274286649852936524549319189030085},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":45333917073410636826969324252517361}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1219558230722779925501025489112891687},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3283960221097979601708698032246330299}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":972682905840250909180114506130318135747},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":483353749850362725114097215685657658305}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-10962294039632923696139121488923368701},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-1453375417312805439879943377689460391}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-200406751427282933686200694619016718225},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1619350687714757697187601034336038528973}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":144102400025136762536486906332539315181},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":571696907824351326157781245423113028549}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":59402822996610899210786334479488459391},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":58610349135063198532221150147657761037}},{"hi":{"denominator":1329227995784915872903807060280344576,"numerator":-31078519302719558788756424559173901},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-4394898985573693078106611340756431517}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-86970570485699803783060382438441880477},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-174592317599972090087585247724226283291}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":186372453955484252683272175451324444779},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":185614783915704645387854069779596183013}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":205819973486181533510369941549155588709},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":6364715502042637291545977700805375403}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-70446621804916139675942096792616235},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-178459687921561113160681254457796407}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-100771680712690455293112315501722236703},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-50904638684988589518977998993021319693}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1620710511036474331244882750479635549603},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":802242779168769373090801663768924123521}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-2485891752590890313696915794975419215},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-4971783505181780888313240255573149571}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-502013446854080040179013157913043826807},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1004026893708160081391063677450430259079}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-190936795741371160432980625235370555869},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-95468397870685580755636224944237630035}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":126194599707718668716149051532522018421},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":126194599707718667968287944413171109337}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":103765173167561607235719401686193555185},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":103765173167561606520464779664030193575}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":107681892138298624416424368693132420615},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":107681892138298624183337226909245139331}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-110205339064769349036567523495017196041},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-13775667383096168667619630549988596821}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1803421889192892125700468029608081619},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":901710944596445779773072309725193457}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":199060753864373075567930028120705643},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":199060753864372912071477342425773225}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":208140243211316518459708607661465907},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":208140243211316070709143790425161203}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":244167455175436968745819855990029074073},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":976669820701747874384579494113264020393}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-12051229996605508684590605714672452955},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-376600937393922174195143385139508679}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-815288477196758948950334633573235007561},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1630576954393517899259603206023174375007}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":579610581805246808234821951008027074549},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":289805290902623403444312825813600922569}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":239797478562386555393565670874780495307},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":119898739281193277245163810356965895361}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-230830781313956011623224494333489801},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-3693292501023296523683412071016445365}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-175038555451700427760568517871965578129},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-10939909715731276777065864752016616321}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":46723827303620391735425661851717322423},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":93447654607240783028590362935759853065}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":207270373700700885836399948290765907441},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":103635186850350442653724267577614879879}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-168651986499221116623186672711232703},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-168651986499221482444795952749429859}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-205014334175360171995806004184616906133},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-205014334175360172418099059623174314731}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1632048283036585142506633840172786900987},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":816024141518292570847614904151584010101}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-56739713226165359},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-194599113531550755}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":623624664158484857},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":192548329464234893}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":31524416109224273},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-159352300852136791}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-14784551109472305},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-29348751073435955}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":8327629852215471},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":72045827134203}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-48482831203808983},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-61852391746947921}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-139205402568210227},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-137745405883756423}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1819184115411017},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-461832631930363}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":265145662598885},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1113500865690379}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":192944160962999},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":71082123271333}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":740900704585924835},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":377660690989535263}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-6212728050248849},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-64994453455602827}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":55704544039849353},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":26242509370738353}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-50132059738982791},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-152873671857350169}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":30107785924440087},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":42110383733420653}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":4073906481337383},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1092289327752603}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-10445000000746001},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-71624097083720135}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":21453939343205425},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-9080431454887835}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2767197273805987},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-4874155670227263}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-579302179055},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-325684151304655}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":5015899735931457},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":194753515705669}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":53463951288118071},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":57940813862730895}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":260838288978543091103},{"denominator":340282366920938463463374607431768211456,"numerator":516303142644824177749},{"denominator":340282366920938463463374607431768211456,"numerator":538955035609590991035},{"denominator":85070591730234615865843651857942052864,"numerator":93480817864923368179},{"denominator":340282366920938463463374607431768211456,"numerator":357624299929389720317},{"denominator":42535295865117307932921825928971026432,"numerator":29126489978949649303},{"denominator":340282366920938463463374607431768211456,"numerator":304321378200291927217},{"denominator":85070591730234615865843651857942052864,"numerator":70768720172082876493},{"denominator":340282366920938463463374607431768211456,"numerator":163495763362430787785},{"denominator":340282366920938463463374607431768211456,"numerator":223872763959028915031},{"denominator":340282366920938463463374607431768211456,"numerator":299168344916627943163},{"denominator":170141183460469231731687303715884105728,"numerator":222403459767134304335},{"denominator":340282366920938463463374607431768211456,"numerator":679437507403683068941},{"denominator":340282366920938463463374607431768211456,"numerator":673071844914222922411},{"denominator":340282366920938463463374607431768211456,"numerator":451609972486366622531},{"denominator":21267647932558653966460912964485513216,"numerator":21106700006908462179},{"denominator":340282366920938463463374607431768211456,"numerator":336227737031609773437},{"denominator":170141183460469231731687303715884105728,"numerator":221122846791137872575},{"denominator":340282366920938463463374607431768211456,"numerator":264472216010734749571},{"denominator":170141183460469231731687303715884105728,"numerator":91455239622759441725},{"denominator":42535295865117307932921825928971026432,"numerator":26392841004038677849},{"denominator":42535295865117307932921825928971026432,"numerator":50709690298806585971},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":405},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-9885054616324840334949571530398434107},"lo":{"denominator":2658455991569831745807614120560689152,"numerator":-78200019212444400528013606950298443}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1000905221068792545556676470049632421719},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-502239164442328904040746607598722722391}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-187992484722128347071539618432964402291},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-191382234774307599287789382253014732699}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":126300401950045730219767535169208439647},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":125681782267006470719706459234437162319}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":103994384990545881080948823496974112723},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":101905682452606983601815985733945416255}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":215466418008942470342192478839214591975},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":107647141335876670971673918556504903251}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-220344939066060576413405738495454606701},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-220476066010393566639169604053653188969}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1800800042091427743090388700773985701},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1582828597210078106057193909112797191}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":104402575428204862195765835217955305},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":189262972178402252015873225857960067}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":217311708244083820592019136013027507},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1652559911103767469788315489977840377}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":488668261921527788063859496904944618681},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":121428392279566941509953517159186100703}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-716430324561055408458840108772576981},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-6074221263840419603561124864086796695}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1616092155999471982622237417991639651783},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1632225063533604651194689491331918772425}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":145029711730717360405179009748355774267},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":287715342551619895448869045611461980453}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":240139850838021214481982616599476794645},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":236952482519436346493802808123579105779}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-7282968191352360593731414460127260399},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8143045726686074896061695379459884331}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-87218327116808955433395846472976159793},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-87564301337337932713674899508471659299}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":46747080646525640592754912245045528061},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":186202975167445929570843494636774414183}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":207497283921885519761726718324250020755},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":205378173850653321859547139912831203717}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-74823490432671628818028150834032521},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-187659831738609168328359057649686699}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-101595404662025769350566159450550365143},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-205234584885809431385072702726524827219}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1633723982742735750797569367251604547277},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":404352926814592965745369124389855136669}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-2476054998568807802345332100084005519},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-9904219994275231741662318406812796657}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-503334206521019327313034902374354341611},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-125833551630254831960153649882396346495}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-96833891059301140911004455275107674517},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-96833891059301141465232343677102430365}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":126639936637465897234653269206504024715},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":126639936637465896468427927521515877855}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":13177137860144048385891651309936265859},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":105417102881152386351066907389327551331}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":107657008578116163116494985325584690307},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":26914252144529040719102402402966375303}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-220438973600920143612110886118807727221},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-27554871700115018029881254259387865183}},{"hi":{"denominator":1329227995784915872903807060280344576,"numerator":738631201710924611502736211428389},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":94544793818998059069540450569816149}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":414245366842068026008081385982369975},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":103561341710516922127321487310064033}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1877805201217273147974317845098960247},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1877805201217272687012471308789549625}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":490626218142190761786596349011012327137},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":981252436284381522965229396530934713807}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-12588252685420423328997281322541351939},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12588252685420424238356957386328395725}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1643475645692669411859248961575357040499},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-821737822846334706622475684949309735265}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":583298673422910814128491636825339463233},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":291649336711455406376246279270566823503}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":60584502895918021158070560314830536519},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":242338011583672083704160804313840994459}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-3347543747512048106231418357103318155},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6695087495024096908301736903190936911}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":-2743803976878778382874051452691028657},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-175603454520241817191846648609693920161}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":93765366769199300733716317678709812769},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":23441341692299825070407559701949990397}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":208926661485654070609197238494302477365},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":208926661485654070064583277285989846913}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-177805642593191393187670870562674795},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-88902821296595885820194045223461013}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-206608312502832349817531907958536396231},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-103304156251416175126309814108874771341}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1645122788188112248898711758432089767699},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":822561394094056124035397875895147231211}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-234031380057560237},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-408476277077833331}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":70327420506096771},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":54093873443351641}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":232986301716433747},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-171574925058024489}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-15609421649017673},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-31259593480095297}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":8487328827548681},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":252013896293473}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-60435749461942837},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-111028681440313853}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-80138005816733729},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-303236174563255389}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2046282094555707},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-308730153052313}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":352050124983787},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1073170095051433}},{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":44027609979465},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":346117332252863}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":718024821567785175},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":40594063586409101}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-33103265302292335},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-76097034501767055}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":123603777442258289},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":14992209907404787}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-102782091702478715},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-80254892061847309}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":30891519053585805},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":41779598959634241}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5537277632690931},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":310602450624857}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-11220637267101991},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-76681106399868009}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":17720801706757137},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-14670137586837681}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-946378896135953},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8213640085603725}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-32492084033207},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-707250773269313}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":10789671014341553},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":6743455972881199}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":15056813520460805},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":8500285564150519}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":266053272554728250743},{"denominator":340282366920938463463374607431768211456,"numerator":527352481346650008925},{"denominator":340282366920938463463374607431768211456,"numerator":554025607788607526729},{"denominator":340282366920938463463374607431768211456,"numerator":383104845756578534617},{"denominator":340282366920938463463374607431768211456,"numerator":368029915936252687321},{"denominator":85070591730234615865843651857942052864,"numerator":60001141226752461665},{"denominator":340282366920938463463374607431768211456,"numerator":313398093896682703155},{"denominator":170141183460469231731687303715884105728,"numerator":145600227386122704811},{"denominator":340282366920938463463374607431768211456,"numerator":168748685108261039311},{"denominator":170141183460469231731687303715884105728,"numerator":115239139279891072991},{"denominator":340282366920938463463374607431768211456,"numerator":303785014589106714049},{"denominator":85070591730234615865843651857942052864,"numerator":113664585286823446133},{"denominator":85070591730234615865843651857942052864,"numerator":173204846673181223861},{"denominator":340282366920938463463374607431768211456,"numerator":687970675295892300161},{"denominator":340282366920938463463374607431768211456,"numerator":464050716753166807123},{"denominator":340282366920938463463374607431768211456,"numerator":347914534021760709083},{"denominator":340282366920938463463374607431768211456,"numerator":343937778540068313033},{"denominator":340282366920938463463374607431768211456,"numerator":452069883401263053771},{"denominator":340282366920938463463374607431768211456,"numerator":272303346973561581339},{"denominator":170141183460469231731687303715884105728,"numerator":94613010615298752781},{"denominator":340282366920938463463374607431768211456,"numerator":217539813914565112871},{"denominator":340282366920938463463374607431768211456,"numerator":413931777209072411493},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":8,"numerator":51},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-9841194268985991962137280799275974889},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-9979965642346392125107762528474789045}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-501842289779598262336562032529024021485},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1007107721048832081522146570539420893857}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-190582112374374471161129456088020197967},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-194128946044341363879641145362500521429}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":31686295597346638180319746875916352589},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":126133423854200014106844494936558047495}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":3301464412486472536300505375459883059},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":25889024179890248445639767289626733953}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":215379547177284050132683291076408705931},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":215248070008228241970621446404844909637}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-27546604437060606110515780971896879651},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-55126192424558916949756592157652345693}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1003768916157503867247000155536975667},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-8405399726537088360330076140372565}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":54191593660117170686964148605552387},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":394186925334057875103759051183087761}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1053202778100167379867647224956749371},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1389062449287447369103263593619015}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":981924583034819291925802264466100039501},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":488042979110147747328888481914862050493}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-5990289163785712912753171328773122651},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12687095017912254416348971029785066273}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-101810022425735645774457522606595903871},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-822563157314622993742404706957933369121}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":583804727915266077618528994485524529937},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":579144565570800221251969724398607851765}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":242682781671782412524710262691473866577},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":3741826395750144327046121427515313863}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-6588794107187848995478524337067108853},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-7475228434808675719798857698031672667}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-5467668730822365140678651842985403933},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-175696960040163117090233445740836193031}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":46906451028561652807711885580835741933},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":93407071557253836074497761899601713223}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":104575334934433328667659142758508414951},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":25882681488029752718599542553281354335}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-79292115477531983250551431139549583},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-197030158286334902053717542667770171}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-204813102091670046789181133675755704093},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-206825422928571298855429836565344468941}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":823403176872326541580389129212649520853},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":203801062175294421302659997533435526455}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-2463209381447285929061475911053409035},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-9852837525789144260001911287415813777}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1009183518791225563538834652128771945749},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-504591759395612782308614976037093806607}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-98261418236405931566530581473357124153},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-196522836472811864272101496644596675037}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":127079558592150904077808766793931110857},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":31769889648037725823206396298399205741}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":53534985686324237733365231035422137087},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":107069971372648474709335488680944326869}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":107651399069671952445275292269150326249},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":215302798139343904395823505639496440681}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-220507040993436511141624392592376203363},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-110253520496718255893737707829509037321}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-721378617004652280774133304308340475},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1442757234009305160628563362941648331}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":107703093028467777327277576489284117},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":430812372113870761005792165380516831}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":891135494204127455803705482121615945},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3564541976816509348687447325122143245}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":492879028884172343357300221829034485943},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":985758057768344686096254954957512141719}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-13142596857232749896005518943813908353},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13142596857232750825503484712148070655}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1656398906376295960617703546524475700405},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1656398906376295962030813461961844254009}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":293480512523234328275514039820144651067},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":36685064065404290946528912479650750129}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":244893657208678565885992300832042623321},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":30611707151084820616540718398030654343}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-1495643394969427997227763490752563013},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5982573579877712705700459203733871957}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-176199524370027074862665380505757460897},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-176199524370027075566417373512937915725}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":94093246351467042538767501757064650135},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":23523311587866760519146137867743787347}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":210558966793639296562167213173670399345},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":105279483396819648000713559826889376113}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-187126631059170939055681179496593365},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-23390828882396416315148628086876261}},{"hi":{"denominator":664613997892457936451903530140172288,"numerator":-406595981792429685420282325138771251},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-208177142677723999383453180333261205613}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":829132498095403459475699139622184469717},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1658264996190806918106631764329787126751}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":-3620221107026129},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-421102938220514815}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":487946689647843073},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":15080907685959747}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":100742258089180899},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-19782870151691497}},{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":-122401163255099},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-16082982500126975}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":8510518468815207},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":400551666575563}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-16599355510152661},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-190921598447424955}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-44140663894886209},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-81002442856116623}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4487890539055421},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-330198395003315}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":225846863271891},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1017272084832851}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1246754137057355},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-284415388816807}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":681379124454732293},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":125969655796312861}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-20360886377235317},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-86656595210810861}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":66045886892927071},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":16321994049021505}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-50934535781653251},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-162588174751819519}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":61174439510891681},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":20039256027766795}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":7098758502039927},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3633656806888915}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-47100318165693511},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-81084695719627761}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":3490064662177651},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-19838793235235505}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":246199924366337},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-812221890873599}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-15293420720855},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-379075656289513}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":11435601745952149},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":3555734101476013}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":66821887764995079},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":77060755617700623}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":170141183460469231731687303715884105728,"numerator":135891649713957833769},{"denominator":340282366920938463463374607431768211456,"numerator":538961217081726892069},{"denominator":170141183460469231731687303715884105728,"numerator":284654395448843502909},{"denominator":340282366920938463463374607431768211456,"numerator":392483341492115343307},{"denominator":170141183460469231731687303715884105728,"numerator":189347016269524358587},{"denominator":340282366920938463463374607431768211456,"numerator":247276378327933469761},{"denominator":170141183460469231731687303715884105728,"numerator":161425893987699237405},{"denominator":170141183460469231731687303715884105728,"numerator":149768869666347727161},{"denominator":340282366920938463463374607431768211456,"numerator":174150924587382621501},{"denominator":170141183460469231731687303715884105728,"numerator":118630454689009614375},{"denominator":340282366920938463463374607431768211456,"numerator":308958024443847361797},{"denominator":340282366920938463463374607431768211456,"numerator":464726015472938911037},{"denominator":85070591730234615865843651857942052864,"numerator":176630388954972348185},{"denominator":340282366920938463463374607431768211456,"numerator":703252380431344393525},{"denominator":170141183460469231731687303715884105728,"numerator":238411364430085507621},{"denominator":170141183460469231731687303715884105728,"numerator":179194710345131607241},{"denominator":664613997892457936451903530140172288,"numerator":687224617802369649},{"denominator":85070591730234615865843651857942052864,"numerator":115541512690036881923},{"denominator":340282366920938463463374607431768211456,"numerator":280366305472533596489},{"denominator":340282366920938463463374607431768211456,"numerator":195732405433784360557},{"denominator":170141183460469231731687303715884105728,"numerator":112064995398781081213},{"denominator":340282366920938463463374607431768211456,"numerator":422354965947334761573},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":411},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-9782450448101709824571487451786958193},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-4970823289889580235104142950524369839}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-503170633306331743764387639215236194753},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1009612730906415158501720539413812071109}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-24162199055322037428047623382203696567},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-196999489202836123400660219784464081963}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":63592115032814613791095510594234869817},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":63289729794946096505671569545981432409}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":107300234557403607406938532353667407191},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":52603933014117792005762807741143602809}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":215368949489162788314977976653090840869},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":107618116882539977098299228270263997227}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-27552981457724142378773787288140506051},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-110287535526531592424698087121468790493}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":395378984356560304659067978061975437},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1667514982829075736484604902277847535}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":449899109286521786700296883193879799},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":410283839903795010932506712242825107}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":237198611911481114265260711126505035},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":208095475299847625581674159872891113}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":30826227367704403635511522797202144179},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":980676120786363812590658359288872807643}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-6257748949676374070637460977190943837},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-6621522880014750009249256718476637383}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1641856055128920483663266260172469713695},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-829025980383204882811546636001159863089}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":293732244474569930903709846454812312333},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":145708951257776896269930719175074683051}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":245240920193987136086078140132315285013},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":121007733091262983386418327822615078001}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-5873607917022190711945040706113624239},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1696590750922743843640898070133861123}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-87763225000630182142117751161945930287},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-44074123797768721620318351652052084939}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":47071004728018981103182960487838092235},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":187447035163545564579985881333958178585}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":105390181456973496290267079684556853497},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":26090086832536023723129147379052243147}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-167695373493678939143484732121130393},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-206561260655456541490773597993546461}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-206410225693099596602594888225028828441},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-208391093790427128751965083361081250787}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":103747259488342403400195384662034448137},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1643474636674182669589425706790152244275}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-9788684960413165597468117087462706663},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2447171240103291538443226392856543199}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-505784458044268293525412573321798387471},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1011568916088536588153528916541482886803}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-12468752634511097433895182049607714943},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-199500042152177560112272978955551327217}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":127513352250654098617566446548034649947},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":31878338062663524453355583673933156857}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":27180853263072919931745152339595121695},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":108723413052291678947728315129684294513}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":215332982652543871999563218378111691085},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":107666491326271935744853336162162582863}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-55154353487719782975023018198647541479},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-220617413950879132565619482873279423095}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-3091613463996219893823719226565982767},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-772903365999055127503467232811592553}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":447828759372578330897132696402168965},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":447828759372577971482600075277836691}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5267749316793926866262145435412577111},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":5267749316793926377805152859857740991}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":990178810376581323472053373908976454969},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":990178810376581322842166673118125557605}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-13714315772701488534611480556830072813},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13714315772701489484710300862051996143}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-834672035210779054826362614410345220105},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1669344070421558111093908894178754489587}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":590594886861500054620260005893699505827},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":36912180428843753323896752390593849119}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":247465242355799274732368637429700527437},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":247465242355799273752482717815932808905}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-5249081442603497333977438919505153565},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5249081442603498072271411948910427397}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-176825645221624224444741094990484420085},"lo":{"denominator":2658455991569831745807614120560689152,"numerator":-1381450353293939259099846702597697033}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":188861224250424309462279672629756103501},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":94430612125212154258577389032366714613}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":212167334961016147896519156765928705003},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":212167334961016147319175037471353979381}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-98302316292812774317378058384877839},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-196604632585625953505136311049665165}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-104860438033080313974670620997899438895},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-104860438033080314205594483932423521363}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":835736654355611774555453809242876191555},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1671473308711223548248922131015252086193}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-109408142814241901},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-106926540853646341}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":204835074040071683},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-86245213762033969}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":284823199053458441},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":15481534870518117}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-15075436602036479},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-16232688929342595}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":8453062911629169},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1023810863531337}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":35002015508713247},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-38553858188774603}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-187448666735043679},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-169460716681371791}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":151486197135343},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-34741187395779}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":283620214711735},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-237378997345735}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4243753252579937},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1609542691239025}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":157915905068977563},"lo":{"denominator":2658455991569831745807614120560689152,"numerator":1241352972713801}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-47312566697530637},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-24200904044973807}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":138450147811537261},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":17098125296189349}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-48905644449884019},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-5042009224751631}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":59259001276844131},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":37159223287014415}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":8726811088429281},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":2976147764062627}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-48112161886747527},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-10586915080766745}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10299326157038387},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-24964717519443639}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":752706879983163},"lo":{"denominator":2658455991569831745807614120560689152,"numerator":-36533619625187}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-41883414767193},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-804779524263321}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":23894046222524939},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":3645595323114633}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":146087949078780453},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":21110174759932465}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":85070591730234615865843651857942052864,"numerator":69511987325772170571},{"denominator":170141183460469231731687303715884105728,"numerator":275551963634010983631},{"denominator":170141183460469231731687303715884105728,"numerator":292376068010671279045},{"denominator":340282366920938463463374607431768211456,"numerator":402063360955522686903},{"denominator":21267647932558653966460912964485513216,"numerator":24351402030520252951},{"denominator":340282366920938463463374607431768211456,"numerator":254833664302761356849},{"denominator":340282366920938463463374607431768211456,"numerator":332687968656030778637},{"denominator":170141183460469231731687303715884105728,"numerator":154046308165999316227},{"denominator":340282366920938463463374607431768211456,"numerator":179706507932352762931},{"denominator":170141183460469231731687303715884105728,"numerator":122112784819902754289},{"denominator":340282366920938463463374607431768211456,"numerator":314706965175541176819},{"denominator":340282366920938463463374607431768211456,"numerator":475024664627869779369},{"denominator":340282366920938463463374607431768211456,"numerator":720556803855718634755},{"denominator":85070591730234615865843651857942052864,"numerator":179731054329738204471},{"denominator":340282366920938463463374607431768211456,"numerator":489931909917888944407},{"denominator":340282366920938463463374607431768211456,"numerator":369141235851378270261},{"denominator":85070591730234615865843651857942052864,"numerator":90000337472907676713},{"denominator":85070591730234615865843651857942052864,"numerator":118136203815168274031},{"denominator":85070591730234615865843651857942052864,"numerator":72167054020467846129},{"denominator":340282366920938463463374607431768211456,"numerator":202434829590792590275},{"denominator":340282366920938463463374607431768211456,"numerator":230919207102059049263},{"denominator":340282366920938463463374607431768211456,"numerator":430961920110230623161},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":32,"numerator":207},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-9708089475666224969740099282465374773},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-9893945305967977853783972633311001411}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-504435838583305095160353435781008691833},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1011990093412763922501984675030539748939}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-196137384380018105197749663118816262365},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-49997976326988921137716164799693216555}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":63808714682194213312168779503897770131},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":63509897586506700350217682818286079657}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":54477069874122623437615897868969041791},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":26715154832728875006058974690902275821}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":215399732668070042508117238116661404429},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":215265825248023955052983256744810075117}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-110243297785225511749226484724395616963},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-220691049800305899930167198685617672741}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-617179141345984832649186488859495149},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3318347795865318627797307087672641265}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":466715890655674604662937422378330571},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":106705773068973139038749500900099505}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5500339930560072124250916648137069091},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3349453315289446818069283822673456423}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":990872778342454255562248859082331708541},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":985189755482332511711144520921529605899}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-6533867978979582012599041162637637317},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13816344950695022733272446311638356271}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1654776657621669245932293711431666781261},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-417749786291984098196598015040183179287}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":295547689086455414535290340037707857443},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":586501652476863969152671701607742338911}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":247815089908711898240783394744086636445},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":122284526787670763949026337494407914191}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-5137448916416205943703604686576637975},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6076476320262324568144554394420593017}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-88059398016859412264479302562079128087},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-176926079396801327866026356741127047849}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":23620137675824490110139953920498603543},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":47025106267298470018071427662680302885}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":53096533195633967547301272712291997273},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":105177974175214282768059227971644237645}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-88484985125335381333899393887828669},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-108121468864527737567440297473690621}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-207982186587860653815719401556924751143},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-104965873743247052505185444249581394637}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1673171855206005346726970861805564156113},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1656608678522451537148816308810364872871}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-4855496835468111413019730029810074937},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-9710993670936223395999267116879737351}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-126727699294060956844412390319067607173},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-506910797176243827941686132805335499815}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-101298577416894626947674650111464299377},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-6331161088555914221765209220441646867}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":127941187783862525649592164498836803039},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":7996324236491407801617137230625144819}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":110377067475433041090691735119451058717},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":27594266868858260072260395273775991235}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":215407376963941352834069975667320908109},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":215407376963941352308503826771480171211}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-55193136315564173904225053887377191787},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-220772545262256696302880515783235328381}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-2378493245357709536416098151170127387},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4756986490715419706579542489207323173}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":465300556062417329081179818510137471},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":58162569507802119780058141561685543}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":6986837155853452436742294833147363153},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":436677322240840745873832826705510589}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":994506832454494376483680462556029167643},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":994506832454494375841074074152923916889}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-1787928276317695591886726639958749859},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-7151713105270782853142697778647353525}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-841154213220626324882237049733664581929},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-420577106610313162808606032956044513993}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":297098758743691508740234852632624112087},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":594197517487383016010415808767683446547}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":125026789655741688151116506104241068551},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":250053579311483375295441197440238432197}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-4494659387335852013000291526523369215},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4494659387335852773371858236715634433}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-177480600535823062327936855979074521643},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-88740300267911531532362782002047101113}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":189553496263940643223889865315395181557},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":189553496263940642257419057793228286907}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":213751837328265978628731839713057780759},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":213751837328265978034291182338131999443}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-12889282126874964677956000354100463},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-103114257014999926762653744129208291}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-52809898523585501512494232380991742157},"lo":{"denominator":166153499473114484112975882535043072,"numerator":-103144333053877932873932576180763669}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1684745983254090441403000424105692699479},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1684745983254090440523398834225325042347}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-97639987191531299},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-419733408696424703}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":327704242475317239},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-190126863753141621}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":362452030556349287},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":129028163640608563}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-13940795887142659},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-4030649696952465}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":4071985388489647},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":299374552122191}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":11556410112868705},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-3366100204495779}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-192610480573055297},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-347429652837370057}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2579153140064105},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":167374779887295}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":172269040779295},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-864263890282197}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":417030704903783},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-340762086692299}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":550771409924425635},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":23680151324877843}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-53006030694139745},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-26323308714793385}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":71240001632488421},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":34743823708687515}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-45518069621461881},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-157219171842586475}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":56282334763894097},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":33230994695300859}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":10222551622720191},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":8209400164591463}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-24032257090926703},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-86582182038739687}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":6626577645001163},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-29888848998369751}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5068561088183247},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1394518711020629}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-3177131372805},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-419918199926973}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":6098968930335693},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":14587099865596803}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":155755087562767457},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":90372269671602761}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":284867676811473112685},{"denominator":85070591730234615865843651857942052864,"numerator":140944413993987710423},{"denominator":170141183460469231731687303715884105728,"numerator":300167636774343154885},{"denominator":85070591730234615865843651857942052864,"numerator":102962458050893251109},{"denominator":2658455991569831745807614120560689152,"numerator":3131415271203602487},{"denominator":85070591730234615865843651857942052864,"numerator":65670747801049240291},{"denominator":340282366920938463463374607431768211456,"numerator":342912740530731123235},{"denominator":340282366920938463463374607431768211456,"numerator":316871177627683413741},{"denominator":170141183460469231731687303715884105728,"numerator":92709790336490813437},{"denominator":42535295865117307932921825928971026432,"numerator":31422181703970401567},{"denominator":170141183460469231731687303715884105728,"numerator":160525744323957645201},{"denominator":340282366920938463463374607431768211456,"numerator":485569647616729837191},{"denominator":170141183460469231731687303715884105728,"numerator":367469260000250322575},{"denominator":21267647932558653966460912964485513216,"numerator":45937116045780159841},{"denominator":340282366920938463463374607431768211456,"numerator":503384381714087555833},{"denominator":340282366920938463463374607431768211456,"numerator":380179665503555708149},{"denominator":170141183460469231731687303715884105728,"numerator":184187547589290698575},{"denominator":340282366920938463463374607431768211456,"numerator":483217146047761761867},{"denominator":340282366920938463463374607431768211456,"numerator":297216399888207778405},{"denominator":340282366920938463463374607431768211456,"numerator":209338636657198442493},{"denominator":340282366920938463463374607431768211456,"numerator":237913588859190639757},{"denominator":340282366920938463463374607431768211456,"numerator":439768103531238246217},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":417},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-9619103024855249758400727326274725103},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-9820343198580416334585716657726153829}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1011272481946468914305706636006022690435},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1014236823367145641756891740182740279951}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-199099612539302797312854932641891073063},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-101551954334025206803767365980595738877}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":128044648219550742084962879778079631711},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":63727159682610568669403359165567965945}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":13826027076076499341229682393455404401},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":108513990434922754971938409994464050485}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":215477222997360464661516163674913094573},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":215316955947564250026172284152146145237}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-220591341468708820414234003281946536441},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-220852066290411935272814696209359575637}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2881167304863873293290732272083845921},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4985628896187339298620599617881958829}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":483989384032371609747031581017053879},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":443810912188156456119885219193117497}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3610651558057968455554986458328863513},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":5050687783535925207437950386988491925}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":124399200858726195206701489282614624163},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":989621610766222629640894979413479480799}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-426167192940962588262326724241702031},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-450218942500551872705147087114602739}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-833859752879101494937693982984843493461},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1683965152391754187648760592280698264243}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":297347326588877355471220211806002616911},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":590139357270805091209004439631554152185}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":15650381211020690924072794705371284669},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":123569240232314537929981247815242459933}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-2190183264575048043444333358134609019},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5345605321876098292869494996873145721}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-176741271973766008170844560772193984343},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-44396251113087042727452475189018771551}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":189655784746167353204306101109579304047},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":188772939750897303551915741926525748073}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":106984026901158756377131671538032255581},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":52991813772440110012152417484401445197}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-186396757657436353021491092739708237},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-226064186022150151838290720701284733}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-104764501721045293028177545765609784245},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-211447729682791004986216593977989405935}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":52701623871435165465612508285564773175},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":208726126711476530383189181150214234233}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-2404740745167658129768648324493506037},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2404740745167658275957881218369415291}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-507969417052354571472738434222494312359},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1015938834104709144099969529640474345345}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-102905805400517123313333115707151150191},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-102905805400517123929612335008466197955}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":64181459629218287905563601583660638369},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":128362919258436574967412274397511812047}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":112030579603602152416524712666181884767},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":56015289801801075795961887388926114725}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":107764364211177233779245884525903750591},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":215528728422354467016626080677179032267}},{"hi":{"denominator":664613997892457936451903530140172288,"numerator":-431591403992303364189917829773296875},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-220974798844059323172459232206191204369}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-3219198520639256270499369006562052341},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6438397041278513192763198726404477263}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":483233550481553658888413511338221495},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":483233550481553276298033420205749271}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":4360613857653718566323808139727748247},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":4360613857653718307598819297622741729}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":499367149296852147653110127432025540465},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":998734298593704294649686835563366398637}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-7454953345770508522899612419977335133},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-7454953345770509019303070306448974947}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-423822306043605292925607346364071091879},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1695289224174421173201865167070449168603}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":597766191075489599017821235095915163245},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":298883095537744798757407376757842000063}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":252659463032845274978001859558508287675},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":126329731516422636971802621285070303649}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1859682941280463006916649050074361147},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3719365882560926796875133306641812505}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-178163078422654684429430750049616043321},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-178163078422654685183451330917120073573}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":190261810398184054734815664079491884291},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":190261810398184053746389952893524092491}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":215312570415586666618365934072783707471},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":13457035650974166625395079418848507747}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-215986322927759567419445344194564461},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-215986322927760000318824267513541515}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-212733407668670409104334903201099748709},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-53183351917167602398645923670294136941}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1698081133685886787788322377730805452837},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":849040566842943393445338599307660519585}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-40550981249966185},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-200888133272370865}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":61292099605875351},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-296718755398511551}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":870728793842640045},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":189646972843163455}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-12298594508426421},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-15749626352809425}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":7682645144445967},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-281377623376691}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":77383948233937095},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-6947444510665779}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-95902598118295941},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-349513453312501995}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5416390400752017},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":45426016495415}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":817501506725713},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-768784828227399}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2333962704564743},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3911445162031175}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":225197016131036265},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-81498560699190215}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-14330015696941845},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-112390071020759607}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":144277372355303355},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":68065216594488099}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-81065268764948785},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-37584693106238015}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":52300583406370953},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":14065053961005479}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":11620843675380363},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":5143044564373779}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-11681915782543615},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-43519988179998925}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1577191943108595},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-34596837138399605}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":445538255678259},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-433916195742273}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-113158796174805},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-433137494530893}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":3057251482015453},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":14186043280224411}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":40786641158476089},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":47120032049631321}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":85070591730234615865843651857942052864,"numerator":73064669904244845003},{"denominator":340282366920938463463374607431768211456,"numerator":576975387020831853835},{"denominator":85070591730234615865843651857942052864,"numerator":154008375469309222799},{"denominator":170141183460469231731687303715884105728,"numerator":210923932027903068065},{"denominator":340282366920938463463374607431768211456,"numerator":412296346243969227983},{"denominator":170141183460469231731687303715884105728,"numerator":135413835230518817123},{"denominator":340282366920938463463374607431768211456,"numerator":353531797552593647127},{"denominator":340282366920938463463374607431768211456,"numerator":325879703865505791941},{"denominator":340282366920938463463374607431768211456,"numerator":191294396902398759555},{"denominator":170141183460469231731687303715884105728,"numerator":129360933069085854279},{"denominator":340282366920938463463374607431768211456,"numerator":328000763353861709773},{"denominator":85070591730234615865843651857942052864,"numerator":124093980720588785925},{"denominator":340282366920938463463374607431768211456,"numerator":749679784729201992915},{"denominator":340282366920938463463374607431768211456,"numerator":751468604038285579921},{"denominator":170141183460469231731687303715884105728,"numerator":258593111628220830095},{"denominator":340282366920938463463374607431768211456,"numerator":391514439804135538521},{"denominator":170141183460469231731687303715884105728,"numerator":188495067138568551715},{"denominator":170141183460469231731687303715884105728,"numerator":247096989991235793751},{"denominator":170141183460469231731687303715884105728,"numerator":153009166731681311707},{"denominator":85070591730234615865843651857942052864,"numerator":54112328225890761259},{"denominator":1329227995784915872903807060280344576,"numerator":957497108420900195},{"denominator":42535295865117307932921825928971026432,"numerator":56098517038434360747},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":16,"numerator":105},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-9513270251115419504063353385795979971},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-9732962939805201606214368886891627677}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1013540635714861400047591608651073451681},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-508175111045561973562333372733362126577}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-202182072556285240130505794702809903421},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-206332895331325377778940847704973601199}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":128465738520344543469159114442267004871},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":63941452184348928043865713347707383923}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":28065527597357697062276211903807667957},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":27541904565691655962258637809355158945}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":215604938160147740844421240651361434743},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":53846356429979605062239361801789361717}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-220740553380237063795107282668894570399},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-110530236100216691006518304638006641165}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-2272276906343015785245351002036773005},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-3334440296489953296952821393858689047}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":62715703753858640402212868554409869},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":461253325621477828798549575275145437}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":4478745456354290273987030782313233595},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":6767875627313993199093243167692441277}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":499704704321079786670615578855199264851},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":993962101766976020563278842402201931515}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-14224361949149961371982304344101739619},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-15015004563065995003097389900761076591}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1680681892822606827512876836674243698813},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-848473614504532525014424731203037546853}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":299129794049964516474917692051589751269},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":593746176308211236350480300152736856375}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":253014739532853839618129485418146625745},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":62431140377277219814896735744033734463}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-3602420353898488915166470089107819941},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2296898528858891045475117470948432219}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-88696372748950182797096231606921903513},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-178271295877127332931636388667127697643}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":47591586397586029659322248119352894415},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":189463179672118033770766842583983115095}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":53881556335861324952287280564909565143},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":213554683104357164503751410991406497589}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-195963641678370817442941274645314975},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-236013193831063790819958073489931959}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-52762697529329541369117980440749696469},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-106469414943778285605760998586828678919}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1699794248891860793356948625147363928323},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":420768488434695655885473325414079534433}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-9511762549551152884104592947926637311},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-4755881274775576742417901714471859569}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1017918212470542268174076060112385779367},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1017918212470542269356018682958227689349}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-209140536845305566579540372137550832417},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-104570268422652783921850398614145063369}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":128778385058962381629150853621529693855},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":64389192529481190382502714439056875611}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":56841800032975185125398115701892204327},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":28420900016487592350669701744955754001}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":215699715551202554265056183941975081511},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":107849857775601276853145760099853154757}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-221226441977189520776732587447228511667},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-110613220988594760752996464997262319109}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-2033844994984231583639119075543232293},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-1016922497492115875601364279749979935}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":250816629964943851126763327846035533},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":501633259929887307581247725881203411}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10470356575374395719414497783254760415},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":10470356575374395186879439025036344521}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":125356680456592293587252511815537163421},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":501426721826369174013162020067314956469}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-15533695822730881102776764497708257847},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-7766847911365441058876334477191757541}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-213535460131524126423415732568150044227},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-854141840526096506458496262753011923187}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":601298204314563038401307216985055633745},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":150324551078640759216130958467225283955}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":31910458565293135850703397124037304795},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":255283668522345085742914859741514557589}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1461634795203598037318166944346973593},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1461634795203598440480622574223349997}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-178871673359156598591796121526787134657},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-178871673359156599363551717186009842957}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":190984605111828460942412373930075611289},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":190984605111828459931400792388330793367}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":108424827513803462297530965648570611071},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":108424827513803461982445282054842013209}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-112932642230597161970693122798849663},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-225865284461194771487148483403423053}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-214202456506047898295899096068604463967},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-214202456506047898800994918718063956229}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":855738365599889645149828919477988794515},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":427869182799944822345877611112199351427}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-60358119418450725},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-187125096071563645}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":81188859663442161},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-399120006748574013}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":997503389827761577},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":485140084084231757}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-2562600511046697},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-30185459583604621}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3541895704677611},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-380604111416695}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":110198838894589235},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":8922473408279}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-185150750844651877},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-172117844154970293}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5598018179483521},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":526724592787075}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":947511928588935},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-330849913612293}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1267426168927257},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1284106146422301}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":167165771104401781},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-56113105927515769}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-30165724249677505},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-29478296315318077}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":71871938976950461},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":64873980866768379}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-68867888029137489},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-35199105602744921}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":47376518087121143},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":11110672541128655}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":12889178497035369},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":6083008117909933}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-22017156712568023},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-85988687605839319}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-80394684554977},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-38976695495499889}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":1142240699880295},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":549633676586705}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-29792664178153},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-441196101270711}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":3008037720080303},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":6679561094787361}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":168062460756095421},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":95822634548553583}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":300238838263855427993},{"denominator":170141183460469231731687303715884105728,"numerator":295345281279941612911},{"denominator":170141183460469231731687303715884105728,"numerator":315912015446248941125},{"denominator":340282366920938463463374607431768211456,"numerator":432062744842938262399},{"denominator":340282366920938463463374607431768211456,"numerator":424054409108053185323},{"denominator":170141183460469231731687303715884105728,"numerator":139636209275694430845},{"denominator":42535295865117307932921825928971026432,"numerator":45568828600614427365},{"denominator":170141183460469231731687303715884105728,"numerator":167562341660560053465},{"denominator":170141183460469231731687303715884105728,"numerator":98667667429513763533},{"denominator":85070591730234615865843651857942052864,"numerator":66566081863432974929},{"denominator":340282366920938463463374607431768211456,"numerator":335568635211874263895},{"denominator":21267647932558653966460912964485513216,"numerator":31716197584997291873},{"denominator":170141183460469231731687303715884105728,"numerator":382396948765934090003},{"denominator":42535295865117307932921825928971026432,"numerator":96044465911360790983},{"denominator":85070591730234615865843651857942052864,"numerator":132835895259722377117},{"denominator":340282366920938463463374607431768211456,"numerator":403155649459497250967},{"denominator":340282366920938463463374607431768211456,"numerator":385856820642521002513},{"denominator":170141183460469231731687303715884105728,"numerator":252743231606246884485},{"denominator":170141183460469231731687303715884105728,"numerator":157540832132302831693},{"denominator":170141183460469231731687303715884105728,"numerator":111886249754064973729},{"denominator":340282366920938463463374607431768211456,"numerator":252542558734944212279},{"denominator":340282366920938463463374607431768211456,"numerator":458037577340486320741},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":423},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-9397086087525523617097147796166445315},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-1205451996099733436405806988022686415}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-126959295497741865371136402790022028213},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1018319065209677122732947681369276960287}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-51345559856065218371905821648142725689},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-104837976595997302439026366305430811729}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":128880536536175814225906075981741423639},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":64152703113788329747123148099686302293}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":56957736009318946094580288719460281435},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":55910573556521312429448731563365470893}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":215782598700859606242452023803954023887},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":26937565076703959221164010844011292267}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-220936607420666899895203187110271034345},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-110659260827295562797775301123908717669}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-6224036774736161368365145349309440893},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8367639440159673094701069788432823227}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":129982596605386755545924636375780107},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":479156124265998415644070384170124081}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10708340380952248462036708760820860053},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":4250218709562339871663315277367262165}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":250878972231056877393732071418322549489},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":124775376347400214401693612052240979623}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-3707188656173099000756007448437959517},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-15640275293178606430775978056756904495}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1693661072397011951924980313801163461093},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1709942590171104149699471028153349269771}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":300893740312549652740877727383994050835},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":149329845281383240824066446616384129001}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":127820890541311285248405438455748205299},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":252328094360647796548804616287876267425}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2803680193663434496333839912394825109},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1910554368441435192912083075169253083}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-178071916513595933756314998368768827273},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-178983535604183440487472512978217732195}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":47772803585381660654499229661169040313},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":47542413601119830412386183558098375225}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":217060770915091361831400122117994631267},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":215118325915641699803534731410971483633}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-25707211896069043056071105536602851},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-123038668908076554669060948731258165}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-212547653939164654879778153213366924659},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-6700162226069443660167051590364747175}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":856598331914863547441357989044322167591},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1696401630336571197113784000651726977885}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-9388535216996011448233625012762125917},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-9388535216996012066150243516545814167}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-509878803666255512069692099829460835541},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-127469700916563878168723155077885014085}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-53145190429376385371389806994063767217},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-212580761717505542781448589593748009047}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":64593704161942597051829067836404211583},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":64593704161942596609318891222564722857}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":115335785420580206201692931231679945167},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":57667892710290102664740073632652702009}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":107961469028684244101354212725879372003},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":215922938057368487626437129293538941395}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-221529637851959229630708106092081346219},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-110764818925979615191407261794335562833}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-2461871266115315203089365077267636299},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-9847485064461261501588084987941425963}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":260252448962139115307561376338788843},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":65063112240534727939964391048034739}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12233673718242982378771955157684601817},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":6116836859121490915372171893647583121}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1006856587556073116771861726660472875315},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":125857073444509139510467907011302432893}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-505459086853218678948782872666601335},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-8087345389651499382045596241959785055}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1721288988807409528052855177999508704141},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1721288988807409529613523285015716305419}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":604790883309512395972026869444339896725},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":604790883309512394400629437223388649699}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":64481737071657198309787497050502753347},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":257926948286628792147399210273613002233}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2106449375734621153145927041140355663},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2106449375734621983387362617701849891}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-179604888220241300471369590378116307587},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-179604888220241301261384262487159914691}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":191720259090853583054672803246104502719},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":191720259090853582020422269162182658031}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":109181617644970515064321480790687751135},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":218363235289941029479806626828395710071}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-117925900501138537471449157435050159},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-3685184390660586524557077688137093}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-53911727093471988950699842637743431641},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-215646908373887956323190392703374061683}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":215616325717336625729016036018699008561},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":431232651434673251224247113579895587753}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-17957590025936661},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-84313070218056843}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":41281963553422717},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-494180933306243199}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1101272646588849387},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":571267557329283831}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-7844522197731153},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-28408298169176133}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1584013293584089},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1281869002234097}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":287752444369603979},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":15004972737822861}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-21597076262563731},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-331484864365739495}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5692913599643135},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":81305906410729}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1076874393737917},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-545437317308383}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":73834627624685},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-3185398403220839}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":203184951089222757},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-378113140705394491}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-61868187905521167},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-121578703449998287}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":140997714925055359},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":60002966258609049}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-27403474726261155},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-64500795998545193}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":10425084214478007},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":15679504271515231}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":27953213390803355},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":6886659914783809}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-39930286653659413},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-41610058042676401}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-942471055976579},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-21492871950601573}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":11053942685273557},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3067529579740063}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-118724288537505},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-886476408815919}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":23155040948555919},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":12089398127160123}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":169984434265859977},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":94885383744543333}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":21267647932558653966460912964485513216,"numerator":19301599893219225235},{"denominator":170141183460469231731687303715884105728,"numerator":302456074025936338241},{"denominator":170141183460469231731687303715884105728,"numerator":323839839132058343655},{"denominator":340282366920938463463374607431768211456,"numerator":442499894725853766235},{"denominator":340282366920938463463374607431768211456,"numerator":436101942087597868299},{"denominator":340282366920938463463374607431768211456,"numerator":288021781802400745037},{"denominator":340282366920938463463374607431768211456,"numerator":375973854621162274899},{"denominator":340282366920938463463374607431768211456,"numerator":344612791106261261731},{"denominator":21267647932558653966460912964485513216,"numerator":12721680791018195421},{"denominator":340282366920938463463374607431768211456,"numerator":274010546452163872263},{"denominator":340282366920938463463374607431768211456,"numerator":343768586239129397461},{"denominator":170141183460469231731687303715884105728,"numerator":259417607510760962567},{"denominator":340282366920938463463374607431768211456,"numerator":780293556133770577483},{"denominator":170141183460469231731687303715884105728,"numerator":392830809394601669737},{"denominator":170141183460469231731687303715884105728,"numerator":272931189273952903589},{"denominator":340282366920938463463374607431768211456,"numerator":415113627841500129245},{"denominator":340282366920938463463374607431768211456,"numerator":394985691139805956857},{"denominator":42535295865117307932921825928971026432,"numerator":64638207389015284241},{"denominator":42535295865117307932921825928971026432,"numerator":40551771771242141169},{"denominator":340282366920938463463374607431768211456,"numerator":231313993452525197609},{"denominator":340282366920938463463374607431768211456,"numerator":260189978254789469661},{"denominator":340282366920938463463374607431768211456,"numerator":467532367389744200415},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":32,"numerator":213},"tube":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-4635677094496404207979737891715952001},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-9538474589613191825822062300558726993}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1017671230926823393629327784723015596189},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-510070523182006069538405268208847086205}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-26087159650231674467919683512551678281},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-213129873636375104105186506272764232383}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":129288863354630003329168334010056227061},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":128721665248332644924542883619117558845}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":115567958363799225414640884324262933611},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":113474226921744940956905242586104885653}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":216012792894257329353737545112640166883},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":53916232294938005769699379296816657575}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-221181783995648019019756970622421883103},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-6925886369095719893422285520983278537}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-3959574600643277928197891668005454829},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-10081456987790260638002710798607849239}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":269304547207383276362868378301469767},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":497524833876011835898526478131759891}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":6236651558366634542087772029933874499},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":10247806959667853642735427110163604517}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1007505376012467026657897811489685269907},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":501168281139717580755852365980977255773}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-7725235905146355786726026586966104377},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-8141355967337203433349582106334722065}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1706654264922964755855330964697906142425},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1722948426215247311175279920971825000777}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":605275658860887296091532822534876635719},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":600856264920527008061522834883901274103}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":129143985988151317165438560189082942907},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":63737464256865228419396429856609900959}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1984226064651499135478134153809814963},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1513803879967803870785239973871135585}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-178777391046202316005128792443951173075},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-44930053543936285467950520268321883335}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":191828761964340823480141946376103581753},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":95445404952996876435214776406010060909}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":218571837194442611119095247099815549983},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":108329150726757034918322799544333414369}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-215465157831776373099255770772901865},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-256243182132769177518307180576653507}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-214019731143337942498273702189984690963},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-215846984770437500474527638777159165451}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":215832127677575912700774706382334327293},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1709790032286353954692100754581141798131}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-2312100074961676035956356713561918787},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-4624200149923352390087444583266148667}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1021455200118459637621694040137701569927},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1021455200118459638861539261454448030923}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-6754025907493911181538621302950057075},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-216128829039805159136926833798516425423}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":16198724673840688140618356443835582551},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":129589797390725504218595818423774969171}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":116986798415135641807441753468606147045},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":116986798415135640910541074960083029339}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":54050226704906233825567254642581274121},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":54050226704906233676968661594382583523}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-221886438472859994881556643488425100825},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-221886438472859995657325100579281526191}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-11574277658708273701440697907705865041},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11574277658708274410147497973727803123}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":134963335163890258963591028597241605},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":269926670327780307992672899863030759}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":14010644539032112984423788224494377071},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":7005322269516056210242174966750617601}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1010736160738869022579569770159447733421},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":252684040184717255468435379385877815165}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-8416372970690463510418732052179655583},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-16832745941380928081939606262762524077}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-433575580024088912983790776109697063953},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1734302320096355653527628475979272628111}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":608241590300939045641243009942411312155},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":304120795150469522017191168612984903623}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":65147507472735032873352119874845668311},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":130295014945470065185942365012946329567}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1268994291709595623376470803947980303},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-634497145854798239094578979485069861}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-180361136625193075783826188838034324531},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-90180568312596538296322736280995718493}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":192467094851182513178045551816729283331},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":192467094851182512119880592489230948741}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":219853477620723359008138633495542684181},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":219853477620723358340083123233461406659}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-122965727166884572825579119296105735},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-245931454333769623811433759853650663}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-108533479119948399852119155709517124923},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-217066958239896800240385983666390374871}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":108652527993184896698354333960014458127},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":869220223945479173109507055441384553539}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-15622863955920987},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-36675228584647861}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":9408758892118687},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-289935750190077441}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":147453977611358839},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":634117460857468051}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-5122617098025539},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-26211027755772937}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2743332910090317},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3709747963753397}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":355979366528964885},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":120899730775763563}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-154880935829150871},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-312115212239541483}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5706382547477741},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":719496317346091}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":603082776910553},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-423428910815575}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-247768932009007},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-7603508954618335}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":62935564339649175},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-541335422588135737}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-15384155831801459},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-61672809804708655}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":8514922207229065},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":53406580263709251}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-39190583889008351},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-115381461192889917}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":35461880811475859},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":8663687451157381}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":29739582280908459},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":14978200851274265}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-17100758560769173},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-39368693542346653}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-1754776888695509},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-46606709519843653}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":3207518561807725},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":618350779954993}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-3421395741917},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-439319109254159}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":1357444281248137},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":10326262273449799}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":168778209208659475},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":22704699764385237}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":170141183460469231731687303715884105728,"numerator":159017920836890840071},{"denominator":340282366920938463463374607431768211456,"numerator":619627970528737093713},{"denominator":85070591730234615865843651857942052864,"numerator":165893179718010149545},{"denominator":340282366920938463463374607431768211456,"numerator":453164972358125971919},{"denominator":85070591730234615865843651857942052864,"numerator":112111435261842397959},{"denominator":170141183460469231731687303715884105728,"numerator":148539823139260390267},{"denominator":10633823966279326983230456482242756608,"numerator":12118925356475719293},{"denominator":340282366920938463463374607431768211456,"numerator":354350906589895903215},{"denominator":170141183460469231731687303715884105728,"numerator":104966847180049567055},{"denominator":85070591730234615865843651857942052864,"numerator":70491603232220819945},{"denominator":340282366920938463463374607431768211456,"numerator":352611990814504343923},{"denominator":170141183460469231731687303715884105728,"numerator":265260083290530250359},{"denominator":170141183460469231731687303715884105728,"numerator":398095634841358104127},{"denominator":340282366920938463463374607431768211456,"numerator":803392240919568811671},{"denominator":340282366920938463463374607431768211456,"numerator":560748475640064847815},{"denominator":85070591730234615865843651857942052864,"numerator":106849740721699065653},{"denominator":340282366920938463463374607431768211456,"numerator":404387373926996978747},{"denominator":170141183460469231731687303715884105728,"numerator":264531342931383318243},{"denominator":170141183460469231731687303715884105728,"numerator":167011906748518421641},{"denominator":340282366920938463463374607431768211456,"numerator":239079753183853336109},{"denominator":340282366920938463463374607431768211456,"numerator":268068139700564802315},{"denominator":340282366920938463463374607431768211456,"numerator":477288636533655552213},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":429},"tube":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-4564311809345554185450583050147286317},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-9417414283474334698955696807131869399}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-509764173357996240444472740220071754999},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1021820952881177913393332670428901865283}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-106062025140975923031387967654719260271},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-216691164637488800290608859778580748243}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":129690525328153675346828142363985192151},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":32282876608630507134431935552452389151}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":29304808123525300421169749151975421015},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":57563256761761158422784581880340505587}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":216298018967546997825976864184610443463},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":107940631200340993246577468141764206385}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-13842391268782857589514029403178266249},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-221992035814860803417060824664119866777}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-9629438906130884304942264751670730215},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11809900489434649379094218126645624467}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":557766844223957193604499510344924373},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":516364681668757893510294397163844355}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":14251846258876121595557604842271330117},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":3002358081209824908663495300879363243}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1011370311928032981795087834502801976731},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":503177531312927676613463595789020522175}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-4022353961693726540228079736614161177},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-8471082586027910907699823268089684637}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1719658664310582876645003321314637848979},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-108497619329928086920220117872770196565}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":304360744022496759858243479217560639141},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":302177074725007245793878189533318997953}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":130477017492704397620601101063237651801},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":257590605320097680692532210934514607019}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1144148181249951701626339989031301663},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2213371730677363125805254265223383645}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-179507683229986357146356957617954931093},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-5639991660391743449890102594392045015}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":192577303609328795957514890288920029737},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":191625031922134113805189755459320366113}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":55014898247832451378590207936436683115},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":218174751100897832142633937148798568077}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-225371438882445420398877645721366839},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-133248240107642456590526566752970391}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-107733593063500729998368344353838778063},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-108632204297933209028681752470808002475}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":870086497730382843763851835734738455207},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":861618503440342464524565603862629074675}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-2272614334452241426559817566000793707},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-4545228668904483181151592083713070475}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-255752369304583491620264950553454803625},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1023009477218333967751308191775551582645}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-109890505787150320681788267252502689583},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-219781011574300642723083193146546884231}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":129985346246239386481911302040537248345},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":129985346246239385553762136321234349021}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":1853692316342030951921720279523550391},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":118636308245889980000794945008657491203}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":216536033925008479737097260357785767707},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":216536033925008479123954679297292863027}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-27787347246564572707563823358852700593},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-111149388986258291230382886662554888145}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-13315339399731869102065940541158872519},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13315339399731869830763108516114739573}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":559683092877338186881138001934966735},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":34980193304833609617407224699619277}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":3950187705440376687907246174601187189},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":7900375410880753085673121344109836557}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":507242365045666579718180912595861416655},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1014484730091333158711512070420588091995}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-2188458962755466584768280422775956451},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-17507671702043733763271061261753777129}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1747320835100995307041149632047977494023},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-873660417550497654333116343960842742557}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":611647730194092700426966679413990898079},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":611647730194092698783782755729404897071}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":263273613619735110720522140290108159867},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":263273613619735109568479417304847916643}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-102750884641166001605912700674599011},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-51375442320583110810509978803905531}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-181138745600365537209000971620768646257},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-45284686400091384509298063211804268905}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":96611691253892201361584706264300841297},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":48305845626946100410098009204596879375}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":55330142410165947282501691049079623313},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":55330142410165947110540390457885026815}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-64022252660320201633296230629618907},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-128044505320640650342881686896785791}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-218462827332220399869292902241733650631},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-109231413666110200210836144642071898959}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":876001905635182506185261636075736546781},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":876001905635182505697898189569783482371}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":11751663608417531},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-241725025643033973}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-57121458485905903},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-654484516106892921}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":615260284363805661},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":674561814257744371}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2180301036342307},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-23635896866781625}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2262723499609423},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2462192529126269}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":105762994790685631},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":180797087202650545}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-65657425175917405},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-286540487895249557}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5635096838834927},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":362909003467883}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1331622742896045},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-300556051220605}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2115139670243177},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8810497040347489}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-84405216498521477},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-710432448825751101}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-59376194257886757},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-15377563124107323}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":32365710298347123},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":22670119551298195}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-22476031012976187},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-100080296539906981}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":28731160641873559},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1368993810179947}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":31054044021631071},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":15776181625367339}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-13421996877737101},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-72550703240502821}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-5014848437405583},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-49807015851370049}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":14445110962541211},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":3346953203042137}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-91057052914659},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-107366662271123}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":19770882933871181},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":4032490924111095}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":164246541947701337},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":20898014180468187}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":85070591730234615865843651857942052864,"numerator":81971897777918282753},{"denominator":340282366920938463463374607431768211456,"numerator":634825513252055690563},{"denominator":21267647932558653966460912964485513216,"numerator":42467209371470988691},{"denominator":170141183460469231731687303715884105728,"numerator":232031927530868115001},{"denominator":170141183460469231731687303715884105728,"numerator":230546425762198065609},{"denominator":170141183460469231731687303715884105728,"numerator":153225081542133203175},{"denominator":340282366920938463463374607431768211456,"numerator":400049980408372378399},{"denominator":170141183460469231731687303715884105728,"numerator":182173064674030991973},{"denominator":170141183460469231731687303715884105728,"numerator":108250247556986735413},{"denominator":10633823966279326983230456482242756608,"numerator":9066813228950233927},{"denominator":85070591730234615865843651857942052864,"numerator":90527965942350938961},{"denominator":170141183460469231731687303715884105728,"numerator":271265293392202788423},{"denominator":340282366920938463463374607431768211456,"numerator":812499466635808599493},{"denominator":170141183460469231731687303715884105728,"numerator":410776579854764767553},{"denominator":340282366920938463463374607431768211456,"numerator":576007680409214274805},{"denominator":340282366920938463463374607431768211456,"numerator":440022575582668292235},{"denominator":340282366920938463463374607431768211456,"numerator":414072787258481700371},{"denominator":340282366920938463463374607431768211456,"numerator":541368799195618803105},{"denominator":340282366920938463463374607431768211456,"numerator":343918725580110964527},{"denominator":340282366920938463463374607431768211456,"numerator":247075905287514920813},{"denominator":340282366920938463463374607431768211456,"numerator":276183840570662249147},{"denominator":340282366920938463463374607431768211456,"numerator":487323119263340150115},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":4,"numerator":27},"tube":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-4483996215234309410018437771010195697},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-9279556729777603220190224258036204167}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-127655481835722440772092181920477732535},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-255839327253145160156575825225898925299}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-215659136133886084218099646914850306617},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-110178032596538410064730996255671124445}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":65042657262548238580043498467162552273},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":64767369965675475834770621394688962867}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":118868963940924224357672904631525230661},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":116777668912270242749748649196697978575}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":216640675147726185791381015043330777697},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":216152043672058129031929494059216589741}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-110914051586816750666780250222279521253},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-222411456165898436813521928684196370139}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-11354469224807497596246965914359828971},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-6776276781907629324092141824398467059}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":288704170052355120266850001828950935},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":535680562938988435479972866064384195}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":1002715841341749979971160867858753493},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":215387138765370007856432158420571251}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":126887909804041355765833833862011778949},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1010250925439595485845638278037777235495}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-16745446422415385631954865848831390063},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-4404610403017699880195211551271836385}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1732671444563805215298428552131650077219},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1748980199889309581665774073004008607593}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":153030594264420241130447401492305251417},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":75976298971551520497528246723492414045}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":263640665383824041124400474600383591781},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":260251070391730806954938535939946638223}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-70886728443140516042344122357735495},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1378488444813711413080245033254856755}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-90130608807343126667147998887160381213},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-45315101929938619457399476553108281981}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":48333775600550223312348976906205283689},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":48092662391934006331928055974124030475}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":221524228152072682765192761390851677655},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":109833919336397827813091026041374396299}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-117680561251625846174294935144673583},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-138411089653837503916522242730157327}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-27111276326225411840808072340780207855},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-218657686910738344504201903455144277341}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":876871061633253521348441342227866590985},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1736740261738119602165917602463659403695}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-8913790272702524868327142905835839209},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-4456895136351262772710705553702987239}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1024419230035692252535306261218373961435},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-512209615017846126918443436237128285659}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-223533326732789537550926029287261411159},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-111766663366394769471101331686043425069}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":130373834977394634306203261065655886907},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":130373834977394633355776368707295375091}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":120283990814431241672617134344958337665},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":120283990814431240724506426786309943045}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":216930622824705718618508863771584427369},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":54232655706176429496496569571708410041}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-111384233190677129263358495041850369351},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-27846058297669282419036358061504548403}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-15070268817930647637181500699214038043},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-7535134408965324193198933263838515379}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":579998253430871070632128552002226239},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":579998253430870624126135745967048329}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":17603491677445475673384457566203129709},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":17603491677445475076314355791222652141}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":509047512622087624364727427950003228337},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":509047512622087623992125356733050373581}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-18199233462081656065633438414215999145},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-18199233462081657175465061606225640509}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-880170844040233783366408435593692375295},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-880170844040233784195681031721234405053}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":615006756867623304171578065834336279721},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":153751689216905825622800276776164768071}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":265978370253254671939488605576410300243},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":66494592563313667689042394883517924395}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":116853401924501784515218105306507345},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":467413607698006232053869103893560255}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-181935958556596424669810906052874853727},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-181935958556596425517963596848760369551}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":24248417962041289461018656394809768447},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":193987343696330314580038956653525901239}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":111382359512772660084032213796034061729},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":27845589878193164932480297685069480271}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-266308428356281639894680932076014009},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-133154214178141075256470935721023887}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-109917381055560108359530284521028541715},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-27479345263890027161020076185232532757}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":220702264423697274928990883074604214651},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1765618115389578198436538422693270347129}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":57792951149439301},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-45785170942895641}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-57739980227450425},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-715634449717012689}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1253054651654597599},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":345933067461684185}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":899174393850837},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-10379881295355929}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3469372579891965},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6217260810608657}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":485947277274360883},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":238190253927638717}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-103375874821075269},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-7981581484173763}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":685657035847109},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":668841213845351}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":723857943951527},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-22427620730457}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1597093382122269},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-4970359874085953}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-235774183870355609},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-220212099513604361}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-6908960170214339},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-30119660584961761}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":30201397250879187},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":4500557403288523}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-5125654787565585},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-83516406789492911}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":10849099800383501},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-750968009394723}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":31837241988005043},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":16084242987425765}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-18014132151251729},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-16161553596180685}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-6384790498690081},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-13112133447190633}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":15833935365129901},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":2066613972941823}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-63034271647019},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-103359483257647}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":1081958846346133},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":1341644540780105}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":156205348127784579},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":73164477315167323}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":338397770807749837051},{"denominator":340282366920938463463374607431768211456,"numerator":650490228383310249021},{"denominator":170141183460469231731687303715884105728,"numerator":347678861392023552437},{"denominator":10633823966279326983230456482242756608,"numerator":14850081772208999205},{"denominator":170141183460469231731687303715884105728,"numerator":237025255231314473499},{"denominator":340282366920938463463374607431768211456,"numerator":316137414230702032519},{"denominator":340282366920938463463374607431768211456,"numerator":412710919837831581687},{"denominator":85070591730234615865843651857942052864,"numerator":93651443676673757649},{"denominator":340282366920938463463374607431768211456,"numerator":223252182834590715599},{"denominator":340282366920938463463374607431768211456,"numerator":298531677620998275099},{"denominator":340282366920938463463374607431768211456,"numerator":372279534109860823837},{"denominator":340282366920938463463374607431768211456,"numerator":554883208115515754515},{"denominator":340282366920938463463374607431768211456,"numerator":829230195562653425475},{"denominator":340282366920938463463374607431768211456,"numerator":840149283988837640055},{"denominator":170141183460469231731687303715884105728,"numerator":295822830024665669469},{"denominator":340282366920938463463374607431768211456,"numerator":452995625159165944923},{"denominator":340282366920938463463374607431768211456,"numerator":424053029356826022405},{"denominator":340282366920938463463374607431768211456,"numerator":554035307776080431983},{"denominator":85070591730234615865843651857942052864,"numerator":88526809829004864835},{"denominator":340282366920938463463374607431768211456,"numerator":255308748548885809803},{"denominator":170141183460469231731687303715884105728,"numerator":142272023919106190229},{"denominator":340282366920938463463374607431768211456,"numerator":497652800516375376411},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":435},"tube":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-4394271791638237839795105501619686193},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-9124003310534798660382403652227254741}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1022816203117041637711857343282014407183},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-32023404504061403918871310325032475775}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-6853088731782338140351429562375322523},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-28015070123711628651819203610867206185}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":65236504590505361836914693164596469793},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":64965580737854618436877331926895960837}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":120516828956072382763496929515873196755},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":118427361500314157471605835374630939969}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":108521524918719520328007014254312881855},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":216479698823627305620392529140586623445}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-111116631176486828251191821626837417819},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-222888418548402908083653077226119271143}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-13093819687558786094882858734189555079},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-7654508404644808083356837302429736961}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":298768932540446624337600393758479453},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":555477007076942698901105885044318873}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":17847625827949485040007821070694364397},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":3893330066379599352040405655902197533}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1018697023363935855627229988913054258137},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1014016697505488414609765634788200378473}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-4354594839621677066412225774150304797},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-18311302794056952390622303753642287835}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1745689766390076979869237074911759418009},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-55062514171851882862136332627341153831}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":615475784709126137775817634507009715183},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":611222390803533427784667768954223999997}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":133174264372943568791517192712825103585},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":262931956383495995344639976158200633745}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":298733642144967059297192600463109125},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-523055852215175887048353967140212921}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-90518165894204968525824980818005884149},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-182060469907965938625160059284557292329}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":194100373384628790563196090968395899967},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":193125939077023913982302697224050668831}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":222965952406498735985381078637243202829},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":221137749333348794270692726386570512691}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-122708988088870918934049011470570383},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-71801106955380166618227370958679487}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-13643063919068031303420158646349613593},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-220027068976407491000426175143968893361}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1767361808612388353612281321070041302721},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1750297367121251306705075829791845009905}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-544842002599201321871427813527742313},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2179368010396805462354207784068605859}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-64105222105742943796512935357364725053},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-512841776845943551039008976588154673365}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-227381553201048512419174368376122279915},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-56845388300262128460528745129006931009}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":130755030219291220664899102892734816847},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":32688757554822804922925570057741162191}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":30482382245228052232411068886539139869},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":121929528980912207954982030166903121427}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":27173357335436772757708010637150633677},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":27173357335436772676140241504844494595}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-111648591948039050001007669381939984393},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-111648591948039050426873609642695926299}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-4209670477217325456267201194508750613},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-2104835238608662824418535028756111143}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":600802480623272971068071924898340541},"lo":{"denominator":2658455991569831745807614120560689152,"numerator":4693769379869316489678876926790121}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":19418384441437331703052110785900539271},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":19418384441437331088737609061064720481}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1021559965025333450176786287326612103633},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":255389991256333362352468412840831585019}},{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":-147712115826797955253876691221974579},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-4726787706457534851938188270270033459}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-886681016920622010220078016669410391753},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1773362033841244022133031402629189417709}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":618316179234425251926804175374656643391},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":309158089617212625104177795871436287249}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":268704938968853271108106784339236653777},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":134352469484426634946371471811127116041}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":683068949895233533084287830261255649},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":683068949895233066746645233336634849}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-5710966830553576394487974843508018265},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-45687734644428611373085298755520219255}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":194757155632511307655395105965682525257},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":194757155632511306521208666561400186163}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":56046538076359941773300964565952274487},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":224186152305439766364000790436747713973}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-138286434458060318246172532813275817},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-276572868916121164062619872784916093}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-221183033153928854879271239290070463665},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-221183033153928855465595113907798245575}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1779280649032752168829201926981716071225},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1779280649032752167812526915766928155877}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":188087704271183409},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-119230233643363699}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-164029423077647007},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-763014000549204503}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":311896047288612659},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":685804463266268219}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2015146566224991},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-4419177940246311}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":293367793766295},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1882533227195673}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":135615149142347245},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":72299980461490403}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-35530706267732871},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-219664654834082155}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1314149522455295},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":267883306569625}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":194177025590713},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-4020026462667}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-1045853759264447},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-10952240679790825}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-47969742277760133},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-65441853553065087}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-12321738257866771},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-115778838153633325}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":55316375734867731},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":12824238584652851}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":193954919961205},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-66209278931101403}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":7279720489553271},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13280370732031341}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":4005615277116799},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":7945671922769309}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-1953100950476549},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-55292339295599707}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-1894569288339723},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-27304146701613437}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":4251105094840811},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":4813827885274325}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-13034168314465},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-783472882206289}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":225544874977017},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2269346561988903}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":9054857220888105},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":59657588748496433}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":349583334090957999659},{"denominator":21267647932558653966460912964485513216,"numerator":41662875090031318387},{"denominator":340282366920938463463374607431768211456,"numerator":711189416207008630851},{"denominator":85070591730234615865843651857942052864,"numerator":121646889457109591607},{"denominator":170141183460469231731687303715884105728,"numerator":243663092075998631249},{"denominator":340282366920938463463374607431768211456,"numerator":326144446191862842643},{"denominator":340282366920938463463374607431768211456,"numerator":425791638639606633699},{"denominator":85070591730234615865843651857942052864,"numerator":96284344327567150595},{"denominator":170141183460469231731687303715884105728,"numerator":115096889485410269169},{"denominator":85070591730234615865843651857942052864,"numerator":76788466612399135719},{"denominator":170141183460469231731687303715884105728,"numerator":191562331061164700807},{"denominator":340282366920938463463374607431768211456,"numerator":567595022359772610741},{"denominator":340282366920938463463374607431768211456,"numerator":846395192508034102221},{"denominator":2658455991569831745807614120560689152,"numerator":6712382661085841603},{"denominator":340282366920938463463374607431768211456,"numerator":607668000452635641905},{"denominator":10633823966279326983230456482242756608,"numerator":14572798931491841341},{"denominator":170141183460469231731687303715884105728,"numerator":217169630023582649757},{"denominator":340282366920938463463374607431768211456,"numerator":567073493832592915001},{"denominator":170141183460469231731687303715884105728,"numerator":182298922765613142345},{"denominator":340282366920938463463374607431768211456,"numerator":263784758701306393549},{"denominator":170141183460469231731687303715884105728,"numerator":146577927273072810431},{"denominator":340282366920938463463374607431768211456,"numerator":508294895544001101049},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":32,"numerator":219},"tube":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-2147337395748317262313215337018993489},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-1118729904778222033402239610069542033}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1024244145455233003022506969414154858731},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1025994991259825498150499885257322630217}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-111519603675721532218464695946750293257},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-56995100291226948894223940908021394353}},{"hi":{"denominator":1329227995784915872903807060280344576,"numerator":511145992759253966239656281346004289},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":130320552847508590911156852983261488597}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":61081255383299183315555097223010882009},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":120075266375301560068217119024228267875}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":217507311993666245480428983136252744521},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":216866546250376770486603755281451155729}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-55673891045811818166238270813796915549},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-111712293082158565641296074670647585851}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-7423543322750607504230011046331279995},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-17078908369795541295674805959154084961}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":9658738212210334047138561273106695},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":575758143191916095804943037685377695}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":19663882804095257712175959510984331951},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":17374559330039943672329732911357659323}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1022144487125576401914363451161362100623},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":63602817814695667207834331120143209135}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-9053992789887787976673397622626768323},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-4755116100709094269053306183963726521}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1758710783763135318377437088939644013929},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-887509913468228900965617454609014062493}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":618779225774122098794917014734098992219},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":307293796827895051450949669672970470837}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":269078258869665162275796285196212237575},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":132816969092382308071438861552526749037}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1498773982664523785200298996334994757},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":22051125654969017606516596135953835}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-181831279315664940190932318950959229183},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-22859758965622473122464773471386527383}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":97435643795791925136981324731718911589},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":193889127707968810614047434985866437073}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":112192497081220771221922085194524740675},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":55646172113694768115404990061596824577}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-7985155061337368039323507782461641},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-148813292794250185309314532005646903}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-219663865902382319179163293654505418699},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-110686413994880647289068022665499405227}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":890514662584072912717911306157995183705},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1763905758747515128769951290268632205369}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-2125142389392721225695763429699914399},"lo":{"denominator":2658455991569831745807614120560689152,"numerator":-66410699668522543953275193782233443}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-128350230551538138057467941318253536623},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-513400922206152552913325805389515478579}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-57830312135470294644913289596594298473},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-115660624270940590017046148618382005037}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":131128685596453929997851136264067892871},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":32782171399113482250344767669193605535}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":123572612812705400905465316029063615707},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":30893153203176349975900048261953074205}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":13619174937404609490107685277445042947},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":217906798998473751168515157243932075011}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-223886475686120186165278288093002418213},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-55971618921530046761003644002814766051}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-4655053163890980738622739759167217855},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-9310106327781961873196485454740167691}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":622098957687329659426239713790902667},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":311049478843664592381872199148823219}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":21244965527183973193605098541421921761},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":10622482763591986280787873436755826613}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1024872683908290413914105414916346446361},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":512436341954145206562055923108344620717}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-1226943563193208944529285965162406539},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-2453887126386418034237831883227956643}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1786379034096264647053988154726619133893},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1786379034096264648782084855456335029065}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":621573567029034493655272621907661648135},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":621573567029034491897865996239142749095}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":271453925374854039405869748334543765205},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":135726962687427019078840762546795369545}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2285040259780537350436206101575650725},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1142520129890268195173732506875821783}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-183581772014305739159394731181444372523},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-183581772014305740049328654096988982841}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":97765477646626112170020448477652043613},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":24441369411656527897376532867233740503}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":112792556807621026094835736193972608709},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":28198139201905256429858224990531904443}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-143432355246034647895086217468156395},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-286864710492069840812109580280810097}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-222507933955640347586766363565080806647},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-111253966977820174095415893497196823813}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":448247143532458889729372792233394911993},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":896494287064917778939435063876799388801}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":262190109595558721},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-13103728557711967}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-25060741102118701},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-796057917800391183}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":607598148272898913},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":655832404345000173}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":7142380858258267},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-7241784842899453}},{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":9366638185335},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8841702965199383}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":591070601536128635},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":332940346452736189}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-35147025825303099},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-180687918573499561}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1236520939012699},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":330106463075401}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1647496030754981},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":21059365328313}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-5045990013804223},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11823367262449147}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-524202320292120985},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-602024947352046321}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-20741987195776485},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-109013697035637621}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":99253381488483915},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":14476334819774827}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":14868253289357275},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-12158131642667771}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3752684053754601},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-20280733854831105}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":31685405620191577},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":15183894274236237}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":903978628134467},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-44548771147318633}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-8568537324038391},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-56275467033196947}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":1120776067750137},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":10730632072607179}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":4991285976145},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-729370438928035}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":2787581462405623},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-295271319593583}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":130322143830301541},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":21613543867097259}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":361460783030749908259},{"denominator":340282366920938463463374607431768211456,"numerator":683156254122009611299},{"denominator":340282366920938463463374607431768211456,"numerator":726939887479093009263},{"denominator":170141183460469231731687303715884105728,"numerator":249112609909187353389},{"denominator":340282366920938463463374607431768211456,"numerator":500927541174299198311},{"denominator":340282366920938463463374607431768211456,"numerator":336474838470052609847},{"denominator":85070591730234615865843651857942052864,"numerator":109823843378188556191},{"denominator":340282366920938463463374607431768211456,"numerator":395948697947759244283},{"denominator":42535295865117307932921825928971026432,"numerator":29666305621137072367},{"denominator":340282366920938463463374607431768211456,"numerator":316011287145330811805},{"denominator":170141183460469231731687303715884105728,"numerator":197328430281311308317},{"denominator":170141183460469231731687303715884105728,"numerator":290341637475145265967},{"denominator":340282366920938463463374607431768211456,"numerator":864005961841523593041},{"denominator":170141183460469231731687303715884105728,"numerator":439332064158842378351},{"denominator":340282366920938463463374607431768211456,"numerator":624080218569495342903},{"denominator":340282366920938463463374607431768211456,"numerator":480036119788239025909},{"denominator":85070591730234615865843651857942052864,"numerator":111235719778735594227},{"denominator":170141183460469231731687303715884105728,"numerator":290247373906262260759},{"denominator":340282366920938463463374607431768211456,"numerator":375399235339339293429},{"denominator":340282366920938463463374607431768211456,"numerator":272510593904880832345},{"denominator":340282366920938463463374607431768211456,"numerator":302026546009092422077},{"denominator":340282366920938463463374607431768211456,"numerator":519266973061942381673},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":441},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-8369477508590176477609922315659323877},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-4378069050404557889808799513672675891}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1025526739179521489027108863133933737777},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1027094884303177606198089886773929112935}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-113438023109984642712556183010169129215},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-3623923687980649302589568552799300277}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":65613080663582655570284382386859298777},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":4084458822450510020057132067142029981}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":123805699825034469739125510609093166731},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":121721065553787512201188309873434976887}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":109017750892584429839268309490599758441},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":217314787227752550490298077689704088351}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-223216705816826774468613565143148410299},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-7000671456541875931332228098482523113}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-16613883848624357811743272184150237863},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-18861864451073797944998595923974628201}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":159818954055623310107373132629211905},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":596527665556692429595496415194583523}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":21491763027042991710677862038892227535},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":2398501130379587766343030921843496135}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1025438829140195552195340749609844279279},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":127641122515460263081991607803116609249}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-9406995142290613330473492282355280339},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-9872797848535171388219650741354579733}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1771731650408170419731459454122261631723},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-447008871184726606704606311022207473499}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":622030276748827973743731738641743791583},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":308951750866412473796656898699331038769}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":271830455833000509071089336204606845395},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":67089414829320338607120558272747561663}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1210121458659549205826445374230823423},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1249015120065062547031112413249754953}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-45661058246793492879570821094592826053},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-183711288892578702571602388318200851335}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":195645976249352913273881942968197946881},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":24332299723274446554697287783983064711}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":225781599252342715061304449434665664963},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":112004440211225274921039080707432678845}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-132832125375436662255502212183707147},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-77017809264876348587453705883115267}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-221015007962818668505361010080902560805},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-55673814968480133061115824993389583463}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1794741820436341309239215394779530646637},"lo":{"denominator":2658455991569831745807614120560689152,"numerator":13887208914836094070213588333932923313}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-4131074522964590137178267003831208483},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8262149045929181022769948431331366089}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-513886897817466303357383759694751728833},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-513886897817466304057802567504435105949}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-29418470954241084352397767819694554331},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-235347767633928676304893135622211820875}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":32873635538565487038901048047411529059},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":131494542154261947135337960807085706609}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":125212939827184663336428496093895023723},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":125212939827184662306693366374846895621}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":27311545570456991452045448154616093287},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":54623091140913982730459862662016047471}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-224537747272807783189040527432947330143},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-224537747272807784095634017240512834915}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-20414513500181492851599256521636039473},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-5103628375045373416424800290659746327}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":160972589640114986398810088907419915},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":321945179280229728129340866263753113}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":5770697808400386972935317593167479537},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":23082791233601547241512817822364779819}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1028026558264114316953747564353501989579},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":257006639566028579034821572976330763135}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-20370698484620946971980789577307206263},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-20370698484620948160380028460030864709}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-224923732960568199957965121914806883433},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1799389863684545601427952700841787528547}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":624776556298406552705627317069146531647},"lo":{"denominator":2658455991569831745807614120560689152,"numerator":4881066846081301178971636370623597369}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":274225899683618525125770326556903892283},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":34278237460452315480495904635356699053}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3223981958650164462088143307942527951},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3223981958650163473816729267341432225}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-46106618093664372545845373622798433087},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-92213236187328745547590430961498987765}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":196306843703291526528851324362431975721},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":49076710925822881335047891567420177191}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":226961863401414711679988329668301209861},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":113480931700707355453470343866806182251}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-297165564720344860774663939104289961},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-148582782360172711880801870170760555}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-6994055614003194570529128086479305273},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-223809779648102226879271613948649636801}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":451684732532882847478220611639070040593},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":112921183133220711803226265480170035975}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":335903359066637569},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":15298020026624327}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-224983564450336781},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-407139371215834381}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1157610324521816803},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":604802224803954935}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5085399410505863},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11259167213356659}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":48856340160379},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-10123745177176311}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":314398003904265693},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":91928810734702909}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1643092984929865},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-34948047532870181}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2281005499591113},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":6526356078967}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":863335508290331},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":34223173681413}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-2883672290205893},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12514804509056021}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-652263624274630065},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-84068611405431303}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-7990309400207161},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-100255412293264893}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":43465113418166445},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2739073499136159}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":46387100823494505},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-15614009189150635}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":357123805381357},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-13410335163410153}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":30746104308085527},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":13949681154838013}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":8010649446226577},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-16290006357117285}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-9322288189059717},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-28696750294953325}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":18586826292071913},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":11529649991967809}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":73970608812809},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-665273400602855}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3754105490743199},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4901163422880253}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":14086206268708079},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":24145894130068341}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":85070591730234615865843651857942052864,"numerator":93511601135578616985},{"denominator":340282366920938463463374607431768211456,"numerator":700124160220692711125},{"denominator":340282366920938463463374607431768211456,"numerator":742579092482468762179},{"denominator":85070591730234615865843651857942052864,"numerator":127530600177065755155},{"denominator":340282366920938463463374607431768211456,"numerator":514862478558765395705},{"denominator":170141183460469231731687303715884105728,"numerator":173565763455998709165},{"denominator":170141183460469231731687303715884105728,"numerator":226612602857866041079},{"denominator":42535295865117307932921825928971026432,"numerator":50880964677553274709},{"denominator":340282366920938463463374607431768211456,"numerator":244667484422390159211},{"denominator":170141183460469231731687303715884105728,"numerator":162555426272594123523},{"denominator":340282366920938463463374607431768211456,"numerator":406884219144983333127},{"denominator":170141183460469231731687303715884105728,"numerator":297082736177007805549},{"denominator":340282366920938463463374607431768211456,"numerator":882073767184997632175},{"denominator":340282366920938463463374607431768211456,"numerator":898590123255062136319},{"denominator":170141183460469231731687303715884105728,"numerator":320443888639028179209},{"denominator":340282366920938463463374607431768211456,"numerator":494127308808723924105},{"denominator":2658455991569831745807614120560689152,"numerator":3561526430157021701},{"denominator":170141183460469231731687303715884105728,"numerator":297155252292134869935},{"denominator":340282366920938463463374607431768211456,"numerator":386520292379194370627},{"denominator":340282366920938463463374607431768211456,"numerator":281493100278613907741},{"denominator":170141183460469231731687303715884105728,"numerator":155581776451726875353},{"denominator":42535295865117307932921825928971026432,"numerator":66323353444846249405},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":16,"numerator":111},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-8127994389507950752266217211786370857},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-4270983399233383639329224057138649541}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-64166458959310501760673659978032121033},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-514024176991169395530214133212317122765}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-230804938867138133257269062054747733475},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-117984017807284293240555011586009541043}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":8224444382200422531134340220313555991},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":131077305094370281057293473449300452221}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":31361523513430286445342319815329889525},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":123364448230370317028292516557531128283}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":218629521605327160398835202677731530651},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":54456624121650287535731010210071276775}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-223798249948379192963913419800344996809},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-7021265853930910155548815641496748603}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-18393842974389074710838331463374118865},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-20657539786137557147364604997298388861}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":330445192488900503615684554253302337},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":617788799099498982267341408382956017}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":23330825127582192267144800992089108503},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":21013203349361948149845851727111574245}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":257143363521781384646448842792883369783},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1024461487221753176961702565421815075517}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-19536072327387032789140908951934035053},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-20486319164430136022417571659555475209}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-111546845386220085646939644362072178863},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1801044605346954137380572756928774327105}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":625226581306669239780461462921684358389},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":621167676553741742133133166363413319667}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":274605684188841972664982181516663509951},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":16943983121942350061887729633473754343}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":840433543219938975348432963465248063},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2165407602769512000231212898292465317}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-5733540261747787649641308453248749711},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-184558124759694548497250475079780552909}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":196422535077605180905979511188306937865},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":195431890872768561209349235110152116313}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":3549312963076029419381516214986656921},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":225410567390617181283137884364931450771}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-275817239555691859757368655681618243},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-39815025935823833811103708548812871}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-222342739729791129824107420076323527265},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-55998670497070826862674213191218266383}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":113031020011824235101815917780295094005},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":895632745617175989842202588380680167577}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-4000640848596125247611316206803804127},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8001281697192251270260196519854656573}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-514299696445849341823806311653850207205},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-514299696445849342541588819281066953009}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-59864070449468509427989997893126043149},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-239456281797874039228656796484410339619}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":16481541097206139728431259285835662669},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":16481541097206139597857079637382938029}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":126850215227247193505899643078734873221},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":126850215227247192447611150063304655949}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":219145330856885501558683918246458357461},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":219145330856885500842188932243942510339}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-56313065127800196307105181430805695463},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-112626130255600393081864157436060393627}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-22221255764270712706331270996297302399},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-22221255764270713543218742378171605735}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":666178814227363341856944464182210407},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":666178814227362837434683208600834395}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":24931438503354848410547868219956984583},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":6232859625838711935405456583018151409}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1031015232223067864988207684126972012311},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1031015232223067864147880389618864733715}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-10562767416473346298098283358046666153},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-660172963529584181637000654630525475}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1812391716624170363131788373127513151163},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1812391716624170364933090958986838297607}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":627922854575441336261701067014341353923},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":627922854575441334423692772933356977139}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":277021395029395316090102580212328625823},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":138510697514697657386941626351432310227}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4182814837268590901476974870697863031},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":2091407418634294942114531647280702041}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-185282984502527633725093456164069535459},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-11580186531407977166214931058332366099}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":197082890309954420610292932174994658397},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":49270722577488604848297540104523231443}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":228316677090088438043825466111172622857},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":228316677090088437247878350934997141951}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-307456296454131291508903613464460137},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-153728148227065936494128357072927285}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-112544452820695451614569418764978682351},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-225088905641390903870300133735559794337}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":910264319440093382000886174437173262651},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1820528638880186762917138025068842446833}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":407517462884709485},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":41166850520032723}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-14737647042995297},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-817818782087849225}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1077512844165740641},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":266553040152093153}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":6515760897915685},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2023591865223733}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1074677501325633},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-5673176449586091}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":163438379061565137},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":97920487314122105}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":42942401890960123},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-98424335941805657}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4120800156510253},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-288976068549705}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":111659920742583},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":215848129646825}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-6321159912757953},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13016012549157557}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-381775225655805769},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-366339249120420951}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-20780446628056951},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-44783915814072969}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":73936367319723119},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-9540182565327649}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":31116607146588205},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-3607573570882969}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-2822696082935615},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-4104503015888919}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":29201033022684507},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":12181371901286461}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":7287003312053357},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-9808381995654389}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-19561883156886965},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-7241004028753423}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":9472392006878969},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":5994366553903457}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":136610135802071},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-295763971356579}},{"hi":{"denominator":166153499473114484112975882535043072,"numerator":1752507951271},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8807408378651041}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":23046433663981291},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1358084465480931}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":387356190172201202139},{"denominator":340282366920938463463374607431768211456,"numerator":717491499412516783567},{"denominator":340282366920938463463374607431768211456,"numerator":758076199074022306343},{"denominator":21267647932558653966460912964485513216,"numerator":32642884728073908463},{"denominator":340282366920938463463374607431768211456,"numerator":529139110670016185361},{"denominator":42535295865117307932921825928971026432,"numerator":44764557152220379687},{"denominator":170141183460469231731687303715884105728,"numerator":233791555602766309905},{"denominator":42535295865117307932921825928971026432,"numerator":52305191350353077711},{"denominator":170141183460469231731687303715884105728,"numerator":126105172636244785377},{"denominator":170141183460469231731687303715884105728,"numerator":167229836758811994835},{"denominator":85070591730234615865843651857942052864,"numerator":104953185995367150791},{"denominator":340282366920938463463374607431768211456,"numerator":608059333423541696953},{"denominator":340282366920938463463374607431768211456,"numerator":900609554654720047837},{"denominator":42535295865117307932921825928971026432,"numerator":114870726910775479281},{"denominator":170141183460469231731687303715884105728,"numerator":329048034219375691311},{"denominator":340282366920938463463374607431768211456,"numerator":508615445957507530451},{"denominator":340282366920938463463374607431768211456,"numerator":467148337996004399959},{"denominator":170141183460469231731687303715884105728,"numerator":304266101401957148051},{"denominator":85070591730234615865843651857942052864,"numerator":99492519890658691235},{"denominator":340282366920938463463374607431768211456,"numerator":290739312481301439601},{"denominator":21267647932558653966460912964485513216,"numerator":20035903114404361737},{"denominator":340282366920938463463374607431768211456,"numerator":542272427119889557583},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":447},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-7863972895168285786545103473835248461},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8306390840458169382350487004277963109}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-256913403716190401326887904291711346515},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-128606927820808952422463829649300355821}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-117410631526179525838676385371766517259},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-120043154434027641547823243342371890131}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":65973973902638411690688045366575853603},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":4107630117143550861013901094231535081}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":127083399081816240734605670599944889281},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":7812819438819655432863388826038200079}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":219291127516805456909457776312836745471},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":218403613124417094700992969774309099757}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-224441620118495617311482023645804501719},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-225402891661617276087067059318209530403}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-10093307052927163969526877590585263967},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-11232804024562988532254383193401193885}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":341502599494030064133908275599503809},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":639544265179614937146555397228088787}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":12590324241494490391690679755709359893},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":22849695983669610181305201834800646983}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":515771018861676949841406966415622399055},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1027635949435309917967783220446995830193}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-20273863825888995570441271203692380291},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-10621105206604254792918226370408692227}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1797761583302212084085425804259085800355},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-907022193562773619934188756326877607943}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":628365855433069179829873606732280948057},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":312188872641722018291878941414827801595}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":277404471305250902362259766436820119419},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":136936362529496352004300700121816252737}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4323098406939937641770662756419516015},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3101857908840188566266291968663505631}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-184316467691691038963701097508020876621},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-46354128630338887790126266285181544583}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":197199028678246204737213244452130999573},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":98103856019703836036927912002536268473}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":228508562070678408970791571304763075071},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":226790007993718744455401700425815257155}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-71491142959480748924307604881046739},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-164477291053580957529603917717010287}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-13977960866107270696622060790245762123},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-225271431761575282255744231678964686091}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":455572433349829577547498880384468469779},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1805011063101777286480689661454478735703}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-3858524796595820947509230322732910123},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-241157799787238834317466682380465479}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1029278907522408473595931922817694978209},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1029278907522408475066983787677930458201}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-243641798458261680243145627838108633475},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-243641798458261681790482670833372697865}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":33050440648650931481971877717013212877},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":66100881297301862429209611752705544013}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":16060519016011844763661273673397991499},"lo":{"denominator":2658455991569831745807614120560689152,"numerator":1003782438500740289232408383780868739}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":109933659962251265549650561973235119823},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":219867319924502530360177210226681144607}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-226031130199405127829976579022467545667},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-56507782549851282198714344746976321717}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-24040130016813997947904773920978951865},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-24040130016813998808185442519801398921}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":688965879875614861467909202097430613},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":344482939937807170768559553676639195}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":6697626407354074428485602685620842743},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":26790505629416297025805646397156088461}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":516916321473715830509817954961088475443},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":516916321473715830076016796891411129349}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-21895138876411662723523272923254255951},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-10947569438205831984178933995686925281}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1825381811973215322278229162580995633021},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1825381811973215324117559621135610100353}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":631010245717294044130870405845187817419},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":157752561429323510562801937839891339167}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":17490056620960116954907397984741879501},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":279840905935361869927070702293236313219}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":322586348185591468419092200317799977},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":2580690785484731223831009317048106509}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-186149189029128739292264162118730286209},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-186149189029128740249859578059989870577}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":98928568714215097934143728316702281117},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":197857137428430194621907101751087325635}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":114824921860939480712228982292208189875},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":57412460930469740151233871321779211205}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-79429261634233952687894714802496423},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-79429261634234102816302329480195873}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-226345666191560784749965498313180731973},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-226345666191560785410511733868991617381}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":917177254984040840285309572955707653597},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":229294313746010209932730670390188397241}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":475055921850812141},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":146019668294947907}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-58954642473791831},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-807827467482271935}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":979739823911033487},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":445500755957079831}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":7815078923303919},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5055823413228157}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2108086625298995},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-6240132812150273}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":664347055341135971},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":402805205263746745}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":82114822871487067},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-56421447312953989}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3617913683259827},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-21112976838361}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1822398746123741},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":278029286316853}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-1670148414746257},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13281196700190531}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-425832894395603937},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1560054492755987767}},{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":-63946376691699},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-4824882646747067}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":60527175330057543},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-10895553113445269}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":4791925846930717},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1381540009878663}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-11425003670479711},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-19062448718410117}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":13544283409184331},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":2472416115160527}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":5335649657851145},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-742528586287001}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-2508322750449989},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-57799843498703033}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":18971859295990903},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":6082089377433855}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":102413066095849},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-63591055933601}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-254002834742747},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-1599958648293237}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":34658204603108535},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-10334292115889073}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":401405718468576605423},{"denominator":170141183460469231731687303715884105728,"numerator":367619963990662093845},{"denominator":170141183460469231731687303715884105728,"numerator":386700700981827527683},{"denominator":340282366920938463463374607431768211456,"numerator":534723800690690963743},{"denominator":85070591730234615865843651857942052864,"numerator":135941443010529216481},{"denominator":170141183460469231731687303715884105728,"numerator":184715592967427926453},{"denominator":42535295865117307932921825928971026432,"numerator":60296391480953331259},{"denominator":170141183460469231731687303715884105728,"numerator":215069093767470089919},{"denominator":340282366920938463463374607431768211456,"numerator":259964622862642172667},{"denominator":340282366920938463463374607431768211456,"numerator":344065081871143038503},{"denominator":340282366920938463463374607431768211456,"numerator":433446963717694956147},{"denominator":340282366920938463463374607431768211456,"numerator":622382791040994089505},{"denominator":340282366920938463463374607431768211456,"numerator":919624070136528759625},{"denominator":170141183460469231731687303715884105728,"numerator":469896841303020361985},{"denominator":21267647932558653966460912964485513216,"numerator":42231905174027106821},{"denominator":340282366920938463463374607431768211456,"numerator":523513128834315430029},{"denominator":340282366920938463463374607431768211456,"numerator":478773395257653239599},{"denominator":170141183460469231731687303715884105728,"numerator":311585655405205533369},{"denominator":85070591730234615865843651857942052864,"numerator":102439458952094801467},{"denominator":170141183460469231731687303715884105728,"numerator":150128229226032784323},{"denominator":170141183460469231731687303715884105728,"numerator":165133485973073506251},{"denominator":21267647932558653966460912964485513216,"numerator":34646368681139691689},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":32,"numerator":225},"tube":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-3788248645960833632993393627204298991},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2012119991111134595461532781754478425}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1028497503497787684751859983747199202873},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-514758198718448836854693188576594031345}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-119460105254782385301658804689074207005},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-244280923392657441689741429122682744313}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":132296389996748874438817802637683068467},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":131802988642193588154416507350436524255}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":32179332118368256091597156860267148855},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":126642758199888766678858096776994967613}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":110010960601642002581372925925164878595},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":109523965964753944625507970466115116147}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-225148096616919428835952985919903757789},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-113094867779866496380315190877035371431}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-10995933079214125471831677562154394719},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-24285762216852868570342511645170663495}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":705621911262601911755462012150426167},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":41362265493132128212440054686351821}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":13520416958894358527788877267917715449},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":24697061235084417817848945176207485545}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1034338552090925319270253490768263012727},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":257661493614993147839126400089482251913}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-21026950002373723691528896676451182411},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-1375799894256463296137849679615589113}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-905382506225011655671959746415043777187},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1827032054191493829222608293605320266707}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":631445892221399017713250501475909547667},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":313765702974056351473537623647702053787}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":35028413231791335009249548617092254423},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":69166295678878401879578781552580136489}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5304177118442985471535707867150151753},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":4058219028249212596750546986604514835}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-185171723923868106515567737474504666561},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-186284329710463378610824922171130099985}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":98986747496642424469736379346136269555},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":196983934234028816110269871476625940339}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":114919743367882043370401051170451049709},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":228147476018346698415331267201116229393}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-148043080434840533816807551438525335},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-339354728332250045298266368968995663}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-224929243462415224153200274736267136511},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-113262932626086007456292950237073081433}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":459029714413864265326425576074575796197},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":909398196174800587103648774677283223777}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-7408551856826424697392215741712222969},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-7408551856826425530143667015766035557}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-514906444644759075239104008227110801477},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-514906444644759075992733826647952839875}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-15493698824231022347621229814427862641},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-61974795296924089784877955752815995021}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":66271274681205962912246866370063791921},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":132542549362411924729587796855343749187}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":65057235886856421824062728148590329043},"lo":{"denominator":2658455991569831745807614120560689152,"numerator":1016519310732131582270418372052499953}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":220659792837079392986622851207842775233},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":220659792837079392224209950503831655387}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-226875321334761406921199289481256187123},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-226875321334761407916516153322401186221}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-25870846389567956409939810805383141405},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-3233855798695994661779565441430931687}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":712252503115712757735023622288935395},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":356126251557856110930693718060749303}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":3582451613424468685352560782540328143},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":3582451613424468596868098099974928725}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1036473045115260277209377195915262117569},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1036473045115260276313085886933851877169}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-11339498516160112743025984214752408485},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-1417437314520014172526799312281929501}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-459589349868749692216992581236791789613},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1838357399474998770746306356506654047763}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":317018297196642313318612965846492512779},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":317018297196642312357500596654988904461}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":141342443466556242651325692746586333761},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":141342443466556241957576316121101017347}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":6159515979567045154603945336342815673},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":6159515979567044076920138598762388919}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-187022907084488069729791822933177971849},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-93511453542244035355682276751973211543}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":198627604739480056540146013059482621495},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":99313802369740027631815324354872002927}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":57740416139738255153240125073870725655},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":230961664558953019769167937474642961541}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-163963628789678916051816225574756805},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-81981814394839613052065766796615627}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-113790216449776596879990547143106094089},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-227580432899553194440491219779695902379}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":462053311642676473272752921278819442797},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":462053311642676472989323647586749921035}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":133876242206062339},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":204701658537615859}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-112061675257642173},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-785338064051293131}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":867224322493321203},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":344908472266569839}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":17918194735230449},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2215368539408051}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-758714418609785},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13475164126037351}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":82431551295038157},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":50093908310656553}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":120489429572619845},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-16222518901457911}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":385347394188039},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-273771452025391}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1832661321768119},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":39795377642331}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-6823204957320639},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13293558082833621}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-457159533985725849},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1623852186299951535}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1375878824710149},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-7919714625950343}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":23502293975555355},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-4242809310811053}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":89488568284548855},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":15860230856238199}},{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":-128934390315647},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-21293272276257565}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":24431896774384757},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":7155076457492107}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":56268731113679533},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":8098067688514051}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-4981555381507103},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-57022629587214931}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":18675848823847811},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":11969182551275827}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":277763858439437},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-26192573301707}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-2342187223251271},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-8386202444033371}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":11126797731430665},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-22669270339425339}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":416210323981883589545},{"denominator":340282366920938463463374607431768211456,"numerator":753349211064074034005},{"denominator":340282366920938463463374607431768211456,"numerator":788524915065095713231},{"denominator":340282366920938463463374607431768211456,"numerator":547442901160754598077},{"denominator":340282366920938463463374607431768211456,"numerator":558750732184004532945},{"denominator":170141183460469231731687303715884105728,"numerator":190538549890034016753},{"denominator":170141183460469231731687303715884105728,"numerator":248795037973167730335},{"denominator":340282366920938463463374607431768211456,"numerator":442146267430551353107},{"denominator":170141183460469231731687303715884105728,"numerator":133968030471966701829},{"denominator":85070591730234615865843651857942052864,"numerator":88483653888424710295},{"denominator":340282366920938463463374607431768211456,"numerator":447790887931540870281},{"denominator":85070591730234615865843651857942052864,"numerator":159288494916837451463},{"denominator":10633823966279326983230456482242756608,"numerator":29347735695266395159},{"denominator":340282366920938463463374607431768211456,"numerator":961075555022789452989},{"denominator":10633823966279326983230456482242756608,"numerator":21679260473568414383},{"denominator":340282366920938463463374607431768211456,"numerator":538833264958631767051},{"denominator":340282366920938463463374607431768211456,"numerator":490762279953671642877},{"denominator":5316911983139663491615228241121378304,"numerator":9972486468294354915},{"denominator":340282366920938463463374607431768211456,"numerator":421892928077283684547},{"denominator":170141183460469231731687303715884105728,"numerator":155025983442751420537},{"denominator":42535295865117307932921825928971026432,"numerator":42531127341440134375},{"denominator":170141183460469231731687303715884105728,"numerator":283406812259168378427},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":453},"tube":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-3632334808777149576891685684126149305},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-3883657017464562657100331621806661679}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1029195245740285341209045188191392150945},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1030031863561516665077912532255397168027}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-60774201640417309353722778834571085695},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-248546725527593665697436238137503994173}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":66318070488823721744234261703183958889},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":132153498329821089455080412160968856325}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":130347603945595633896515939267035353533},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":128277101926150215146774087752605930759}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":110411671250649326807205850347498208695},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":219761095193747405554151155485865752569}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-28239851626357174848661768680491177491},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-56760496224083672299029610757571855441}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-11904643627255567483157053063586728713},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-3264714359692470597777597733275643283}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":728741548529672455124809993106848279},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":684546361136274551138486542378075563}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":28911004349946553519013792060199406455},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":13277447330234245374391259428463234589}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":259239322477469991933400818590899154071},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":516742729975802035210374036736977928619}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-21794869267582605703707626140010381463},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-11398782677936587950932045886712935395}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1823757028634411979787491066031364432031},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-920002431011222702347436014664326593187}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":39654035394708502205760653897217713339},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":630626432317511598579989672115682988633}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":283074636453175565247713680409673278833},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":139740801272246840779055185573537033211}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3152401480979135583888417354092395621},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":5034334749748483700982594381528231487}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":-2906827269694538455043725057438773797},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-46789845736808310704363996475886474865}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":198743949813561530100496429131406867591},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":49439650679742789336627071838345642589}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":231149105847795600405611146033544468719},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":229483259041221556182638189404288969325}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-76540304029545602672669021627940413},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-349700320922590939440117106790699289}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-226188700697228836242251471228969681077},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-227758355640548321319391739872056934485}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1849980385050075059776252579653036311971},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1832618301625637970538022338818112467973}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-7074910971608405253976179962756100595},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-7074910971608406117871731592792510391}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1030202157969432998616091213442826931545},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-515101078984716500080119008465581316521}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-252223169980646574304217274168690828613},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-126111584990323287955780261991131245429}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":132874383835017953865725597065249258593},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":2076162247422155511637553298179621849}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":131740903741423453883518955886795244181},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":8233806483838965795956829416885201479}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":221524042786472267637571544657831325453},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":55381010696618066712802108960204607353}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-113892823515354801498701233964450985131},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-56946411757677401006004889523925194197}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-27713134839340877337427207122949578525},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-13856567419670439123190216777077826531}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":368019496758376057776983028976432591},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":92004874189593945411421179818937831}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":30538403231270252855858792895600804419},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":30538403231270252127700413178277499467}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1038931034415269459232662699068738655101},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":129866379301908682288283240296395727089}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-11738274965465929969743697083904427411},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-23476549930931861244337958068208257877}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1851315764966053445784763968849017127957},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-925657882483026723851551592124350260457}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":636999850210054839259167205960414547011},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":159249962552513709323367457029434368511}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":285553751336687061863708170158628317981},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":142776875668343530219662484640880359363}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3588521692125700624350003294376495643},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":3588521692125700069752379808463004815}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-187901905251182729296272733405340981251},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-187901905251182730302573651110647337041}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":49848073455313140407601186073018307815},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":24924036727656570040359284008075067423}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":29031556458750604386000202516615366683},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":232252451670004834219225115165705187969}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-169032851351338821030053872632514105},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-338065702702678282327737723544749383}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-14299599571664105398988067579316508043},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-114396796573312843542439084906977416329}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":931050725869351722369341067010316461845},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":232762681467337930447397637218490199861}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":293649220674315823},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":256394480952726591}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-102136912553192303},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-376447646667153891}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":745876457415370129},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":236712026356658475}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":4978279591511137},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":333751204873001}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-3841855455622003},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-14299841922065839}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":319216402008307531},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":96221285232836609}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":39242690296907871},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":22469922165689527}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1255373727000423},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1542651764807075}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1816658606543821},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":337615661760725}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-6728007586161653},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13040872161591375}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-237044478226086905},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-206724110189197315}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":19917464349508743},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-48395846440548957}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":33829391940171601},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-45491260954808049}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":100264374588725699},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":28479966427057959}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-10343917549209835},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-11524422317087497}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":21286226342675497},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":2014595690449999}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":69536758224420213},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":22174182414903903}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-2414809526927429},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-27821631553717005}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":18067153468589429},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":179282195672057}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":44114639883429},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-162520336324389}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-1102977555174429},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-10306413884389597}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":4590394317423583},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-70681679186319949}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":170141183460469231731687303715884105728,"numerator":215891161917410126185},{"denominator":42535295865117307932921825928971026432,"numerator":96474886376256736145},{"denominator":340282366920938463463374607431768211456,"numerator":803417042691256475295},{"denominator":170141183460469231731687303715884105728,"numerator":280225651653648072177},{"denominator":85070591730234615865843651857942052864,"numerator":143524903403770697085},{"denominator":340282366920938463463374607431768211456,"numerator":393054780576963813707},{"denominator":85070591730234615865843651857942052864,"numerator":128310323665972108071},{"denominator":340282366920938463463374607431768211456,"numerator":454474586515993633307},{"denominator":170141183460469231731687303715884105728,"numerator":138065279394114144859},{"denominator":170141183460469231731687303715884105728,"numerator":182038016713186968807},{"denominator":10633823966279326983230456482242756608,"numerator":14463924402015056367},{"denominator":340282366920938463463374607431768211456,"numerator":652391125294804672677},{"denominator":85070591730234615865843651857942052864,"numerator":239782486843348551663},{"denominator":340282366920938463463374607431768211456,"numerator":982812796717257702613},{"denominator":85070591730234615865843651857942052864,"numerator":178044723877837208617},{"denominator":170141183460469231731687303715884105728,"numerator":277294497484216301539},{"denominator":340282366920938463463374607431768211456,"numerator":503126777564748419739},{"denominator":42535295865117307932921825928971026432,"numerator":81718384215036292331},{"denominator":21267647932558653966460912964485513216,"numerator":27149059746071005241},{"denominator":340282366920938463463374607431768211456,"numerator":320133476010244002481},{"denominator":340282366920938463463374607431768211456,"numerator":350528649768781660103},{"denominator":85070591730234615865843651857942052864,"numerator":144926499127031913815},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":8,"numerator":57},"tube":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-865952002355783367783462181077206457},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-7461989172157554262129886100896217719}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-64359209846807030136929939857252211751},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-64400167184685572816510551431179642615}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-61836482534136847142662977992360728139},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-126439220324018539241764780192224277001}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":132966894089585202717194295235602154401},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":66247699974140780254371315062156226773}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":131973955573518519560465544427798677605},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":32476965615655830715157499155566055741}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":221696662582004951371341964172914219519},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":220544585087643218985639726518486564311}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-226754753318473906020666601149250252827},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-113980216740674457512996741135143170115}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-25638585045474990584642362081553491441},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-27961198486404648837616847120826735529}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":376182240244989059728357807089686787},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":707795616740793788795239616445817437}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":15395402690063447504920423909080137993},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":7105703435939738687211305499466965735}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1039392887956912757544507275892417758331},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":518074309066427222532575088402615430989}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-22577113553198675974836926915237021479},"lo":{"denominator":2658455991569831745807614120560689152,"numerator":-184343346440735711617088592647591569}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-114795929805025380449342093111291650569},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-463240025706583225993610459811662661757}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":318709918992839424356401066067250983023},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":633660678438574155381912199862916985291}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":285946870458787622659098992741729343597},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":282322444319148579610269703053474194199}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3662400054634075971278456950967448759},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":3015019982577904934813581660370318673}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-186909959768434334376669396480137725435},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-188039432928971687907893658811516934021}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":199508391319944737363887668655553075535},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":24816217445484108545450261336706440659}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":232437732241217447034270667083386669655},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":230797657038701416739712078384891076689}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-316168272610156772678585365445863753},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-179985185058841640180959251786459749}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-113713057629791977708132594976878373475},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-228969291659276338853424231079287903671}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1863870908522218119783970141381503577901},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":923236753176935599988276431104970555997}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":-104926237702886639274796393873337367},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-3357639606492372905094079506940435187}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-515223897001184018740642524458678078903},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-515223897001184019531478542004237396333}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-256608401606386144481190398149563022639},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-32076050200798268264723041276845639191}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":133196950110310885489765521781989119721},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":133196950110310884342232034559934083483}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":66681593066421517995855302390815962683},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":133363186132843034812058415163423569187}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":222461188890313961909351225085107050709},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":222461188890313961098376297573738612703}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-114381383551209665671384679334967690975},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-228762767102419332401551672211417370397}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-1847921584814969495995838703669251923},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-14783372678519756435100857348016175119}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":760324993705910522025428259662121665},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":95040624213238744114455622045617385}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":16213271315151722966612063177836996995},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":32426542630303445184223369104400953679}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1041201569856041917875833146074263256753},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1041201569856041916917913903021588671761}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-24287193285823863406664769085169951319},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-24287193285823864742957465281728292281}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-466063558881844947725541072884497311543},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1864254235527379792861523703414874950613}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":639898051464486005044713200851593550065},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":639898051464486003034630593013783435609}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":288447870172094375087094833341391995817},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":72111967543023593406245801739636327237}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":513361313273147621140393748689051013},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":4106890506185180398320831463138261057}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-5899496898168030773435897572623658691},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-188783900741376985781752387627823414259}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":200149192696772232837327156643566720729},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":25018649087096528937234850846142873071}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":116761263249444101002827189790956584505},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":233522526498888201111160550035087725435}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-43513814649222331745458981255241771},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-43513814649222414372750729344538517}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-114992774236103857934324192980802178623},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-229985548472207716590887964705291666513}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":469003908782068792017028515139685933201},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":469003908782068791720487826223395962791}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":39272262017664413},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":298183016253873083}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-21856003958471645},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-711195410656606959}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":154527306012227281},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":121265205866194067}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":5391299478630507},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1222876723083391}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-1123203133449307},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-14930853278158313}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":300654876521726811},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":44392796779911231}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":47688494151736675},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":14566303511442525}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":478521802877163},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1005817769363081}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":887710603020741},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":167807821014759}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-3201238372973997},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12521552723173183}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-474580614584003597},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-411710142892234335}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":17395861611608233},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-32759254621910761}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":10591942570738745},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-56537379624302659}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":54613964475645173},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":4899387051707483}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-11989475444965329},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-48760546417908811}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":8883288578839413},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":72274861536133}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":10266038067496109},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":17935191726945195}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-18158256767810235},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-53683112354209639}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":8588621219443811},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":5343529808273925}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":26790365948037},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-57069862624801}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-12813338598584285},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-24209827623360387}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-8295764254364733},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-96028481576353973}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":42535295865117307932921825928971026432,"numerator":56016938539372407585},{"denominator":340282366920938463463374607431768211456,"numerator":790567843856064900529},{"denominator":340282366920938463463374607431768211456,"numerator":818048544023509687915},{"denominator":340282366920938463463374607431768211456,"numerator":573757183888793340495},{"denominator":170141183460469231731687303715884105728,"numerator":294910437894365998773},{"denominator":340282366920938463463374607431768211456,"numerator":405364380066282137115},{"denominator":340282366920938463463374607431768211456,"numerator":529324912389460405923},{"denominator":340282366920938463463374607431768211456,"numerator":467132184857287042327},{"denominator":170141183460469231731687303715884105728,"numerator":142277085869433292655},{"denominator":42535295865117307932921825928971026432,"numerator":46812164885955988445},{"denominator":170141183460469231731687303715884105728,"numerator":239305390927568413711},{"denominator":170141183460469231731687303715884105728,"numerator":334056286304678303433},{"denominator":340282366920938463463374607431768211456,"numerator":979640845306059962145},{"denominator":170141183460469231731687303715884105728,"numerator":502503143751318120993},{"denominator":340282366920938463463374607431768211456,"numerator":731043422393659354357},{"denominator":340282366920938463463374607431768211456,"numerator":570793724337241452165},{"denominator":5316911983139663491615228241121378304,"numerator":8060604745177970763},{"denominator":170141183460469231731687303715884105728,"numerator":334853206254709334189},{"denominator":85070591730234615865843651857942052864,"numerator":111810917420500387975},{"denominator":340282366920938463463374607431768211456,"numerator":330508838529704353085},{"denominator":170141183460469231731687303715884105728,"numerator":180557045563665633291},{"denominator":340282366920938463463374607431768211456,"numerator":593037511473918946199},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":459},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-6564493193692769169368444178599728837},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-7131624058043476889927652660927625625}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-257538656513525678776351926433723490505},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-515314972603702775106121390307600200859}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-125831167015734128152102750900374547815},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-257270693523251436304323223281143169905}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":133288332072441480375127939641039822641},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":16603548698301917320457030124929095905}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":66798060991456865805340529429731227649},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":16441846047657233274200161745043701747}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":222642977848442931432676431548706452515},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":110699858334237763171078218036691921447}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-227656749842084113068329452604138805857},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-228945721728339012359059603652747194353}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-1717467936287825346207196801083371915},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-29815965567961923520435729674466973937}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":776490390724643139341311700671401399},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":91443049228373229077394173414171799}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":32679905821826278528199907996682823621},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":15150229249493124597155790088170495305}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":520820174616622137279217814647434993529},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1038629999435494478722691510246418324945}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-23373128896971535802364408215839501619},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-1525458702285923573349641596031861131}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1849695837667596929469664611821070692159},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-932947555326081046310329089950755897291}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":640309756832550767166031161529366504413},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":636632082807555289529851901938776108941}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":288844372917781847890702412044831809119},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":285188126716565417389171919841528013621}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":8363984659243345834186553257805708637},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":7045161020363406173429004523603459123}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-93894270159501308031501433532554846217},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-23615273705100468549462691033549915631}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":200264804638499956210295025142241382443},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":199295348174891738557605299256082306205}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":233705687938767216575605092878996222247},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":232090980973475680624071784064336933543}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-326085223219577378961395027394810499},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-92535813166055446253281748116157459}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-228641872833302924465469832734129344339},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-230159075966530543648862315884453932273}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":234723366079352927778026467179196615305},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":930179310486233945198199957658145545049}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-6328845130104576337278879568023008341},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-3164422565052288634083758565818574101}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-515275564144026332687628992517361238181},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1030551128288052666994943900310237718631}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-130524714947332012300285519028909688419},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-16315589368416501641614577529827157993}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":16688740244573199388565170515966391359},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":33377480489146398483441173501772354889}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":134981065749553122948985669121580354743},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":67490532874776560868564542974746157965}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":223472170764969297000159622726357959573},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":111736085382484648082008495721945002913}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-229807187323529230562964683622324129663},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-114903593661764615827337682938480415075}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-31431448123502468373382740792712236321},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-1964465507718904333352695944713417529}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":196277363068563888584012650300532617},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":785109452274254967908468775369510077}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":34323720745127002101506610589901973645},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":34323720745127001331087572129346599631}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":521639997349147296008606089889432996337},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1043279994698294591026522213127782778449}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-12555139508928336952162555312633776697},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-3138784877232084409132911290776836083}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-938585092180905879694936967438792483723},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1877170184361811761391286982169305217329}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":80341166064718381859305811147925614817},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":321364664258873526409533129600875799971}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":18210473203885818873834103812225492221},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":291367571262173100480651304803033650387}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":2317384612660645935364778384989587397},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":9269538450642582566519988053121161427}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-94833283388068224411233745065220928299},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-189666566776136449880568829509064814739}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":100448140189346814492481233764807452975},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":200896280378693627612673172046419318737}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":3668315912854492919772476261640015443},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":234772218422687545944474633605831223297}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-89509808249248111964109569484850199},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-179019616498496565114651157377793863}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-115578356450298483052530217698703201763},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-115578356450298483424548926399371501743}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":944976110073005279642125514776464917301},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":944976110073005279035258033100506052007}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":651991369484409729},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":330383131085020045}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-8699189041928355},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-656213712586242993}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":15131730279340591},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":5026482790669243}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":22799279712078699},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":4227238975549675}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-2486695868069719},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-15241540033986851}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":540471431636564879},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":312385447742893705}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":218079425774439863},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":22534415619143735}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":316092836528139},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-307760648877089}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":104959085652225},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":327817037211617}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-2940108856763969},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-5787322586228587}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-918347694897113253},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1583131925840924667}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":6088214299608575},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-16278858315733885}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":4311104843336373},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-33150256964478063}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":115735864128647517},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":48200393066459781}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-26417672765286097},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-12591421867273045}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":13820292293730275},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1475741380864327}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":91836727846102427},"lo":{"denominator":2658455991569831745807614120560689152,"numerator":383238827375901}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-16666762752645795},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-50324471350300937}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":990877231454139},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":1208619939097547}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":244052800181797},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-121169658280555}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-16588402831985797},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-26893033613515843}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-35340325350729793},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-59031399541906193}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":21267647932558653966460912964485513216,"numerator":29080219666412960943},{"denominator":340282366920938463463374607431768211456,"numerator":809584444293799926477},{"denominator":340282366920938463463374607431768211456,"numerator":832391506766633460689},{"denominator":340282366920938463463374607431768211456,"numerator":587369049039952591145},{"denominator":340282366920938463463374607431768211456,"numerator":605923157511895095699},{"denominator":170141183460469231731687303715884105728,"numerator":208978636324643570643},{"denominator":340282366920938463463374607431768211456,"numerator":545791370245669417781},{"denominator":340282366920938463463374607431768211456,"numerator":480128333933082657437},{"denominator":340282366920938463463374607431768211456,"numerator":293213115148749698203},{"denominator":85070591730234615865843651857942052864,"numerator":96301668004137055597},{"denominator":340282366920938463463374607431768211456,"numerator":495012591210069701405},{"denominator":42535295865117307932921825928971026432,"numerator":85542074695514658299},{"denominator":42535295865117307932921825928971026432,"numerator":125083632785506538813},{"denominator":85070591730234615865843651857942052864,"numerator":256914086813823891357},{"denominator":85070591730234615865843651857942052864,"numerator":187583801022233802383},{"denominator":340282366920938463463374607431768211456,"numerator":587461176855890864615},{"denominator":21267647932558653966460912964485513216,"numerator":33064329913146280345},{"denominator":170141183460469231731687303715884105728,"numerator":343063909443649483017},{"denominator":170141183460469231731687303715884105728,"numerator":230239415515734819801},{"denominator":170141183460469231731687303715884105728,"numerator":170593063690389385695},{"denominator":85070591730234615865843651857942052864,"numerator":93003389096319383739},{"denominator":340282366920938463463374607431768211456,"numerator":606826120439092323997},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":32,"numerator":231},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-6174494876061200109268344990366136693},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-3387683180765903221811847074859212367}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1030383076914226152615484591666557782023},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1030718928659033720953024970588506940347}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-128020332637501415829514932025967413371},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-65429507147208989970158800707298382539}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":133600127388086278035810101462220627471},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":16644019079375313408145975582473568775}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":135213850526207945490254395848532007699},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":16644694594475311147643468799815005953}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":111831602304324418796362705446232324665},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":222327631588276752599004173627322024683}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-114312740834927253785950897872243571221},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-14374895999718921580036088924996642623}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-29331740522813383913063288092249248173},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-31681788865074664141764597557813818569}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":801118249502271447441473179231473677},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":755792409728536453523886042821629063}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":17288999085184998629556885363993598133},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":32187492014740494953679990901888787219}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1043695063731075252926754340152481671291},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1040924514981038212916931631984931310085}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-3022789535284954134408143884101816081},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-25231086317721936389261328997345499803}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1862637232116493659991344901886768209625},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-939403633112677484549769398099977659771}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":643132465106790589560089459536290388363},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":79942334021362075566475228727812787669}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":291767465670602811382175381831097399759},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":36009878278476957289828565077157394919}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":2355541274128352900256088688884014201},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":8079516114132244040599141367578434309}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-47167602434659663818371930427320983415},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-189805319766021950038097725656992122621}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":201011166391171296873334001392058232755},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":50013354460459750502929279558343009927}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":234953302711195148843069103533236424241},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":58340887841046857285237122072739377071}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-83972338450559855875855629550425289},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-190098372835744232035002457016647869}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-229836373472502283890659088950778395261},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-115664061734778301835276028430007379777}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1891724860762049310558981400960838776475},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":234283770701676421642507383969110784439}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-739355001771841076919051401899207819},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5914840014174729582136916450820563033}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1030513731218663236984090321138011548383},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-515256865609331619321106737521776176687}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-265540745813368389986100924268833192161},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-16596296613335524479962136354308686139}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":133812963117858843686590450630666949607},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":133812963117858842483981076240367972133}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":68297149125894494087157793435721344039},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":68297149125894493464737542138102088001}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":28069717990240144465938256433487535757},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":7017429497560036089550901724426796029}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-57729814837659327392989463299792844375},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-230919259350637310697337518595887840735}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-33307033612322564479297993800724662375},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-16653516806161282733123262067969126785}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":810390598723022483943692551797520565},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":405195299361510939857472891024148227}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":36229651241160822178737941756025963441},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":4528706405145102673288482313397445705}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":522581027913541384573125220515777848743},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":261290513956770692030382276855365250605}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-25945116629655249497154875138441307347},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-25945116629655250899377908115972874585}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-945030517691345187750301718306320744933},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1890061035382690377545119182175858153521}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":322745953393328852509402858155173378371},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":161372976696664425729304097966816109183}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":36789142308195813670101269990735756473},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":294313138465566507820668261925605037687}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10344118146857226060425001046747122401},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":10344118146857224851198298085423280757}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-190547538144188245342395033406843925949},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-190547538144188246427610154078019071895}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":50407882848269340069476764144613918437},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":100815765696538679435916955534693629529}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":118000931652502000646781726228805410499},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":59000465826251000086339357613212448261}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-367828815949699003119590574931431513},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-367828815949699707467410024222172067}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-232307511223374445479825168533153729193},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-116153755611687223123152110670656522287}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1903907551480423476552351636007818782773},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":475976887870105868827524868803492282471}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":10363834149364185},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":350421945302883647}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-96919486677964529},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-298091357278773633}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":353201413280275251},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-109391806047530669}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":23746522703424409},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":1390826133912949}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-5242472404847595},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-15346116088331267}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":7319219988696837},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":128537592787336163}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":240613860605871423},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":29158412010483601}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":637512950109035},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1460564435434813}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1565589523336933},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":148432464240771}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-5141301881795127},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-10434852053545639}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-53390713458674727},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-743659484962098265}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":62370976024735935},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":34074985686763}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-170078119090229},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-18759607894694237}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":120044333274939825},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":27424029123190593}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-6966095807038477},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-51029725883523095}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":302298331285111},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-3321671224355985}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":100279165812121749},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":61037902771500467}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-14661474818546813},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-46605978303855169}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":14345249284484737},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":4204808025832869}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":273012648974129},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-17918583549809}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-623574528550003},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-14578163814186375}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-15358913138746745},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-69429341737654157}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":483235820897685238143},{"denominator":170141183460469231731687303715884105728,"numerator":414405972669415305563},{"denominator":340282366920938463463374607431768211456,"numerator":846415332090388990071},{"denominator":170141183460469231731687303715884105728,"numerator":300647797793032801215},{"denominator":340282366920938463463374607431768211456,"numerator":622415199475777514201},{"denominator":170141183460469231731687303715884105728,"numerator":215416460348135221971},{"denominator":340282366920938463463374607431768211456,"numerator":562627842592076263107},{"denominator":170141183460469231731687303715884105728,"numerator":246736242923348153133},{"denominator":340282366920938463463374607431768211456,"numerator":302113739022577184359},{"denominator":85070591730234615865843651857942052864,"numerator":99053098712334330911},{"denominator":340282366920938463463374607431768211456,"numerator":512044133027754647083},{"denominator":170141183460469231731687303715884105728,"numerator":350540182537869551207},{"denominator":10633823966279326983230456482242756608,"numerator":31944428568461614537},{"denominator":340282366920938463463374607431768211456,"numerator":1050762064084026880685},{"denominator":170141183460469231731687303715884105728,"numerator":385029683164406411227},{"denominator":85070591730234615865843651857942052864,"numerator":151151298259034250765},{"denominator":340282366920938463463374607431768211456,"numerator":542587939704067262331},{"denominator":170141183460469231731687303715884105728,"numerator":351510300251395776583},{"denominator":85070591730234615865843651857942052864,"numerator":118525010796441026119},{"denominator":340282366920938463463374607431768211456,"numerator":352173627752704621243},{"denominator":340282366920938463463374607431768211456,"numerator":383234925432722271363},{"denominator":340282366920938463463374607431768211456,"numerator":621087368881464665777},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":465},"tube":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-719607287454742474169850433815827753},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6392399222378648098701818893874235061}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1030346203458359298030011892756294767541},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1030680982750476751973691584397236504769}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-130237742719640900522727669525097556807},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-266214929993104036596612326927414490301}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":133901942522886529438756109867838005857},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":66733182057942744994382823778001829675}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":136826897441791227476340106037464549395},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":8423498333706527707603824661516912183}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":224758074578788636871089965607296948431},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":111664646281716906931615552590698880793}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-229661473849067646055577987694980476655},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-115559304296841745564722472384696875591}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-1949694581944716813759743587497514041},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-33558461434985462552424329128457085753}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":826246288720646868512102152952267551},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":780538692669100312285842600191064185}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":36484799008970085548705104393954257865},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":17041800469016662653453923038916026827}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1045552827616457063549611547234438068059},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":521513728853693824817533921213575914493}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-6251008182911604592407059277668926129},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-26066495593748973716596970057570937739}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-937778213451384887909508797783257684877},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1891694001493189611527580986478188091117}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":645886200647151743431268367544920187843},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":642378564947813198306599358030396950669}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":147358213304461634685971039068654646663},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":290995476223645303937174551966000439443}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":656196424933942821693359694410530963},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":1141614468159482507195918378078053657}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-189553246165380329156054981774848470061},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-190686452272941525820180063131759079873}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":201745449223690461628193169392141927417},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":50200482071201272624959404135361889011}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":236180912632928854501886539635343330561},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":234615696843771844993651088247105071873}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-172778690540929579514114209700282403},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-390108063202627401452271777107444221}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-231010029933439498007023551689629527401},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-232476859605014178987392386568375033099}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":952840521329239434077565514396302366051},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1888204573200180745838892181224277005831}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-2736272143952259911154466949183554973},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1368136071976130206655834389557317895}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1030337401043326353166832410284798912879},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1030337401043326354863793221929955386021}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-135038398602297183769174041525692163723},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-270076797204594369258982000933026967759}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":134105727598144330069999178813324064589},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":16763215949768041104861186705497786549}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":138202648298471863333451328300263915415},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":69101324149235931027414696009022007673}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":28214809504452548027480868000350711697},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":112859238017810191665824433700569012045}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-232099181306602645469561861653274835221},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-116049590653301323314685723163363374791}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-17596656320022065414528535634299295237},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-35193312640044131843409239145936039355}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":418082960336755669602926337472809063},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":836165920673510716679490597351632671}},{"hi":{"denominator":1329227995784915872903807060280344576,"numerator":149000281866302014168629769282737685},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":38144072157773314812118026972889791971}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1046843921391487491593930401802523327093},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":523421960695743745266946643357524303511}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-13395487412598885696802903435521850393},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-26790974825197772830389516342507576657}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1902924267501462640043819468251830693193},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1902924267501462642132501865183544373669}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":324092054675647110827690565017942590107},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":40511506834455888719167068391123558787}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":148642405533786762849647744366063467597},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":297284811067573524118830721749275558699}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":11437315959608308265347026021720955283},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":1429664494951038377606385054050157649}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-47856104228915909950374660207820472067},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-191424416915663640914665441599225243885}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":202352920264243766188171057626824577015},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":202352920264243764747351297242516931449}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":237211802050180511095826552361579217523},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":237211802050180510119586341361677814853}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-94363926412531740920770151178791439},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-377455705650127690643346640483951857}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-233438377244828431408584508719208221611},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-233438377244828432198165974185308003479}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1917877902988942428161236382644662042019},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":958938951494471213444743334433773694521}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":661311418710636671},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":357118624128392601}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-12563535625799565},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-133311447755659637}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":228981790537576775},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-218619436816711033}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":12150979039748193},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":1624448558059057}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-5290193773844045},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-15238983958994095}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":96786044496549919},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":190553247694197711}},{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":2018243972246723},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":68883351271660039}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":49878044056827},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1684093676076487}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1437635169334843},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":60515584638895}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-4202019090088063},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2283344597305733}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-757265708794231443},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1361487409202747765}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":37715967246302447},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":7916814801238571}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-12556882585475955},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-82533198487942141}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":122226422386678901},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":59141448648183389}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-28375615282993825},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-12705257971858445}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5434025131841759},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-10381689365646169}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":53688809140725161},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":35759230402772699}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-3071971593756099},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-42764388982608431}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12749488331419109},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":3494871044016127}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":150369316862739},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":38829599809383}},{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":-178247112410363},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-967939680041893}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-42936065869161609},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-19751128094437669}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":502005105432639958781},{"denominator":170141183460469231731687303715884105728,"numerator":424119454999159258213},{"denominator":340282366920938463463374607431768211456,"numerator":860093158327144176251},{"denominator":340282366920938463463374607431768211456,"numerator":615545940502747256019},{"denominator":340282366920938463463374607431768211456,"numerator":639305993746017375009},{"denominator":10633823966279326983230456482242756608,"numerator":13875023213615244805},{"denominator":170141183460469231731687303715884105728,"numerator":289922254036886913473},{"denominator":340282366920938463463374607431768211456,"numerator":507174374905970619539},{"denominator":340282366920938463463374607431768211456,"numerator":311262583252381603095},{"denominator":340282366920938463463374607431768211456,"numerator":407523131302095960259},{"denominator":170141183460469231731687303715884105728,"numerator":264858223346766550937},{"denominator":340282366920938463463374607431768211456,"numerator":718362055583286874059},{"denominator":42535295865117307932921825928971026432,"numerator":130538276288488200893},{"denominator":170141183460469231731687303715884105728,"numerator":537161237701042436027},{"denominator":340282366920938463463374607431768211456,"numerator":790221160783123468269},{"denominator":340282366920938463463374607431768211456,"numerator":622240064937411103081},{"denominator":170141183460469231731687303715884105728,"numerator":278282735402616862673},{"denominator":340282366920938463463374607431768211456,"numerator":720394641940850030765},{"denominator":340282366920938463463374607431768211456,"numerator":488117225626829007907},{"denominator":340282366920938463463374607431768211456,"numerator":363479871108850476955},{"denominator":340282366920938463463374607431768211456,"numerator":394786653513363483877},{"denominator":85070591730234615865843651857942052864,"numerator":158959697110512184355},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":16,"numerator":117},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-5310870574484149080314688150353187971},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2990973864847952596725248808715316551}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1030165065432065073001815927016471962305},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1030552471861618590380035425068674980777}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-264961290760970482024435772219836086483},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-135377920642474780820543645255391943855}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":67096715134576508073023050743793078179},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":33442672247484316908160129408807508595}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":138435027994322608384431732657796430237},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":136389772724840806767813234211691341581}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":112964065631721861872920677612701758155},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":112202739330875990272802621910674886523}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-115382548614145414027320211733533459293},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-232306718451755643227814718589088252169}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-16534696635027208608774797300019311039},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-17722898346367944917516792203937884745}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":851871979206780901934642635271359167},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":805781556447048655023868109576483313}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":38400049350269876538654423702597950391},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":35988495895704259702713795463352716717}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":523604930328702997298704487596365814471},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":522467260978523427034326783156825285539}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-25837509357950017985703034354570738541},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-13456791037501166550110719997126585521}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1888450589003916248931086103394124162965},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-952277526395828757313129716690137088211}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":81071302986793366016620194636616110189},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":645149849330247789004355817708965803361}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":148845744541948603621373452668167490313},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":146968883087320437275774206206705118927}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":11594712593411102183632922297870507735},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":10205163208351238480927784039704338253}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-190434688587594136619331821548854319533},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-23945398019191902981245492241215891017}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":202466375933853094771482861802841979597},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":201538770888546721549650694076889706159}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":118694429319686358819213436235100735993},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":117923876356148182545285968325515177939}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-177532746586945425796417607477223181},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-199926947746214138732170071725277977}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-58040816490284440492471569386691913371},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-58401429645876149267318796302901288755}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1919651742378573660175188927118083126867},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":475539549234046141470161272856182914345}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-5001293749820552568956639341398145937},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2500646874910276806229511851594134431}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-128753018957545686922090220638944118223},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-515012075830182748556448799050608218057}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-274652008053964836107861844394074042883},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-68663002013491209463773109703898937841}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":33596964981299452524741367324169832985},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":134387859925197808838689234035752284531}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":69902944833476832261753010727484908359},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":139805889666953663210286850014074193577}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":28369343015387725470408176997706945159},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":226954744123101802848138916459010647111}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-233346999008330660362017776708454115907},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-58336749752082665389259925435794573965}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-37090116364302168697197866827379503599},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-9272529091075542434922273036747900823}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":431216071775102164253462190980419663},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":862432143550203687173073202380963011}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":5008343273978329033132696230784283525},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":40066746191826631426761442180961963019}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1048322196552453362847730051316835297297},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1048322196552453361751069042561330309247}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-13823541683405272762599111087914389079},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-6911770841702636749413882180518503577}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-478939354651068992264917568589031705925},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-478939354651068992798399443366488214181}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":325402179590203039653203366239201708051},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":81350544897550759638709148166360048885}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":37535347914961247345693152102384753951},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":300282783319689977143871792894340692689}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12548921755092892833562037719335709429},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":12548921755092891552785985174759477571}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-192294778284924200802183490929006626965},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-96147389142462100972081307116138043685}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":3172787905362351141434817863680537317},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":101529212971595235787639416116597781569}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":29800297395511789365472439218891163381},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":119201189582047156959346333792580313559}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-386895857827981160021028574116113607},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-386895857827981910248777234250705929}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-58637437999507750852751366155397527769},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-117274875999015502112183858952581386807}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":965929742952903045699157779567877801587},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":241482435738225761262006423750631162753}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":323032694565972231},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":350417908735044059}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-771914069828393},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-234483977350014617}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":7058858149927655},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-159833337696600859}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":12238660068863647},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":7071950394782053}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-5112430731120965},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-931744070065925}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":298391768225789715},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":28360726454463703}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":271636656588403607},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":38315023653057475}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-14871737990981},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3803768849497529}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1298416361675893},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":40253997964887}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-191968900618829},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1923557830630771}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-628444846551361895},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1207985458802628013}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":87708773163855355},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":30654766898426771}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-2613698521877065},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-88796058802670035}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":122404532084090163},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":30672648496956211}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-14039996958528951},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-49796662602970113}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":607869075746029},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-7041360216246957}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":113183195044757907},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":40097227403310917}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-4748211283275353},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-38871920795464629}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":11099543769845869},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":2706431649758843}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":20496834879685},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":81590956754905}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-6273582902254569},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-32378144413661903}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-53999490089842545},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-21920877641821337}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":85070591730234615865843651857942052864,"numerator":130400842110174152815},{"denominator":42535295865117307932921825928971026432,"numerator":108481727309314580593},{"denominator":85070591730234615865843651857942052864,"numerator":218349748251966208035},{"denominator":340282366920938463463374607431768211456,"numerator":630129414945592051083},{"denominator":85070591730234615865843651857942052864,"numerator":164151171995813211163},{"denominator":85070591730234615865843651857942052864,"numerator":114367693832529622407},{"denominator":170141183460469231731687303715884105728,"numerator":298725887118187001561},{"denominator":340282366920938463463374607431768211456,"numerator":521243948723189156777},{"denominator":10633823966279326983230456482242756608,"numerator":10020823652800157187},{"denominator":340282366920938463463374607431768211456,"numerator":419147752468199841679},{"denominator":340282366920938463463374607431768211456,"numerator":548040734071626860965},{"denominator":170141183460469231731687303715884105728,"numerator":368100063134994951891},{"denominator":170141183460469231731687303715884105728,"numerator":533464903159799594877},{"denominator":42535295865117307932921825928971026432,"numerator":137292030494527052955},{"denominator":340282366920938463463374607431768211456,"numerator":810825853628025713353},{"denominator":170141183460469231731687303715884105728,"numerator":320190188521498061471},{"denominator":340282366920938463463374607431768211456,"numerator":570973067281515662165},{"denominator":340282366920938463463374607431768211456,"numerator":738260067772064955613},{"denominator":340282366920938463463374607431768211456,"numerator":502540579742749175873},{"denominator":340282366920938463463374607431768211456,"numerator":375113627971665976105},{"denominator":340282366920938463463374607431768211456,"numerator":406677484735384009455},{"denominator":340282366920938463463374607431768211456,"numerator":651098400544875707771},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":471},"tube":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-2417937455208699669075600644695395321},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5543285329847534325342464054658353413}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1029835255402067238909755396102419440243},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1030393195003466256636464091710684186169}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-134746265968154779529282870530228119379},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-275335184619157643856389158770713870085}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":67237116993045852324302139796739325899},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":67032391221963976874460591924851167587}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":140038016594484109622021036197346071551},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":68999359243901917273681826765781712575}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":227173727252349974537803866615761565829},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":225556781455983762086520533910732824391}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-57984142240045640694109280855481463503},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-116781346212191694853842251768196205273}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-34954388666430655648855869520244437299},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-4667953550320675931358485600595339187}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":877992010584625614024433397387195483},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":103939822168756688232923199682026051}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":5040439364005834486215745895079822501},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":18950955925871470679525238909402004675}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":524331410869761896719998422522329360687},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":523320910676408395105496445550378005183}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-26682078916129220092158979433422901693},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-3471379750851841638328406451325954633}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-950658683954700718963873571486679077559},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-958693181915006729544235196779530140157}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":325591384793433140522491360452435244713},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":647850924880675101557972024386208406771}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":150346420731003182389696621707582513165},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":74226535255936913233580943663293536253}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12708663358863139854273028470953540167},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":11296055137468881150470863739337312911}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-191312342540991680802088303124357308631},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-192433086287711270796191677994579849443}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":101585695125623806417600685713689562885},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":50565494788644167628841988855521303699}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":238577485091431072364466607321884819903},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":237060059490041558759044089343985563675}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-364389392615369324061064830938178047},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-409410450664499259491778642273277459}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-233296514538038665040034359400486162273},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-117357570802968164362767925194341750049}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":483408291627874821135014426979841073183},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1916127318153102776039423219839676260237}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":-70320087616742109468265370738538939},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4500485607471496090339721481631742157}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1029576199934196265632778088908750545957},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-257394049983549066852130571535505346113}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-139630398588802348894568106631767886755},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-69815199294401174890541795577333863887}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":134658995394630181054021597120284110635},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":67329497697315089881946689508580941881}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":141403805350909924454158137350079194651},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":17675475668863740388188415888971209979}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":228266732667245794843438438473545585675},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":228266732667245793900753259006179492535}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-117331303909793709173158408810518116259},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-58665651954896854894338670533269121147}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-38997296230647078146983197757909089141},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-38997296230647079218369265095959308651}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":889185212930737936410683368318012499},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":889185212930737275745698587585561505}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":41997460914512209925082967063869111305},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":41997460914512209062887860808175275041}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":524796968597437555714768474431536012923},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1049593937194875110294920760642206842717}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-28512635159636965143962508555181880141},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-3564079394954620831655496422352997295}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-964279044605046257703028859264790395287},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-482139522302523129396580690177943212293}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":653351180978724788716625016623381058093},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":20417224405585149577217588867727684553}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":303307204123777577943031572224641179699},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":303307204123777576279253220539406840693}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":13678720049479372343009923777538470559},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":13678720049479371024913098172339057407}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-193156176515356293546397973214650876861},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-96578088257678147359036859304847025115}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":203746036162616530382384394997849285135},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":203746036162616528869101286935921635203}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":29946742665875955927626282119241939811},"lo":{"denominator":2658455991569831745807614120560689152,"numerator":1871671416617247237392526504429024329}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-198062394535736769772085347086928901},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-198062394535737156856235488424243493}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-117821040969750175205899191516846433285},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-235642081939500351249638036830018715559}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1945848457333286312483668189014392360533},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":486462114333321577787458750373449669763}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":617603688337262449},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":10327361930936421}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":12130987810643941},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-405332931544260185}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":8577044606772621},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-408874109442410353}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":24271124965174169},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":3656641556423555}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-4701130740602631},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-7173952373215641}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":25471580481994361},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":13256357281396727}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":280037493892792165},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":163463795239406801}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-472101761539803},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2114359024265025}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":576484891209643},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":6925566877829}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1764242000999735},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6142121010397039}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-469002468697763741},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1028950334856757593}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":12371690763189429},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":22100178725017369}},{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":-216990622584809},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-93697740241969399}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":120628136023549589},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":61558376755652855}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-27025679069795237},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-48001332247645397}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1446009595077527},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-8835042220842307}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":117663938789332383},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":86753924509971943}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-3190279297885557},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-34944382232484565}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":1175469235256853},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3746669606440667}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":44265417861529},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":236783697969775}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-3336847183076641},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-8345480587644159}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-127127079984093121},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-190680471043549787}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":542041804823908976541},{"denominator":42535295865117307932921825928971026432,"numerator":110955646271905250159},{"denominator":340282366920938463463374607431768211456,"numerator":886306758945875249531},{"denominator":170141183460469231731687303715884105728,"numerator":322527815065317474953},{"denominator":340282366920938463463374607431768211456,"numerator":674320581732151843083},{"denominator":85070591730234615865843651857942052864,"numerator":117813489942259116463},{"denominator":42535295865117307932921825928971026432,"numerator":76932580675836679169},{"denominator":85070591730234615865843651857942052864,"numerator":133922847852940596133},{"denominator":340282366920938463463374607431768211456,"numerator":330331943607742527169},{"denominator":340282366920938463463374607431768211456,"numerator":431095364188342219479},{"denominator":170141183460469231731687303715884105728,"numerator":283514060088676547319},{"denominator":170141183460469231731687303715884105728,"numerator":377306672413746654381},{"denominator":340282366920938463463374607431768211456,"numerator":1090099559620820472375},{"denominator":340282366920938463463374607431768211456,"numerator":1122801551548413627831},{"denominator":170141183460469231731687303715884105728,"numerator":415939344008014122211},{"denominator":340282366920938463463374607431768211456,"numerator":659041023769973941795},{"denominator":340282366920938463463374607431768211456,"numerator":585822417690381906463},{"denominator":21267647932558653966460912964485513216,"numerator":47289204507446591765},{"denominator":340282366920938463463374607431768211456,"numerator":517380603651372395109},{"denominator":340282366920938463463374607431768211456,"numerator":387083914409843407247},{"denominator":85070591730234615865843651857942052864,"numerator":104729120831429985685},{"denominator":340282366920938463463374607431768211456,"numerator":666884817064767112407},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":32,"numerator":237},"tube":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-1082819155298813055479487245820820311},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2537870048722793550148460569312370163}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-514685530909721610008585094848165358015},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-128762089649780718765441747132150790287}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-274063633463871335505685158153001815717},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-279947379364806341527452018364700831819}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":134743987841207522918979738916937214715},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":134348290156752285051990288804618041671}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":141635646896605122974998674644220055333},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":34900645827025875253551939536041628469}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":228495022464383774832499749021627694253},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":226783602085181583738765490374383946811}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-116587976825624784331166705155139190105},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-234886407222060485659177072093012481621}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-36849928113884956684839725628201650793},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-39251810618057076808421135420956923295}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":904602273902952785950459579105348087},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":428873286755504671432237235871168137}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":42254986326007229834275074650506001125},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":19911804199569949135185519164449465195}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":65619301395444718476824394902724354301},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":524072952399856562326750005831705009339}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-6884250288935795511447045549811672999},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-7159455816604204209972144941511074515}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-957077185103726830394064461865398889535},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-241273106771959592937942803473133121227}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":653721430987969981994241650174959583019},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":325240120045338377172360566718601170679}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":303720626824378718807420414511301336783},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":299900800708057894736810834692564703839}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":13840778675082295072464787397436777745},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":12405382097316291161710562461237193601}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-192183785938147881834695753608437758853},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-193293709405911071509573124615103184417}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":203858249481403166634737854677814815757},"lo":{"denominator":1329227995784915872903807060280344576,"numerator":792849830707682964026931625631561441}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":239747138352702582620022570590734005009},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":238252961476471172951878233673538778957}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-186752170875989996011348766760719831},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-52344187350464472556182071156822995}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-234410216102294591215405752918836757007},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-235805575059658713171402867747347042141}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":973810734346733335772354627068504597127},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":30157939913827420537180216395337605157}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-3969584234752888048598304481410616401},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3969584234752889175538963454215662471}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1028995952633458226396234207990285468701},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-514497976316729114105938654107234066889}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-283897596221635684592614202231472733357},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-141948798110817843195299221026521051237}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":134918760295648443844466096228417236871},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":134918760295648442523780650887940850155}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":142996187634906566974441192115404815767},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":142996187634906565589505423332331030041}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":114827216353285536047020893732987231805},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":229654432706571071123140380727789644597}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-118022877552292557875417877074506127693},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-236045755104585117018715840668017367293}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-40914723868970042724854178514087900327},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-40914723868970043825911692862022971393}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":916420279738148672371269293226973313},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":458210139869073995918683885148197039}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":5492003615082158584835644573406383047},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":43936028920657267791930263688504516617}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":131332082684698168645480948804715578363},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":525328330738792673994958499584845829383}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-29386788551509686488860414380937763031},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-29386788551509688036154965841964104695}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-970661972902638093027475252605021051265},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-970661972902638094141329587343195113071}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":163955800665652067875285236563003677723},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":655823202662608269205651524391352477899}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":306358176856001818141994466914184761583},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":76589544214000454108801098473642162557}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":7413245347416523807611188345504524299},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":14826490694833046258733716975149680681}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-194006150958040703811245482484348317929},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-194006150958040705013527364843998146417}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":12775859481391981537263265884222259627},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":204413751702271703045170287834613339175}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":240726835983790485052290016511289473933},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":240726835983790483986988195095042143483}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-202558811874119114997010743837778651},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-405117623748239028794481381418246403}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-236715817130602310879963873454501918303},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-236715817130602311742996619894519996527}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1959840928975949244060021358214697719481},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1959840928975949242693525049477073802979}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":576548425182000541},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":74320705389023869}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":97267165188963371},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-85933272493802809}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-2594283368797825},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-242499708205992013}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":11866591778067991},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":1813532901886889}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-4068972424703973},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13571024602423679}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":53930917613817899},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-34772747488963721}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":142005867499432813},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":83948394694122045}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-673658866112499},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4625957385871303}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":506692110102937},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-38619464875471}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-291700985106285},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4560545374950785}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-280043595229520687},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-831783142388821671}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":27226068402658069},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":27909755142938987}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-16573678186742927},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-24321531866453721}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":117107525843435747},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":29997481095031469}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-6329186056509377},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-22766174921700579}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-3380251613123079},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-10511487923653967}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":60332255335070339},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":22534337473818589}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-672547824948605},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-7754437236906729}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":481105300186687},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1979260201756901}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":379580790660257},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":73127189492331}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-27291647113195959},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-33950535610794591}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-8847717035880279},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-12716825343704341}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":563330696684589570501},{"denominator":170141183460469231731687303715884105728,"numerator":453800524992254622617},{"denominator":340282366920938463463374607431768211456,"numerator":898791128736479457745},{"denominator":42535295865117307932921825928971026432,"numerator":82541810393032987393},{"denominator":340282366920938463463374607431768211456,"numerator":692463133365448033009},{"denominator":170141183460469231731687303715884105728,"numerator":242680999851994813943},{"denominator":340282366920938463463374607431768211456,"numerator":633881985786697245185},{"denominator":85070591730234615865843651857942052864,"numerator":137631779463535178095},{"denominator":340282366920938463463374607431768211456,"numerator":340266405449890311209},{"denominator":340282366920938463463374607431768211456,"numerator":443375312027178351629},{"denominator":42535295865117307932921825928971026432,"numerator":73336178232554604197},{"denominator":21267647932558653966460912964485513216,"numerator":48351295834303174605},{"denominator":170141183460469231731687303715884105728,"numerator":556911132676313948645},{"denominator":340282366920938463463374607431768211456,"numerator":1147716154648504430091},{"denominator":85070591730234615865843651857942052864,"numerator":213346232176749843463},{"denominator":170141183460469231731687303715884105728,"numerator":339118599310809576535},{"denominator":170141183460469231731687303715884105728,"numerator":300562838799718740541},{"denominator":85070591730234615865843651857942052864,"numerator":193876704844411872795},{"denominator":340282366920938463463374607431768211456,"numerator":532648051495823050179},{"denominator":340282366920938463463374607431768211456,"numerator":399399996620459668955},{"denominator":340282366920938463463374607431768211456,"numerator":431513043775760239795},{"denominator":170141183460469231731687303715884105728,"numerator":341608600751174682877},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":477},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-3796548844908471952167977347036106863},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4578700803311832105692137740922730029}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1028774914266702411325250587741428034701},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-514832615837514459042220681993211614743}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-69667253104529457616433245159810719655},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-4446669687702914120308832885674196437}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":67501158516733758606007018816580939341},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":134620848545870475602991083371048189265}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":35806927968168188582784460750853650491},"lo":{"denominator":2658455991569831745807614120560689152,"numerator":1103133977114953538822860612773662275}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":229891983360525712194993260548840975985},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":114043074628440679267363295961885038545}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-58620791284924883280004844697357097237},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-118138795969289192691496882453241784547}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-19377930263027914622053944998481570243},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-41170217571968318272860965407399371479}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":931697847196841375038484926066791639},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":442230793450585076801027708375864881}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":44194279278888329665449076636669934549},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":20876684992568542275746084958114420017}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1050945437745624015170910058975077673593},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":524721885233507060432127641402664861001}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-28401473276103259856600137750439552255},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-29513092111440312730223843598839575559}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1926959188474849531742508041973704207099},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-971474097913639684189002402666723393147}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":656185047946964642730747950602510140403},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":653036306871142580219875609430147295667}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":153387471402338232524578076776458288803},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":151460949912949960985743113869007142987}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":14990837515096931665616944773048080227},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":13532929219966308731501559416813248699}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-193046575003533902906530829514393926131},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-12133911882609863081575141519871261117}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":51131238298896367771922888169997842799},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":203659489825619979733702368275577969475}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":60224541346153166060122981524362551841},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":119713402660303544423441222076259871011}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-382385210317426810322685134951013493},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-213929209111887839927827421064633659}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-235504816743611205515200363955013913895},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-118438734351251327240590276271390092545}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1961612758357076735498762981032951923217},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1944096868330642930666620781300667956861}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1704063295378194710365142430428275475},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1704063295378195295979484498677623855}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-514142996542832578959308529591938786111},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1028285993085665159774449279902021909445}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-288556866880240702570097486958309335791},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-288556866880240704392118339679726850721}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":135166772120017958278361969731252017731},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":8447923257501122307899641148126443725}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":144582838144278715717252071487459193401},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":72291419072139357147579480621968574901}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":57779410476253595023267235963677620235},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":28889705238126797386658514669152559033}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-237496043253656341375204856700523621303},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-237496043253656342680774344321441927171}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-42842290940608796270348877695657137141},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-21421145470304398700937848089621761467}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":944131688430554328139806666860678439},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":472065844215276813592358195194752037}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":45882287909970376468683056532228833217},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":45882287909970375556684331815371674679}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":525754179557169735031045030432221909545},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":525754179557169734423731972126442527775}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-7567167458534602231493118146520916553},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-30268669834138410512507072254654493863}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1954052723851982060630459097327808645431},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1954052723851982062906728546286253658611}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":82277394559081976146286361954184931073},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":329109578236327903412041684500344153829}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":77358939831242224058043592284361810881},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":77358939831242223620364029735037149887}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":1999001200759830473055449992690708359},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":15992009606078642388461171229030960551}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-194842232115480292770888164312490836679},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-194842232115480294004711189904223465609}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":205059590549136941566158903269202382483},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":102529795274568469988155889364619343957}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":60465352489153824699656571346133474519},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":241861409956615297701912558367739266125}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-413849142942650026560517455440326191},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-413849142942650850703791171243086191}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-237771409413991720074606768584183254937},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-59442852353497930240891961075293290431}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":493458244018827865780934698307510993351},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":493458244018827865430861387914253252157}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":522057133866576115},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":63207355927515537}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":65748913249642145},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-280325599057673469}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-82046782943982747},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-529676539054207961}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":22466665461281315},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":7120945230388869}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-205700865383859},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12487425086672673}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":7690199842692129},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-83811211594346829}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":282027121285592041},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":167393100199024953}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1677744033553009},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4941949710807379}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":437255135159069},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-227411325325233}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1295107632897035},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2982789257846669}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-36687718188131185},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-311929314257718921}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":116772390272933315},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":65549377124838755}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-37409565820254453},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-48869601995669987}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":110014961139617389},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":57340627032301159}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-23258641942094569},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-41764358713937731}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-10367782950427065},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-12006185839648863}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":30498778620051949},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":90635339541643711}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":767719247449521},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-1690656256747715}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":752932768652907},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":145586208719313}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":805142069260597},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":332200510765239}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-13480563906768909},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-17014218576407599}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-151432216518211255},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-26657954333694719}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":85070591730234615865843651857942052864,"numerator":146369932053292772849},{"denominator":340282366920938463463374607431768211456,"numerator":927710198646293689731},{"denominator":170141183460469231731687303715884105728,"numerator":455413817437062818115},{"denominator":170141183460469231731687303715884105728,"numerator":337988091410249506421},{"denominator":170141183460469231731687303715884105728,"numerator":355520978508070378167},{"denominator":340282366920938463463374607431768211456,"numerator":499808911839307965379},{"denominator":340282366920938463463374607431768211456,"numerator":652727426799915869389},{"denominator":340282366920938463463374607431768211456,"numerator":565761777138954565711},{"denominator":42535295865117307932921825928971026432,"numerator":43809624272179720687},{"denominator":42535295865117307932921825928971026432,"numerator":56999652926247900927},{"denominator":340282366920938463463374607431768211456,"numerator":607037816709709794033},{"denominator":340282366920938463463374607431768211456,"numerator":793241688327711366545},{"denominator":340282366920938463463374607431768211456,"numerator":1138104559660136963829},{"denominator":340282366920938463463374607431768211456,"numerator":1173077426149341912347},{"denominator":170141183460469231731687303715884105728,"numerator":437674936120131700203},{"denominator":340282366920938463463374607431768211456,"numerator":697984392061882917829},{"denominator":170141183460469231731687303715884105728,"numerator":308447916454198516211},{"denominator":340282366920938463463374607431768211456,"numerator":794909653160304140803},{"denominator":85070591730234615865843651857942052864,"numerator":137088499340882855915},{"denominator":10633823966279326983230456482242756608,"numerator":12877231262097566635},{"denominator":340282366920938463463374607431768211456,"numerator":444477004203825314703},{"denominator":340282366920938463463374607431768211456,"numerator":700115705077439809139},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":2,"numerator":15},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-3231237918286211386624179001643607655},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4051622714360297818751717526615141401}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-514032401914779064056018021290034929255},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1029099413611669350445193004640403859425}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-283305660994129343444708870265202967423},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-289225013269192754923762187728877371205}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":16906104749982533014851330889385842259},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":134882084995180462346555095507255389769}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":72407006930680134715668157631564568959},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":71397103471539188136873217547842105941}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":231364383138051077469106260160865261889},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":229464438214184403751366393879778658725}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-235857968877683974029107458516274379437},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-237735831146695391246390412644629883373}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-20336027509602859063772145079915273621},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-10774685879212241025160792875845205635}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":479636492067566262859234483953473227},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":455829434069241521814178140890763265}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":46141234585364509678518132844837877027},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":43691006069023129804531611315687114843}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":525885358090445004205907857085716547895},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1050532877621662607943039363925162248479}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-14637328801774987386377511321536797209},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-15197983541573545966904468911346012497}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1939729480858550822270037551598472329643},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1955674130325804460119167085515146802957}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":658572365029939379176883665113603607683},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":327758870088674628493312865366716550875}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":77463960389988757525634525373471366315},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":76492386861112864840264050979243827263}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":8079307489317326105362431887029649869},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":7339238442760878354256239098800791751}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-48474562571516899424776297479597781193},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-194977257005798658820508113378939800789}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":25646189846024796469733342331216559729},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":102164888791917703260768674305409869909}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":242030912364534027151306868536227201249},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":240581938608152312524286120023907886447}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-97751631256297741749277113947377673},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-218350121877375133759431881213468357}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-236580766384780094335102313075263834885},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-29741409230375282472964739333577676689}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":987801554837430580933831117721245162579},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1958089575564959029451954250792136049897}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1407863620330043450920672346598295349},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2815727240660088119094736299441239813}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-256862266910358262389263899076228668221},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1027449067641433051453347899851450124219}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-146616558625021488848084141812790530927},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-293233117250042979541266445272979513153}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":67701319878070632555029959060980518461},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":67701319878070631863031872467655430781}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":73081783934546967296917460041466112781},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":36540891967273483283423133318605643841}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":232655965605433227984489998574059160227},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":232655965605433226955082001765372943793}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-29876616656042012798186196642595483359},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-239012933248336103729619486998253450875}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-11194977234342544530494141898653722281},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-22389954468685089642396161719514762835}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":972312968321374016255302122881828759},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":972312968321373294311889324555944299}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":23918050349995569050470107998532718635},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":23918050349995568581496939154037229833}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1052147498299951773591482639186485813925},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1052147498299951772334759711706091934085}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-31157375929658637989558420076367105895},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-15578687964829319808299573592186542305}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1966742230469979214209401761773722960245},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-491685557617494804133840532381624250701}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":330268939866966866455748802792101023151},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":660537879733933730513686927445008094149}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":156269981928934965845577813968112541675},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":39067495482233741236947745959319585143}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":8587524762995541853038754498616316835},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":8587524762995541134733868955610420297}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-48915486930277748919251620475060831877},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-48915486930277749235832889598180816637}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":205681591937832011771663888881274815439},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":102840795968916005070971613625783839413}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":121489004042488118140997769924388104691},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":121489004042488117576485129933998029467}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-211146917609201331026485528794565561},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-105573458804600878067320777382858265}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-238809310593465207470323041598696280157},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-119404655296732604192983835607437637669}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":993910323250143944907480633353101940651},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":993910323250143944189848549545448485393}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":457555816742961643},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":196537624385231845}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":82501591629639787},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-111025368085249443}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-28794141408723993},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-281736522818046751}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":21037903905834259},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":6707119742901459}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2305722932496299},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11229574284271785}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-74536069207220489},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-66682649072398305}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":69134690266242763},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":2531844951587409}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-964661937671837},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-325954228097225}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":367761608003751},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-24740117777759}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1498335659031509},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1408668883905675}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":149733077673501657},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-406433810470493815}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":15387594155900527},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":73053080470828345}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-20052230930563757},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-97276390173536495}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":102090600996885449},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":53204691744151261}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-10351029181357113},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-37731087832331299}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-13560564082577051},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-26697025878781751}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":30376946376658365},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":88385188229940201}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4552892887265913},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-23170324368313655}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":552340792478543},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-690395718882995}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":422545995652937},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":355333899694649}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-25792505450738271},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-33554023523405565}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-78347541106281635},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-219874092099329859}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":170141183460469231731687303715884105728,"numerator":304248093353471729829},{"denominator":85070591730234615865843651857942052864,"numerator":236988156203388209109},{"denominator":170141183460469231731687303715884105728,"numerator":461191260433258037435},{"denominator":340282366920938463463374607431768211456,"numerator":691990921201243621279},{"denominator":340282366920938463463374607431768211456,"numerator":730066731478578937355},{"denominator":340282366920938463463374607431768211456,"numerator":514607901140801921851},{"denominator":340282366920938463463374607431768211456,"numerator":672007706586663103563},{"denominator":340282366920938463463374607431768211456,"numerator":581406234950320212309},{"denominator":170141183460469231731687303715884105728,"numerator":180485570358306358203},{"denominator":340282366920938463463374607431768211456,"numerator":468970966174394504455},{"denominator":340282366920938463463374607431768211456,"numerator":628083380296124942183},{"denominator":340282366920938463463374607431768211456,"numerator":813495339717614801421},{"denominator":85070591730234615865843651857942052864,"numerator":290737899478057704197},{"denominator":170141183460469231731687303715884105728,"numerator":599440448057485304491},{"denominator":170141183460469231731687303715884105728,"numerator":448889157808049696283},{"denominator":340282366920938463463374607431768211456,"numerator":718298317312107794187},{"denominator":170141183460469231731687303715884105728,"numerator":316572988473800811445},{"denominator":340282366920938463463374607431768211456,"numerator":814846469206225778521},{"denominator":42535295865117307932921825928971026432,"numerator":70563717528937659757},{"denominator":85070591730234615865843651857942052864,"numerator":106276977786731336339},{"denominator":170141183460469231731687303715884105728,"numerator":228909217024526581971},{"denominator":340282366920938463463374607431768211456,"numerator":717600494302710071963},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":483},"tube":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1317484172922153922667926887206400061},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-873508265603322168729273288837859237}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-513613590659884721618725264906333891051},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1028403638837431350500782474600730507545}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-287965315797238023584258729616506588011},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-293880826627264813442646300835510810259}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":135483158607286304582229568161426724179},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":67565809032938514704539611852210056459}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":36598591147711023199240276441986105763},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":144381557427993672239403167163600424379}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":29113975363555483920610603348284770685},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":230918290682411102174199593838544811289}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-59324996222436854937577140137420224157},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-239260568528836635999271519859084887819}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-42598400765375916271349689088201787069},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-11259325629426179065335393240933008059}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":123415138235419635871628032675888643},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":939332864269131020541570827051630671}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":48095718192563524045915092449041748941},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":45636351211904470168992024833961304699}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":526191592656007491230671749208525951985},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1051411156203486634001477326879197266219}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-15077842034911086325948186328585131327},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-3910692714123066924082171218410130335}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-976231487062323202753582146284643810887},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1968360471398002956740112337955474602791}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":330441116114050715258752664688055225769},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":328961629583247590984629353246208298305}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":312963329868287317032898293683432271451},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":77260951760594489660601747042195290791}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":8671941531770167931341420282209794301},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":3960450361034613556164690820190743371}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-194736342720426600074834199927015951413},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-195795236670963527035373841582741548517}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":205789985411972654462963755906513548247},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":51244608891094354036115389699634724315}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":15196607708230976682071000751896551699},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":60429677117623815280721932484667349403}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-49917815122389360670042785935210767},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-445253716861858622135171936589150091}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-59409629239299618693188885238274179431},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-59741860381282731947816953766234708575}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1989588570652313894041485832745811631947},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1972082354455644524799218853513921688753}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2192082923180786218147463536478091037},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-137005182698799217698556829997075809}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-513244036019144177225050246848123819877},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-128311009004786044548388438655381687271}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-37240114656319818484192102462416462705},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-74480229312639637435179060137577259419}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":67812981835208222686809984408166116731},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":67812981835208221978413627662188630379}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":147738197161126802190391641451775105997},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":147738197161126800691288194660501074899}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":117134409430356410349845356853669549819},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":234268818860712819639943867388106942327}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-240595748729636965029761229782445215261},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-240595748729636966413347058024880117843}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-46727508933853465129998183674354855685},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-23363754466926733162472391607049811177}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1000956828139599789049547416499174283},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":500478414069799522767720633380038273}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":49797355170812409839899096011725204341},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":24898677585406204437640581761031550409}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1052573030218098996840211627211595898283},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1052573030218098995539977392862579053131}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-16025988622447476333589064384173434051},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-32051977244894954336030297395456990323}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1979390346793741736312849291528454452091},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1979390346793741738689643658160964610319}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":662778315276258163177515644855487439407},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":82847289409532270090902850874283084437}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":315670757507910719823991445469333193029},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":315670757507910717982624063851505603355}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":18375380824744120871240684242495335523},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":18375380824744119392837833118147207585}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-98231414402569235835887382363219195553},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-196462828805138472971589005451205751935}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":206277820257628926545424584036228161509},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":103138910128814462437369723812787394487}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":61019242974401848821716519279596466301},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":61019242974401848531151571983249171773}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-53803243625373329838924295327905439},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-430425949002987515751076225737682459}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-59957492656397597221451364379113048377},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-119914985312795194914454676446324942113}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2001799969947292337898536634999268803863},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2001799969947292336427087473969174363161}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":384955736323782241},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":66091292306815805}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":49565842830805885},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-21361592927672519}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":-4384341742447361},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-294417551717437795}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":1223138037270877},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":6025207955079409}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-144216783830163},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-9831795076213115}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-160617890098753393},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-364177001977605449}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":133987324827487345},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":38067012910736539}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-65852262085283},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-170395857653295}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":598003026611889},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-573703643296135}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2364838471959235},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":120106148148455}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":11894254166359645},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-91521162655769007}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":31867142418156301},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":39077899793117577}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-20664123400265313},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-96230487651621133}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":93957371393152489},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":2989885084914491}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-17750121766789941},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-16839781140162127}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-16234444745309939},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-7228301238463915}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":59462464615421053},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":20873178156064539}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":4354780485625173},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-4828369535834137}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2879698397386901},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1514689269845579}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":876345521269743},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":360591003236353}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-23838331426284891},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-32482403096194757}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-78641800297056687},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-222520159505697355}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":632388336295882485637},{"denominator":10633823966279326983230456482242756608,"numerator":30259966553625957105},{"denominator":170141183460469231731687303715884105728,"numerator":466717795904764772887},{"denominator":10633823966279326983230456482242756608,"numerator":22137174507676776845},{"denominator":340282366920938463463374607431768211456,"numerator":749547384365234229643},{"denominator":340282366920938463463374607431768211456,"numerator":529771643603676652627},{"denominator":340282366920938463463374607431768211456,"numerator":691735060822211437023},{"denominator":170141183460469231731687303715884105728,"numerator":298735813536171647571},{"denominator":42535295865117307932921825928971026432,"numerator":46469558402691824357},{"denominator":340282366920938463463374607431768211456,"numerator":482306661459433166753},{"denominator":21267647932558653966460912964485513216,"numerator":40614705496574431203},{"denominator":85070591730234615865843651857942052864,"numerator":208600356982127966521},{"denominator":340282366920938463463374607431768211456,"numerator":1188369732195829533859},{"denominator":170141183460469231731687303715884105728,"numerator":612561679662797060819},{"denominator":10633823966279326983230456482242756608,"numerator":28771116440270532115},{"denominator":85070591730234615865843651857942052864,"numerator":184798771545517447777},{"denominator":340282366920938463463374607431768211456,"numerator":649889404254080388439},{"denominator":340282366920938463463374607431768211456,"numerator":835328556685769392819},{"denominator":170141183460469231731687303715884105728,"numerator":290563470027113025013},{"denominator":170141183460469231731687303715884105728,"numerator":219259791527149101389},{"denominator":340282366920938463463374607431768211456,"numerator":471547625652263890425},{"denominator":42535295865117307932921825928971026432,"numerator":91961495279448928545},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":32,"numerator":243},"tube":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-501861827230629701149281721870732645},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1452768060982131243686124350330706839}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-513131058008356602271055772936990534667},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1027580951155290812221263050537727047601}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-146321001522854454297434641070163509477},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-149276572544524799803929647396922096201}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":67852439165988889550547163194825250921},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":135369057692159428684393680084937206469}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":73984292587169243036528390398031605071},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":145963010390733427251540949972126587549}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":234533633851663019486484350415315177989},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":232447335800296583340481740559932333821}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-119404345637621080417647261824591783665},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-240851111006181576337245016365963307193}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-44534806797287894758620187847213923813},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-5873228524763841049022997890275040171}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":507917398143647971995469568480203769},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":967477209658492999903105767730642211}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":25028810558147542386543584919469802521},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":23794632549089793714269533946821207559}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1052781856517140157066648493504432397241},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1052077014053597507364549846817495965339}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-15521826438997484096101464140503782241},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-32180883394631666165757844035579723059}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1965157466380623425128540411839218920905},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-495251276818545328984288477246309014687}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":165778401331623212344653109416152412625},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":330125844000713580875458713032580446413}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":158048684673215505046220522910897799745},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":39018087072670392900880258732288166061}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":9273205735806547758328156858037027017},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":17022675976477525242002340355234566261}},{"hi":{"denominator":664613997892457936451903530140172288,"numerator":-381949960366946648908264621870620473},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-49148514960054949650195359805897719985}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":206384418077359755799409065678661313553},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":102801750072275574756667955813221789953}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":244242938865400968654235243484245879483},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":242837460220484598097274150332965717145}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-203683597348527753166974150294683991},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-453493337394456066124559118568907607}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-59669630144688454745900410723584398059},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-14999151295366731490675976733681325993}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1001782586162117755330952010733048490703},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":993035627371035742951948164846880526161}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1536976613941310849552436061089310429},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-192122076742664020515629562816696489}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-512703018875128636280248751821017749163},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1025406037750257274538456111615683711625}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-302614913052621087283557025759945821587},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-302614913052621089171785131590373818071}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":135836336078269622663840304548910866275},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":4244885502445925662920637022824118505}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":149306555702944806090514241151439294847},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":149306555702944804551517767611051646483}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":235955429426526912696161008922520199291},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":117977714713263455802658084917051125961}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-121121840265132020873451122910478838399},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-3785057508285375674544758482455063491}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-24342520647297957700273167312228302373},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-24342520647297958314244230467830500681}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1030055153914804188589592971377007351},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":257513788478700855726697871246513939}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":51765964141950048472758163906933908183},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":51765964141950047480723917373100247191}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1052784391090633603724251931992592820139},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":526392195545316801189535540744285522465}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-8237880168549531946107514140497272625},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-32951520674198129496438965150849051805}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1991995030008729452603561280040178357023},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-995997515004364727516172638747880970713}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":664939511528579319920459045622598365889},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":664939511528579317416811870276126058761}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":159414031187933949859002598770485061679},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":318828062375867897829894586058355360159}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":4898193082529576578245636390041869181},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":19592772330118304791587987314080816819}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-197242415717338409318251276747161140319},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-49310603929334602663142247089737427233}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":206846368813513989619859509092086996139},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":206846368813513987907095905856394387977}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":122579319160285305734924242469412934407},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":122579319160285305136703643160435814745}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-438219546380064863994336031328278603},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-219109773190032884314187893429512171}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-240833835831391430455261995449701956611},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-240833835831391431426622011969872919771}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1007883483601381684332840002309601351855},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1007883483601381683578395177548087817179}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":307987309595958603},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":15060249823476823}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":229831132084967481},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-126347207024736327}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-315807571800636413},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-604527705175767265}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":9046317116890273},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":313684077754679}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":34565599900433},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8359839461842497}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-236867889821462427},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-57085184651737587}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":256624583011944165},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":69211181973537461}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2206802994465087},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5647216636057213}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":234913974306377},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-755179924764545}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":6444757565722435},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1531227657425603}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":614143389993265085},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":31650550140420483}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":130093888368705613},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":20152327822679929}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-41247303978637813},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-94604553939376125}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":85681173198776201},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":41614358177735935}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-14543691170891475},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-29654257477144389}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-18249239407543439},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-30680550822056141}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":57389436606806747},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":76151657207449975}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":13110042285505483},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-15580148280013073}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":22369921380949},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4628253281698625}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":900464948860535},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":87701518196269}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-662892215202389},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-30981891707752537}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-153051912497175495},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-110971889683875419}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":657162427065571105085},{"denominator":340282366920938463463374607431768211456,"numerator":988801214817269254745},{"denominator":340282366920938463463374607431768211456,"numerator":943969692848526432815},{"denominator":42535295865117307932921825928971026432,"numerator":90647927883096835527},{"denominator":340282366920938463463374607431768211456,"numerator":769493987719263102067},{"denominator":340282366920938463463374607431768211456,"numerator":545312512750512754549},{"denominator":340282366920938463463374607431768211456,"numerator":711922047418550758691},{"denominator":85070591730234615865843651857942052864,"numerator":153492335737195350561},{"denominator":340282366920938463463374607431768211456,"numerator":382840788239258787147},{"denominator":340282366920938463463374607431768211456,"numerator":496014666501962682079},{"denominator":340282366920938463463374607431768211456,"numerator":672299178832084465303},{"denominator":340282366920938463463374607431768211456,"numerator":855979712005890987703},{"denominator":340282366920938463463374607431768211456,"numerator":1214365320102811423045},{"denominator":170141183460469231731687303715884105728,"numerator":625900777132862816715},{"denominator":170141183460469231731687303715884105728,"numerator":472023875229077127571},{"denominator":340282366920938463463374607431768211456,"numerator":760691063467336073601},{"denominator":170141183460469231731687303715884105728,"numerator":333569771098945601273},{"denominator":170141183460469231731687303715884105728,"numerator":428183728261281772401},{"denominator":340282366920938463463374607431768211456,"numerator":598217569344852079981},{"denominator":340282366920938463463374607431768211456,"numerator":452316745048327335139},{"denominator":340282366920938463463374607431768211456,"numerator":485675123589674843535},{"denominator":85070591730234615865843651857942052864,"numerator":188602594707019561751},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":489},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1348468664590621668520650092349928511},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2285817840801917018138716100689495165}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1025172719519588990790504307416276409147},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-513317111159071920726698377067404546005}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-297330293699073399299535730830935286227},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-303236529213924885039546617315876184803}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":135913588428872556558811220156297907981},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":67797002681960660167192296160469524669}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":149536506077454277867433177921199740987},"lo":{"denominator":664613997892457936451903530140172288,"numerator":288160908318969993282432458004511231}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":118114540164782676101651658499342063323},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":234051012030840316021792817187040226785}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-60095857054718012701059852248265644441},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-242506633326521193059457614687865697175}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-46481201766357588403632912379229127423},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-6118034180164544458410702891432894311}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1044805800456803213525264398369265109},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":996084720104354137981016230023138311}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":26013429654703005902189096553793106415},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":49549632488746452994270382212669059977}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1052966226614909463602954303877810379557},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":263132335432391124772133878404137691561}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-15968818669261024531196776290220391725},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-33081036402251085110239312260478374417}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1977810829472535552589391523897139382053},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1993606002684597389823969198011266826875}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":665265545947480148988362867217950517487},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":662501956312789050920429466725074775769}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":39907234597549020271300938705497720861},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":78818047174964306045995364629779194753}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":19765968444888670696549379724104348475},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":4555217772293125645328581923842901995}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-196361891187149525653693005847506740923},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-197371267367038985834510592437799987201}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":103475455601825964346176858314773840943},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":103101516187368740003057819857065386239}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":245322894799771533298126064940633910049},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":243938536019589156438659645798923300591}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-415054358531256771564152506143379603},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-230696708376772837933439493137632415}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-59925306935613594632030476068245245021},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-120494328286907241052478717254334929383}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2017528938007188912963014729282491841469},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":500013076707381512536329444672506348183}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-850281039684712628787599909752507939},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-106285129960589249335297565676355923}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1024206118404984507138612259123030027069},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-512103059202492254578871064042741883693}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-307309840468766580214652510879994275073},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-38413730058595822765357891793990323503}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":136033341107450492722873347446407894891},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":68016670553725245619046227553205942121}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":37717120612098787417841705087581847059},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":75434241224197574045762434873123622007}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":237714841690154059104533736786242990089},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":237714841690154057981835537439603109919}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-243955791628994049734084887792456334901},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-243955791628994051199369503689841871531}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-50652475337688351621256905143111803497},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-12663118834422088220770631983454466911}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1059599010245814468796284627532319081},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1059599010245813680330757037717472361}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":26870932591020901676364456700786654685},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":26870932591020901166256212093239728087}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":526390750876088900608850218046093158949},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1052781501752177799826169175368852497871}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-8463758182609551981768100141776636151},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-16927516365219104841811571346179481133}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1002277157536366228595251236928497463855},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-31321161173011444682381937191002443279}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":166755155575724181301043826621184971345},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":667020622302896722646308955047589087301}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":80502939009566845876846061308398010075},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":322011756038267381571569483117257441403}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":5206748046020411471890415976902614157},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":20826992184081644321943368601479719477}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-197998264077832742093063290045814907427},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-24749783009729092932865708358708818443}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":51846340857468932694648442481662219351},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":207385363429875729022614351059282932133}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":3847239662897756390267574499739338605},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":123111669212728203872765337444376429457}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":-6963258719793519970485258864035265},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-445648558066786211131658728155526433}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-15113834196013029045075781905954771399},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-241821347136208465721646950424730102265}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2029717659420264611980382042308103748277},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2029717659420264610432755918548272994369}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":226933713419720883},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-8717459896391953}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":260051620396553039},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-5499978272674221}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-337395360176045129},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-612295934998012817}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":8309056663635127},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3807781688248267}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":196241473817365},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6819198329031397}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-302405971257465077},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-540440315294667725}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":242672849936601357},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":60568208809180375}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2224668659496689},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5789355107612967}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":350268344800605},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-936083392712257}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":4041988183110721},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2822546532557489}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":210568803998813817},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":59040538155680333}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":65329362912459859},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":40253860365018521}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-39868763513095621},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-46168218507679371}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":38641884591011625},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":4322338930353245}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-11110244506512871},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-12833614986044087}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-19624922908426413},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-7987286155707779}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":54257959583104803},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":66534428445023345}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":17664171602912227},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11889573739550745}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":45324676889887},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6150925992187905}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":913574415781425},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":20438018554131}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-8981238975658957},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-14435992516326231}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-144253826166814807},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-27160280348761261}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":682825205991222917327},{"denominator":170141183460469231731687303715884105728,"numerator":504695454422423599935},{"denominator":340282366920938463463374607431768211456,"numerator":953967861448553172631},{"denominator":170141183460469231731687303715884105728,"numerator":371192020502089247165},{"denominator":42535295865117307932921825928971026432,"numerator":98739597592122535869},{"denominator":42535295865117307932921825928971026432,"numerator":70153760312662667345},{"denominator":340282366920938463463374607431768211456,"numerator":732581539732533648011},{"denominator":170141183460469231731687303715884105728,"numerator":315455514526064486967},{"denominator":21267647932558653966460912964485513216,"numerator":24639507538689916683},{"denominator":340282366920938463463374607431768211456,"numerator":510105613892630094621},{"denominator":85070591730234615865843651857942052864,"numerator":173865643457495160761},{"denominator":85070591730234615865843651857942052864,"numerator":219562573890019691873},{"denominator":340282366920938463463374607431768211456,"numerator":1240944519346829589511},{"denominator":170141183460469231731687303715884105728,"numerator":639455911594852900197},{"denominator":85070591730234615865843651857942052864,"numerator":241975025641358627949},{"denominator":340282366920938463463374607431768211456,"numerator":782802985542208166223},{"denominator":340282366920938463463374607431768211456,"numerator":684910197666567226927},{"denominator":340282366920938463463374607431768211456,"numerator":877974932561011741149},{"denominator":340282366920938463463374607431768211456,"numerator":615793925759609422063},{"denominator":340282366920938463463374607431768211456,"numerator":466510007797369177071},{"denominator":170141183460469231731687303715884105728,"numerator":250105882605593106333},{"denominator":340282366920938463463374607431768211456,"numerator":773776547671603739313},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":16,"numerator":123},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-657916390073552518501035653615419333},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1634649972148841013638814618971506149}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-255990558485637637305289110682443283369},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1025566460395558021795933852847343026481}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-151012417488844043946422369663544278217},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-307925615727018081799967601456637952407}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":17013609011694718277938729935693568899},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":135806054298793162879010445068794012761}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":75548983528340852058622210705054830839},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":149107509996974037933103694722375949733}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":237997163931669295646204774632424675313},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":235728570037066646711884102389952732039}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-242023402470425469719354094985691971307},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-122113091534405594997417800569662885331}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-24218766827663994519994345004380503933},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-50912610048007252645565133966693721111}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":268556256700782312970203344599448383},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1025147390260544997465233252493278719}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":54003373462982202459395306973870940775},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":25758681553139904019324659142117126421}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1052953892175297236971257347284864359865},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1052608979442120263561206960476667988887}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-32836686856396892550691802282372734679},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-33985025034409244888074342879513037333}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-124401313191296188256386413289306996029},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2006161200540643417115969284542552886497}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":667337221284770133802078545429002864115},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":664673099333447004485115572792581607549}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":322444724561404931144851274724405847129},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":159213105510959669286338587981118027717}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":21002321628006626982914658986427762073},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":4859038935366011692582366998759920849}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-197144415665964157512374663942963976731},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-198124416179706675571140789785912357059}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":207487592310501763487712407652977090911},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":103387560879146561976847036039552418517}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":246385920978904019555717461808564238187},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":245022273580755787019817266577903200129}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-422377696260200918133152016236885727},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-468928132257101419322865521892654311}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-120353542762055640854652548964219368939},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-241974588596912769168874070942047669651}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1015737946280152664815428448242963510955},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2014021531051925371326338516919645118457}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-131961604496736368095470970431079385},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-16495200562092223370304178920994653}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1022891576345124516513148947289514629845},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1022891576345124518574045573392476292991}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-312000537271436499056347895054044823025},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-39000067158929562623017200945760183535}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":136216554956335974586455981490686905561},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":136216554956335973066436677362777882381}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":152423825533985833664370450450859768807},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":76211912766992916021354984836618095811}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":14971620093777644772487261417445846795},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":239545921500442315204613395564003253651}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-245731022483448361239192924898071376779},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-245731022483448362746688387325962351827}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-26314899478311582723952332854893857759},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-52629798956623166744525485260941792749}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":544789322492815669911489911617405551},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":68098665311601907996519148808701905}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":27862510176180128126064632649901834613},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":55725020352360255202943067264072699555}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":526282382378962614773607536934938488945},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1052564764757925228108350298277093357061}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-1086297586959089710050217489597147615},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-34761522782690872524120610676987212625}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-504266579032489415976446717774819275581},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2017066316129957666442068995543728745005}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":334510453142151914014927672927826209771},"lo":{"denominator":2658455991569831745807614120560689152,"numerator":5226725830346123636069580580004120745}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":325221672074426476718272222206964796787},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":325221672074426474733778164860054176125}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":22077808721113927676756307100652942995},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":2759726090139240758206190439623241555}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-198727950627502380654927948532584466481},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-99363975313751191030699101357392526033}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":103946482943294151065274937448604502545},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":51973241471647075082548576180350066097}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":247271396221296531409453920089013261651},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":247271396221296530141710637982706643955}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-226343419672938803422672557328928487},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-452686839345878569066482477782049939}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-121396469172805142877002507456612837101},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-242792938345610286784352846398451039527}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2043648077364159330441662414564256204741},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1021824038682079664426986475705547918011}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":8860621013792641},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-47286872774197537}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":287060669651796173},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-13525607015509519}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-344828318421243743},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-76486933695017811}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":7584599832400137},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1237444520409883}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1496312424587545},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2583114025195051}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-44528618918452351},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-301026022905056491}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":112005900413957313},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":101346700098864439}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1088731203078357},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5815822444137091}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":222977653754927},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-270865037751789}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":9458331184991691},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":4020489787882455}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1037500902286549961},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":214139721259232149}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":1973973955689713},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":38977837487490819}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-37366570484708381},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-88680876482552167}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":68716522495902571},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":26871302700472795}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-3753066570637831},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-5436684069628307}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-20327532109574967},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-997873532538605}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":48850622620435775},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":55195654758588259}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":22009628227955739},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-3859890935926163}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1194519460103103},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-3753869050751565}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":112104580708537},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":296657750696183}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-14280724956695587},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-12775890079962483}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-16426869596312749},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-12716450429034423}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":709315309389583900253},{"denominator":340282366920938463463374607431768211456,"numerator":1030277731502623914447},{"denominator":170141183460469231731687303715884105728,"numerator":481880661340224436627},{"denominator":340282366920938463463374607431768211456,"numerator":760003304908642521335},{"denominator":85070591730234615865843651857942052864,"numerator":202706540240590501499},{"denominator":340282366920938463463374607431768211456,"numerator":577468482010333900447},{"denominator":170141183460469231731687303715884105728,"numerator":376843199331790481215},{"denominator":170141183460469231731687303715884105728,"numerator":324154295297779024213},{"denominator":340282366920938463463374607431768211456,"numerator":405938683502245409269},{"denominator":340282366920938463463374607431768211456,"numerator":524590380097166930217},{"denominator":170141183460469231731687303715884105728,"numerator":359563888533253883791},{"denominator":340282366920938463463374607431768211456,"numerator":901232636175844664475},{"denominator":340282366920938463463374607431768211456,"numerator":1268115405069226899447},{"denominator":170141183460469231731687303715884105728,"numerator":653226796598832383601},{"denominator":340282366920938463463374607431768211456,"numerator":992239908371886691547},{"denominator":42535295865117307932921825928971026432,"numerator":100693448697670959385},{"denominator":170141183460469231731687303715884105728,"numerator":351606937147929575573},{"denominator":340282366920938463463374607431768211456,"numerator":900162920382854466317},{"denominator":170141183460469231731687303715884105728,"numerator":316934242221916304417},{"denominator":340282366920938463463374607431768211456,"numerator":481110268592114610425},{"denominator":85070591730234615865843651857942052864,"numerator":128792070053752766993},{"denominator":340282366920938463463374607431768211456,"numerator":793808707451533159971},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":495},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":64232565345844185856285333697783899},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-951893662465887125853343642981057033}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1022634017692264227260248932003835083139},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1024380796261953429368574705672225094031}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-306720363753254748379379765067171636471},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-39076891363546633341513402624546845867}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":2129536009680451964043412162835599443},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":136004789606106220742460685604846358057}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":152652817068505115900310526862814504371},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":150670223046160707223882018711181631135}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":7494897763036948302332454611697739975},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":237479076498262026015968536069186684937}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-121863846126084411161050907774708895219},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-246008686020421096441932535780779979513}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-50403769447153259943805010694372582677},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-52890828352504176718323952982741535323}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":552041276278029603413474482507477091},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1054656394433564177386735468126279319}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":55987128741421360423649818884703506587},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":13373097863305462858374289466140772211}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":526412908819848285842544110932714554089},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1052382658764508867011210366332024460937}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-33739744627562540439930121487477514503},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-17446312828159607655676455042372279977}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2002986036379837693523039834763528001893},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2018668823308785330197666223499174004509}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":83665987943106041272073877892733187629},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":333382128860228827571472140285277895357}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":325657741219603431231979007481137966911},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":321606646573674487164857313499157021285}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":22255238951961505416334110285737127853},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":5167074524690414938974988153612133649}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-98951710381273359947215891285552046455},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-49712963478851735470186713779797245631}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":207992625419722101290281878014383947851},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":6478684058607761072693963994372993465}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":123716170027992581887878954197996493037},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":123044502455476606315530491016250685973}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-107327704904898881351290932518058793},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-476071582475218043529174361543299549}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-120848267908612349669227726833039026815},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-60736162251765588291506504939759421403}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":511351094497305997377386976624423168577},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":506993672672595058744944757688500389273}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":38620081501933369363558972344119871},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":617921304030932436319739042238042393}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1021465769405288276225812773802937676993},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1021465769405288278329564482458485137151}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-316681954416362243582681771719969912477},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-158340977208181122765280991968807529117}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":68192773025052528079025878930928513253},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":68192773025052527300966073211454223859}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":153972442160869689451198729866060591327},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":9623277635054355486670348432809528589}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":241447361855196778463710549235610331505},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":241447361855196777275423777435573312149}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-247568196696027178169528001842151815207},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-247568196696027179720011443533702386045}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-54617018202239195945542357598217452653},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-6827127275279899659736790336377519825}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1119983497348550761575912522971610853},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1119983497348549925636850586298927005}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":57715415885421441760252807778976812695},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":57715415885421440681287288632177896647}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1052135059056580628923248580459567391167},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1052135059056580627436115503145270903329}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-17834993189176909959011640285772967845},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-35669986378353821767960077435691275259}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2029529227627179518204119410071674112365},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1014764613813589760397975296011880277393}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":335469863122357551725479995804706225429},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":167734931561178775195512784121698541373}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":164228800342217232524026196634060643243},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":328457600684434463013883345333871477021}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":23344991363353995810584975880005564381},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":23344991363353994152691358407098214067}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-24928634868826355894224043631467467995},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-99714539475305424298977989996808303481}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":104183688589248826338422015477662541573},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":208367377178497650830927865551082525967}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":248303127493426925257322650526833380605},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":248303127493426923952409216643055689991}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-229654113358508367521831214310682523},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-459308226717017727301683776271869267}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-15234314654058081914149226119916508819},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-243749034464929311687509121527850180825}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2057554270572185648166221732855653302841},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1028777135286092823268554986801496477145}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":15247988306961609},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-170197704478730409}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":155201162472420907},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-23991805511964845}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-170266749261007399},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-603388641196064341}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":6913492811373731},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1030295109698537}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1120535785051675},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3560631914759885}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-396535107452554995},"lo":{"denominator":2658455991569831745807614120560689152,"numerator":-5065844195262323}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":201248252819480469},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":79727326228120711}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1035226859912809},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5730847207648597}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":100133880789469},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-605985434096837}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":2658442335246381},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":1261090896763291}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":150984499412673083},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":296838291635224317}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":29993041418593429},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":72701664685313553}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-8488873261099411},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-84278941032212341}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":60216683507926091},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":4739448624145869}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-3895620275291711},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-17980959806377471}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-20222817501750457},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-31360675404863583}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":42661746470628751},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":5279464265878935}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":26094880406361923},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3579923991957205}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2393244029087733},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8673456555165429}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":433790285177641},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":258338190647955}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-10237529991115751},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-10915371078969527}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-114306379244997075},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-186169311447581013}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":85070591730234615865843651857942052864,"numerator":184158251857195162337},{"denominator":340282366920938463463374607431768211456,"numerator":1051708657262545326749},{"denominator":170141183460469231731687303715884105728,"numerator":486904339268742774053},{"denominator":340282366920938463463374607431768211456,"numerator":778053407374217764931},{"denominator":170141183460469231731687303715884105728,"numerator":416116278041513291829},{"denominator":170141183460469231731687303715884105728,"numerator":297008719712623999251},{"denominator":340282366920938463463374607431768211456,"numerator":775180960382479605539},{"denominator":340282366920938463463374607431768211456,"numerator":666174152349657441483},{"denominator":21267647932558653966460912964485513216,"numerator":26123054682247615647},{"denominator":340282366920938463463374607431768211456,"numerator":539479964870522491843},{"denominator":340282366920938463463374607431768211456,"numerator":743259438951132775903},{"denominator":170141183460469231731687303715884105728,"numerator":462472381590789069851},{"denominator":340282366920938463463374607431768211456,"numerator":1295890429252049313861},{"denominator":340282366920938463463374607431768211456,"numerator":1334433798116803471375},{"denominator":85070591730234615865843651857942052864,"numerator":254269370324339840463},{"denominator":340282366920938463463374607431768211456,"numerator":828941239807502118593},{"denominator":340282366920938463463374607431768211456,"numerator":722060271581531318489},{"denominator":340282366920938463463374607431768211456,"numerator":922943245299922119025},{"denominator":170141183460469231731687303715884105728,"numerator":326226788417812903229},{"denominator":170141183460469231731687303715884105728,"numerator":248064353026317699223},{"denominator":21267647932558653966460912964485513216,"numerator":33159684699906850513},{"denominator":340282366920938463463374607431768211456,"numerator":814519948160228882305},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":32,"numerator":249},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":817906052151743715911834979123797807},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-237502455235457953948463499091847289}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-127648941431305615847524740008183760985},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1023080470222311139884473090673146233065}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-311411718866715694313013103452951084659},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-317299902913923741746361017264865212761}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":136457453553784614339342790782861671585},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":136189788445508346258335997849543766297}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":9637557134304770913079142880970818433},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":19028296405430305358581019561636188413}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":30218305688557907831797249598795034001},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":119650709416442216077319775369480500497}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-122747626275155506353604071578642268739},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-61963237970421124506763989591532418733}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-52379894751883689663169155447828298237},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-54878936799278447510524255868399215489}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1134367632760073922641646378809381959},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":542301045394235075377856401753314849}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":7247264306587120460419453881021712641},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":55474676563433954260675004377058893207}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1052635664944870962720291620105382707673},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1051926663075413630989526159949348665399}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-34645826646847416536634565771541069591},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-35802788005281958386358502528194354925}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1007752004845151202553025659413104875133},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2031127074086854993103406839357860015289}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":671236969113662922606408538259690752717},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":668774677081041703506961622438506727259}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":164448356023752150056918260068146521839},"lo":{"denominator":1329227995784915872903807060280344576,"numerator":1268802087107968944107615072163726329}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":11762244767124328659746963289740800337},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":10958533204271700185388961466186359343}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-49659121213085050788677113478012646707},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-99775571301980989078451698959183063903}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":104232107149249792599550440282797611775},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":207829493840820379789204684938820462753}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":248462466339549219179843338700633308533},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":247139055097046231359695893214156652829}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-217913662767448820072760158709560533},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-241398921650818705884107537605970049}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-121335006801498678376365796642285435971},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-243899261029126646765465807372095638987}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":64353447390853824358294847485608860095},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1020953914285237272726349688465136198979}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1399210653570081292473111626031145383},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1399210653570079762655503911946570713}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1019932137970011753179799269117080182007},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-509966068985005877663736230933357721625}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-321349166159498547946358446222144142811},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-321349166159498549914865369887280732631}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":136539875197728001179522237935859334321},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":34134968799431999896603805644931307439}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":155514198447364072767822928395835126715},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":155514198447364071059521617105929444167}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":243417689394075110515505352687545401791},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":243417689394075109293507745960221164681}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-249466026966835628632837081301511034683},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-249466026966835630227072924725219284735}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-56614156826717032354812025067893902497},"lo":{"denominator":2658455991569831745807614120560689152,"numerator":-442298100208726825967624273888043789}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1150802209418895195998633594019259221},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":575401104709447167667345416489480989}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":29856530900128885031596825878540994095},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":29856530900128884476808292630932783773}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":262873433070960610212403028121479578085},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1051493732283842439313290280227643017443}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-36579408626881089389027697760243927073},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-36579408626881091287888548235827973301}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2041941325142751851053960283286309760183},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-510485331285687963425645072368448015921}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":672776547998572257722996178803859494265},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":42048534249910765937326725597158462025}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":82929822347515916097980884455948763877},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":331719289390063662307059213530803331421}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":769634735231632995679201047430188615},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":12314155763706127077860690659367237545}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-100049642521689832019839002127817721057},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-200099285043379665522642307707672363629}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":104403420295294080914930081922057880065},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":52201710147647039984293562928442159371}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":249318838692170330908340923874847403915},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":31164854836521291195651446502430710299}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-58185824378554200357869899190415379},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-465486595028434626017197735758790349}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-244690050069609272101647915320600782985},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-244690050069609273194425057023668601065}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2071432316390055872564888491785539295617},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2071432316390055870892963859786621029625}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-14001147787650215},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-243096725973425075}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":82639728118030925},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-43605514531123}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-81432413112282829},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-293757172920947597}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":6293301532545093},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-228340088859847}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2983125312481023},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1017937275762569}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-105594972388349999},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-678933980311899205}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":88643598430767891},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":56643761199118611}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1895529063088671},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2788723166114317}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-2188133289831},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-82704922081663}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":11594393414897763},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":2935517758890771}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":675032233697905031},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":364736217933750473}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":112193441158649577},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":65274079059736467}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-14831106166413303},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-79520200889378047}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":52036583845655653},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":10957968777195289}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-355979491601931},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-7219375033577453}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-19455767853404383},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-30390168448684207}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":71900467184978393},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":28119618055680349}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":3748137458152661},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":138561597682185}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1711890167489951},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-1210321654451043}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":828752474368485},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":52611159336701}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-5945714676150927},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-17825803577256519}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-93978539317224825},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-166387795378638973}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":10633823966279326983230456482242756608,"numerator":23899820502123418747},{"denominator":21267647932558653966460912964485513216,"numerator":67104454582066689853},{"denominator":170141183460469231731687303715884105728,"numerator":492061284742935956485},{"denominator":170141183460469231731687303715884105728,"numerator":398273493018222823671},{"denominator":340282366920938463463374607431768211456,"numerator":854146654582364597681},{"denominator":170141183460469231731687303715884105728,"numerator":305435263159141434475},{"denominator":42535295865117307932921825928971026432,"numerator":99632199999252864555},{"denominator":340282366920938463463374607431768211456,"numerator":684520100036253281265},{"denominator":340282366920938463463374607431768211456,"numerator":430331314117410074979},{"denominator":340282366920938463463374607431768211456,"numerator":554785671568659652211},{"denominator":170141183460469231731687303715884105728,"numerator":383925310056686746445},{"denominator":170141183460469231731687303715884105728,"numerator":474703482778371283279},{"denominator":340282366920938463463374607431768211456,"numerator":1324285074099462876029},{"denominator":170141183460469231731687303715884105728,"numerator":681431872658563910375},{"denominator":340282366920938463463374607431768211456,"numerator":1042425120761208085555},{"denominator":170141183460469231731687303715884105728,"numerator":426500529449609070191},{"denominator":340282366920938463463374607431768211456,"numerator":741460261301453811735},{"denominator":340282366920938463463374607431768211456,"numerator":946328102076938632863},{"denominator":85070591730234615865843651857942052864,"numerator":167890386632812636635},{"denominator":340282366920938463463374607431768211456,"numerator":511576810117199222817},{"denominator":340282366920938463463374607431768211456,"numerator":546382630807083356243},{"denominator":340282366920938463463374607431768211456,"numerator":835926111371428425921},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":501},"tube":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":801467570054729492676416011592427827},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":508475322244429486427172911130256969}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-509819162217152851116067597225624954817},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-510834409423254282281306090685145817635}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-79023463087719979307328442718105249873},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-321974873005703180762993777148886873783}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":17076234856661360352028145179944334409},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":136360620183084407022566255621167394039}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":38935531315750222972854692286185350977},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":153775810705077331775092997545084434975}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":60931205370746210489729150878582414387},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":120597155392721273933073398257910011577}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-123662460372710292640598555387342568139},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-3902463753929476783820406550786385469}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-27182956696702245177339299204293498341},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-7109620185218943282914523513233537605}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1165068712721783147900698043399792863},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1114974028973746234274200624507357959}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":59976343655420328266799662710903509131},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":57464201688754897616230357934650244643}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":263058092107916180664239796923190211919},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":32851852333775743291245409923745298067}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-8888502769252367960152815871977559061},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-18356882045226476307365716062621987573}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2027973115430894123612816031608481889363},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-127720889837109254345365613377586303989}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":673063897467091171430600156721839708089},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":167675926805001662121941977942974408091}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":332161379805343827167023251358832090295},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":328046069671000089219090022197873269373}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":24809844590182895096049501611040128827},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":362222342089161538942472361564095063}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-99670644432056845386880748014603769263},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-200219189729085254574070024055506337309}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":26112575689554807130655307607837721269},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":26038516198174139600889391561793058805}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":249476604689694844298901335986237302429},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":248172741138286043913910092027255149103}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-441900853814402018928696837735012453},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-489081024524580430615141536221914107}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-60906986315774111313492050653566883151},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-244838837281425098978162353459210362045}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1036593798034782391621630815966595185089},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":128488577150363136681443320152067471647}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1105825884070294201268714312423542717},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1105825884070293407339124022753536567}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-254573548093033520336469672054708947275},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1018294192372134083538514906929060675225}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-20374836191641617983188599291892397175},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-162998689533132944860356553244254887137}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":17084886969094512913194372080801927709},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":136679095752756101674547337396548874531}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":157048969252168691709992948596974935787},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":157048969252168689956826367284725219597}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":245455271637642674869495224518751651835},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":122727635818821336806596660880545160971}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-62855780321752452498085926050192319621},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-251423121287009811631083205430218546371}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-58621255791654077942562879705552312143},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-58621255791654079349284803235177424375}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1182022641014604124216529762708326027},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1182022641014603238145538518978710407}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":61717991456198109395505001750681226635},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":7714748932024763531807632617331971775}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1050642590754415714246246906893486135835},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1050642590754415712659832310758070841739}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-37488767622029425461076050091428320707},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-37488767622029427410402838251197177649}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-128393810371286086586534149725996389389},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-513575241485144347022806528435302785781}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":337265469559682551044166515593742720523},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":337265469559682549652390890604786806973}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":335006443810599255531986463728939971345},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":335006443810599253395381267023384626159}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":6481885884377873500855257155722499273},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":25927543537511492247920953551668138201}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-100368121351829483910472741366396116023},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-25092030337957371167979912524015883903}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":209209644582397586977395682386286510183},"lo":{"denominator":1329227995784915872903807060280344576,"numerator":817225174149990566549634450878781719}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":62579706468457956571973176729936050483},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":250318825873831824905476450583103890833}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-471195914848126645887200687690145263},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-471195914848127700820592265149171705}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-61404096933278711946415353072252891293},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-15351024233319678056937388020870060197}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1042639164416228798060308594152595212555},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":521319582208114398601114415165989214161}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-20292956251462007},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-310422187011399681}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":86839122307499359},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":18129987337712987}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-75406650184129465},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-565081359702344009}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5738113248466457},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2034390370964765}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":7387510903581405},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-78066722092623}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-433362750379301177},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-693233175863647051}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":152373748134440417},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":32277456294187399}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-413444301834139},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2679847706816675}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-101135886961481},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1416451343489439}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":3080375364350615},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":809960633368511}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":730067587895884985},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":832176230617140153}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":51684182890562373},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":56131418879798397}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-24668817447328577},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-37251609805150381}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":22119089161507033},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1501931290383799}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3076294563709495},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11144030756254773}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-18132171180326909},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-29107943211124413}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":28929070343768555},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":6651899657789109}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":33623015392719215},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3801109636633617}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-535482056394153},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-10541879086782865}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":781976389209223},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":154595419128207}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-764537699096965},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13651298893710821}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-4457409563164071},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-18114602280162433}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":793814965108667230323},{"denominator":340282366920938463463374607431768211456,"numerator":1096153496104166300837},{"denominator":170141183460469231731687303715884105728,"numerator":497358015764816398331},{"denominator":170141183460469231731687303715884105728,"numerator":407748532158249662365},{"denominator":85070591730234615865843651857942052864,"numerator":219144821158446174225},{"denominator":340282366920938463463374607431768211456,"numerator":628021016166088492009},{"denominator":170141183460469231731687303715884105728,"numerator":409654851234402253717},{"denominator":170141183460469231731687303715884105728,"numerator":351679554402854703859},{"denominator":170141183460469231731687303715884105728,"numerator":221517418982068271915},{"denominator":340282366920938463463374607431768211456,"numerator":570519049497817499031},{"denominator":170141183460469231731687303715884105728,"numerator":396446659297560166069},{"denominator":21267647932558653966460912964485513216,"numerator":60914985975402110331},{"denominator":85070591730234615865843651857942052864,"numerator":338328735465388242589},{"denominator":340282366920938463463374607431768211456,"numerator":1391755007831084790315},{"denominator":170141183460469231731687303715884105728,"numerator":534147744095058845229},{"denominator":340282366920938463463374607431768211456,"numerator":877744549649595530693},{"denominator":170141183460469231731687303715884105728,"numerator":380712315779490720071},{"denominator":85070591730234615865843651857942052864,"numerator":242582430131945288065},{"denominator":42535295865117307932921825928971026432,"numerator":86400624894625292591},{"denominator":42535295865117307932921825928971026432,"numerator":65933297762280559089},{"denominator":2658455991569831745807614120560689152,"numerator":4395799507114897973},{"denominator":85070591730234615865843651857942052864,"numerator":214510741172000361767},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":8,"numerator":63},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2419053201905723424372154489673180937},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1285894814866119355798098047863252293}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-254494505250328539769663325125830070093},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-15939832219963200337145957153407738555}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-80190459886536278210095904582987421379},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-10207347052489983246879121719839718841}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":68373566523004690989834601065284685749},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":68258423273959478549137945637092203917}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":157276326125624243705476054447995289697},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":155318406483112940765526679379141766269}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":122885102251764758260512854073338257125},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":243156298826357952934894638806279097445}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-15575963908479785185136099255140264631},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-251721466847267219668772518075888984411}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-56361846957972203059934626728208986073},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-29442472822710248004354303963017447379}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1196173443854409087971305274905114855},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":286440240287070396260433357107256927}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":30990926352290418157837256372797423247},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":29730486960999825178916185426335420745}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":525808609216608746011211388323792406597},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1050382356939466980294316137229943060209}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-18231642112380717366957223889724429223},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-9406132061489495321261736347094072291}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1020195809541258851703527701582501084359},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1027944339842429589938052101089527413907}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":674808269844233758836000622384709892809},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":336275400563416043952015303942312265313}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":20965715343769784833227606689947300599},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":331304605377813340637661158452205916563}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":13055539174997142406530280754432762337},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":6115889914559118242893145818873776963}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-100007732233843753402173296080244656385},"lo":{"denominator":2658455991569831745807614120560689152,"numerator":-1569169298629758430919224304007244927}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":209300091310152775059130441563769387129},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":208752034955080980479179119263877081351}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":125237524733352098222842028086696337271},"lo":{"denominator":2658455991569831745807614120560689152,"numerator":1946799772096353384727805261998299387}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-447505145060436548486145832572845977},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-123723831664512548649927293566321863}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-122285373471206966871535443043125891717},"lo":{"denominator":166153499473114484112975882535043072,"numerator":-120001844831234041664473230581405529}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1043516164540046700161926347656726825919},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2069698981646718367622865100039303709873}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1527446000617656684373143733236624333},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3054892001235311721094420187240641719}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-508277750342362714751028654116667276075},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-508277750342362715870335228039971166915}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-41327742490193423636795278099770865453},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-330621939921547391105834846627164651577}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":8550172111306583533986528949043411217},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":136802753780905334873936119072342142843}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":158576637968676459927730897963279614023},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":79288318984338229064319991096496397263}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":30944790613333858301477946477845928527},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":123779162453335432560318969086514649753}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-126718994662960781245436328859360543149},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-253437989325921564174852985066183454461}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-60638372742311008313435122456478076715},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-30319186371155504879423549261763147203}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":303407971958372405920719473581145003},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":303407971958372177876141217789241987}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":63730261047256564522923755884096223119},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":63730261047256563349534023569299310717}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":262395971812972520095904741952552980527},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":524791943625945039373113300920319695045}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-9599259469867899779630290740309282863},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-38397037879471601119896915423940600685}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2066606589262252041371442963861418852967},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2066606589262252044137484158064541491295}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":676202567436145474390977026567436978217},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":338101283718072735774348327663331079565}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":84579682126411535700370844881135940303},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":338318728505646140612065649567779098091}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":3405308192437467858909435756833901545},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":27242465539499741064885123349168883229}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-100668834359227796012389919921777661249},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-50334417179613898397188308529963962813}},{"hi":{"denominator":332306998946228968225951765070086144,"numerator":204662231910688931856061277346528267},"lo":{"denominator":2658455991569831745807614120560689152,"numerator":1637297855285511439302003171442026449}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":251303373696122721988466036316031874887},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":251303373696122720565666276645280031947}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-238205154917129333184917913833391033},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-238205154917129876994775623113572787}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-246528436518654708360740156780748515287},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-61632109129663677379890762650181576183}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2099088467226525546791708578569301539631},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":262386058403315693128732632878147573473}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-140172967361852417},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-371077580568607405}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":22512310788485153},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":15302691910720997}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-269349591617955279},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-536895271821660821}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10482681386324311},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-450527429814711}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":4361126354463111},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":161503378031417}},{"hi":{"denominator":1329227995784915872903807060280344576,"numerator":-1678009159102355},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-691629240184298951}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":127166859213523245},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":3876121180507999}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-675371002788035},"lo":{"denominator":166153499473114484112975882535043072,"numerator":-2484018515713}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-22093114967789},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1488811591739383}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":3201876152129693},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":3429470698677153}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1536947733789613561},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":450790268081167945}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":5845204923065551},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":22743775413778279}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-4739520673765393},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-34568033220950147}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":36784580816884735},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4942545786875449}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1601905191698073},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2022492639200357}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-16292524749203175},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-6872616186713861}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":5438875623481553},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1815218018849795}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":18426861332345521},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":3447645185779869}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-4966419755038559},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11220557395132949}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":728827292420381},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":23060723845337}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":723742264000501},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-4711414294161057}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-46920905707489609},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-7631515264944213}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":823710481333012925979},{"denominator":85070591730234615865843651857942052864,"numerator":279785444532226682653},{"denominator":340282366920938463463374607431768211456,"numerator":1005602538074397011205},{"denominator":170141183460469231731687303715884105728,"numerator":417458564302881898657},{"denominator":340282366920938463463374607431768211456,"numerator":899541419765545009471},{"denominator":170141183460469231731687303715884105728,"numerator":322730893688571008159},{"denominator":340282366920938463463374607431768211456,"numerator":841930456365304930457},{"denominator":21267647932558653966460912964485513216,"numerator":45169007485597925423},{"denominator":42535295865117307932921825928971026432,"numerator":57011062559780975937},{"denominator":340282366920938463463374607431768211456,"numerator":586691891875792873967},{"denominator":340282366920938463463374607431768211456,"numerator":818378499385972627173},{"denominator":340282366920938463463374607431768211456,"numerator":1000663858367380988487},{"denominator":170141183460469231731687303715884105728,"numerator":691497754054843949901},{"denominator":340282366920938463463374607431768211456,"numerator":1421119322057085529451},{"denominator":85070591730234615865843651857942052864,"numerator":273675404045680133675},{"denominator":170141183460469231731687303715884105728,"numerator":451594791191376169215},{"denominator":340282366920938463463374607431768211456,"numerator":781964034026646913267},{"denominator":340282366920938463463374607431768211456,"numerator":994960191812986214315},{"denominator":170141183460469231731687303715884105728,"numerator":355698376383277937137},{"denominator":340282366920938463463374607431768211456,"numerator":543809539417081662237},{"denominator":340282366920938463463374607431768211456,"numerator":579405288011166732663},{"denominator":340282366920938463463374607431768211456,"numerator":880886166102794667023},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":507},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3265895669677399022274888384819191081},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1047256778429359395805977215068238039}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1016214307657876125255640620806658987707},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1018525290673718301125500938964774557789}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-162705444054038810558428784901458662377},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-165637898844980143629228878138752184831}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":136868761398784768838824396660760949105},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":34164505448021562441851360419602903907}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":4962606281007505106021678889906748827},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":156854032392160748463952216241245886439}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":123940396309947861409948558988404409557},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":245185769306281223701337344159452349417}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-125582689053174725623649308434536840051},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-126871404956476519348874743993503204185}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-58367734306569944005405948194889156461},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-15225737289352820844243815275624364431}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1227668702839431426725951308709954209},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1176950856367400106081047964672654923}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":15998675184525414666428450137446127615},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":61465023758208824875432978515305552887}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":525395982752177964717423286533592559843},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1049298218004953777548849913529218536731}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-37372624942638427722100163602361431553},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-19267025868274202555929513147003533767}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2052757867755454351538608962302074901713},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2068188849606684689997983293241724931271}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":338234883851447208744488767766218805971},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":168578878430298793765523340954563201999}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":169383284615918840193705136414263703593},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":167294326048564158531466799733683088825}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":27427968976192366968115691918522142513},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":25760829599880283945677093488792887105}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-6270521264693092631958108242561909819},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-100726151402489500102759825635534518515}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":209661012250432200273677513224542914333},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":104579746309641313894077037712561946153}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":125729041767065676333463339594536610833},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":125096120844677049799324323580163468395}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-452614098556598293607446017311578711},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-62526887224356669775431011404735033}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-7671838217770019967575963384183515241},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-30834308826672840899342083255780000845}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":65651271078030042128735256292236686447},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2083549179314179399547227600343219038287}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1964240541508545637378937707168732923},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3928481083017089565531085245210291897}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-507359838476686684132878840515013325663},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1014719676953373370551330557420393838283}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-335218342557789453482687868847350466553},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-167609171278894727758276255899202697597}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":136910388237400136740873640459180950249},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":136910388237400135031216660030562436977}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":160097096291004213798917525766444258195},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":40024274072751052988205219765511258491}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":124862461425075596519966371001731590075},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":124862461425075595856648875218437688227}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-15969315560392417317028751666728617965},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-255509048966278678802403838372940942403}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-62665581450170041660265953111717603931},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-62665581450170043145406407582479396499}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":622808151392765848802263147045416649},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1245616302785530758600068898726557789}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":65749949039472070512995078715377526083},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":32874974519736034653178279580963391231}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1048320306735615499476145705961981736797},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1048320306735615497786907250281011619607}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-9825798441710446131149222355507951101},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-4912899220855223322455775887345051211}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-259857089546442733035934243842568651371},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2078856716371541867114208945726772959955}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":677791199329369741237310673588317766541},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":169447799832342434583832754539720542337}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":341655767877108490673979369010053722001},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":341655767877108488430650647959004663449}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":28572860410220463814883927332726634695},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":14286430205110230978081766381411235887}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-50475331956973189865847143037080713377},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-201901327827892761069612660732237229849}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":209898669947532106274421307579696224683},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":104949334973766052116964176539439931389}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":252272754469751906813911288781301391939},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":252272754469751905349605395643901034745}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-120276028466594462783402360633094081},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-30069007116648685773231302960334471}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-247426570540422350146786041608118045821},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-247426570540422351340044306329170196037}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1056429472297977295575846472918717696163},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1056429472297977294671336603483944147097}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-189517676793152653},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-212553641353533517}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":11527497878467391},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":38378120612472211}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-231442823431741731},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-504003705123693879}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":4859828457300023},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5189717288884339}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":2494042224442631},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1711796031600551}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-410932237557488727},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-337532906480911563}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":6387416800152387},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-16369169896161581}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-997193464615713},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4770412296195589}},{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":-1821622357381},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-770024620622689}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":6528608508733953},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":3505745369910381}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1582356197072497559},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":935647729419103357}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":41433283586484023},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":33431891560187411}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-12700258596473355},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-31744697606745393}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":1860569164446047},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12640493665078293}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":4774650225015347},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-332627550251255}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-6960406573420781},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-25569063227356523}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":29214252994500809},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-4245418044118079}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":39623055704038425},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":9526857593382821}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-683810278013929},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11716200047424183}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":167648017880591},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":24629361501917}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1808704738978749},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2624880456675725}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-21088792711890815},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-49253874643996983}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":854495600281606629783},{"denominator":340282366920938463463374607431768211456,"numerator":1142621187289434351327},{"denominator":340282366920938463463374607431768211456,"numerator":1016796041034681488245},{"denominator":170141183460469231731687303715884105728,"numerator":427410517763603757221},{"denominator":42535295865117307932921825928971026432,"numerator":115380523895720815891},{"denominator":42535295865117307932921825928971026432,"numerator":82898178624448966831},{"denominator":170141183460469231731687303715884105728,"numerator":432456310966646113797},{"denominator":340282366920938463463374607431768211456,"numerator":742568340625965106345},{"denominator":340282366920938463463374607431768211456,"numerator":469501575256892387449},{"denominator":170141183460469231731687303715884105728,"numerator":301658118456793274119},{"denominator":340282366920938463463374607431768211456,"numerator":844295873606658361493},{"denominator":340282366920938463463374607431768211456,"numerator":1027499941500557912323},{"denominator":340282366920938463463374607431768211456,"numerator":1413342102924803365777},{"denominator":340282366920938463463374607431768211456,"numerator":1450968622914569691073},{"denominator":21267647932558653966460912964485513216,"numerator":70103557803431093993},{"denominator":340282366920938463463374607431768211456,"numerator":929354373159911823979},{"denominator":340282366920938463463374607431768211456,"numerator":803088946329371701607},{"denominator":170141183460469231731687303715884105728,"numerator":510115714575676426575},{"denominator":340282366920938463463374607431768211456,"numerator":732149823709788522221},{"denominator":170141183460469231731687303715884105728,"numerator":280309361360530738691},{"denominator":85070591730234615865843651857942052864,"numerator":149155722517647860471},{"denominator":340282366920938463463374607431768211456,"numerator":904471159956485497489},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":32,"numerator":255},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4143000465497151618874725659035185089},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":91687220648805436083574562549819363}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-507175530740756236702094598909610434705},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1016800438373971316000279485019913969383}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-165018184704055052698464562038714038309},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-335892074542482942371260129085793291119}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":34243575523869031221411287051080277137},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":136783692857064135983746226702230784925}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":80161621210938868101553852020374526101},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":158382570807209649453699123965572848611}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":125027321184953394741606795981867209013},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":123640478149822325651286988198196406749}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-63293327124730293805932437475288082005},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-15988757298057815493447426617363540953}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-30191815526583356680403426352102084843},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-62931047944609662887089548027919984419}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1259540614000944633066388778391205459},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":604265459129663471221069874119734359}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":66014969106587099773085585251116567369},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":31738202298109918540125258235714071347}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":524879404235814349794487480315888669175},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1048009596274242507535415034615146431483}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-38281008066119203119573109791482991567},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-39441306199643163109053639290001134863}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1032535145256532176440403071599884721999},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1040216639002470618893587173808620139067}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":339024085488364230449822381255454466693},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":675997500376080694954146865395187711373}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":85526592773773293065631915927074515043},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":84474469832260228718281356382513046255}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":1797518717227420684789571271283854175},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":27073817324373186632468676772458212215}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-201262648029887261447877324300359041075},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-50503213728892641804225619383324649937}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":52495439927076597233240069370036171457},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":26191104098015947963522274718980915463}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":252425977318053513434230337810281484611},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":125589319980176316234579579246860865517}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-457201829891188372265891864893483509},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-505014890244477303660301467824377923}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-246412564334977364868440598280207215501},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-61892821542937699947859045271649239451}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":528652211553202736670237207888273592277},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2097363980672493833735295755166632028131}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":150996004250627152090380593359024139},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":4831872136020067094280006186930431475}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-506395184954651387346751856648201911497},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-253197592477325694256742943449991929389}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-339782233626621340234789665595583753863},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-339782233626621342291671558094634857803}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":34250382789246008657531235794256180517},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":68500765578492016439831834989660398581}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":80805121976299255267774586889210695501},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":80805121976299254320671474978240115827}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":251953005505914373521470570057506233269},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":251953005505914372158835477242001821927}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-257634632942110481810626378569310397227},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-8051082279440952612101229024933184829}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-64702971225980839954097499570744472119},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-32351485612990420740015862100092302257}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1277961520391448367233074137745040659},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":638980760195723700332328228217517389}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":67777155553761174744546643826790334465},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":67777155553761173503731784904031961755}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":65428434381354846807026137814355035851},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":261713737525419386792621491726084464127}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-40206212903729373306056301979134903817},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-1256444153241542981763901517416326925}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2091049950366112419954445551674038133879},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-261381243795764052855404368948382670203}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":21228021807668404427878163893346144731},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":679296697845388938729430323743277042473}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":345017147122735968481680707271775309145},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":345017147122735966183315839769985703565}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":29918516656727738531530980281353675107},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":14959258328363868309501881143907612757}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-25303129680769368726263322497375723441},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-101212518723077475729886529325919441865}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":105090858654120008110094947844801008775},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":105090858654120007063925000443758280171}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":31653403408444081347492521648190828643},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":126613613633776324636489592349064814701}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-60656490962864637625996554383353627},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-60656490962864782102753486692429875}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-15519446724966892330798575379214043689},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-248311147599470278521443319250109885045}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2126586035746402998201403564423780147097},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2126586035746402996343696839174345290599}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-228756468166041159},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-234774078542165655}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":362626272995915435},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":44697229343726621}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-193517954669993709},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-454649848174243267}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":541930108149671},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6328077166078961}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5522177036934073},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":166341629142077}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-378981417784524269},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-644725258411649007}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":77737932249695743},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-18824109265064997}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-325229897623105},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1097014131192023}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-136228611036153},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1565283350916233}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":6534725306748777},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":434157931109331}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1595210496303439907},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":467833044649551409}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":71414646973859787},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":20818885465004633}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-7083318637288757},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-56735186586956367}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":22394871327344575},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-2326073922269467}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":11891987116433883},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1279344014220025}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-11213324213258865},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-5832659343586267}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":3839956194888225},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-7894328955865463}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":20708018957469067},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":742160396235563}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-2902272542502695},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11909089385032719}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":302429985185495},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-44624883698273}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":2839262249698557},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-621494270945513}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5028061194631161},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-74796550355873939}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":170141183460469231731687303715884105728,"numerator":443092845277910012705},{"denominator":340282366920938463463374607431768211456,"numerator":1166575065729955852873},{"denominator":170141183460469231731687303715884105728,"numerator":514155190151386713595},{"denominator":85070591730234615865843651857942052864,"numerator":218805784279850931401},{"denominator":42535295865117307932921825928971026432,"numerator":118387365058370847777},{"denominator":340282366920938463463374607431768211456,"numerator":681184674487438643301},{"denominator":340282366920938463463374607431768211456,"numerator":888248782038885845781},{"denominator":42535295865117307932921825928971026432,"numerator":95370655439544413157},{"denominator":21267647932558653966460912964485513216,"numerator":30205222651724411311},{"denominator":340282366920938463463374607431768211456,"numerator":620404367999521312225},{"denominator":340282366920938463463374607431768211456,"numerator":870636346859169190009},{"denominator":170141183460469231731687303715884105728,"numerator":527584487704169675657},{"denominator":170141183460469231731687303715884105728,"numerator":722184937011268390033},{"denominator":340282366920938463463374607431768211456,"numerator":1481314958690547044303},{"denominator":340282366920938463463374607431768211456,"numerator":1149175208413322365823},{"denominator":170141183460469231731687303715884105728,"numerator":478128775170094340847},{"denominator":85070591730234615865843651857942052864,"numerator":206202442691528760181},{"denominator":42535295865117307932921825928971026432,"numerator":130769397083156893005},{"denominator":170141183460469231731687303715884105728,"numerator":376738720985774243103},{"denominator":42535295865117307932921825928971026432,"numerator":72238337873351158795},{"denominator":340282366920938463463374607431768211456,"numerator":614326756572572250383},{"denominator":170141183460469231731687303715884105728,"numerator":464406725159471087849},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":513},"tube":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1262452274825156131569125450186342569},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3803889081207807903226038716926032571}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-253102775611630345332106557607840237831},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1014976185231912480464986593996844520785}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-334636952752085377876084372321922248725},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-340450850809126133942119335377181171451}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":137063286428093416853931333361287707191},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":136893399549545325939803918305034823003}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":161835751012353565008065480946405548337},"lo":{"denominator":664613997892457936451903530140172288,"numerator":312312328970852550894128321934683493}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":252289677903064354839796935334915521395},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":249439950066494173588131174092757220843}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-255237642133736187032955674980163803165},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-32243963807395135928499898707010173795}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-31204804505508224605250143462958225445},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-64969333402552373708156946584904725741}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1291774574765102833133460113503263413},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":620243802949455819603734815263281051}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":68042760748855825756764005523200480191},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":65495192182873874145200175988560454319}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":524260190191554307203876181807645936869},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":130814955488522183136460723660151719985}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-39187407846063408027705173620079105177},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-20172633526923586498311164720291420947}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2077327398446014665396145526032127078819},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1046310288850643327154714885458662572377}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":10617864939898389457095872374420882515},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":677596515237800050899908260825206884107}},{"hi":{"denominator":332306998946228968225951765070086144,"numerator":337373468882170985035456625982066577},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":170615958146430099757233271799188178005}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":30107858600778052188760007014851719601},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":3550288131964257880178823866865968647}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-201831125649196772459610147125469734857},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-202533147436156642497394395154977665815}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":52565194529403455221976862715705556485},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":104929217853205956747298670984830730349}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":7918093372619071461234920283240707753},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":252149839641523196304059611686253827089}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-461242728081000212772907398685445835},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-509269516722602342448177723767310793}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-61828086812940991717934603988332302697},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-248454580138347799622214670302194305559}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2128333121130112772231480569481594263371},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2111139591647714791243916833110918380335}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5764423346405402976219466658880264441},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":720552918300675142297889594655773735}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-126346406524692721612550642866096753181},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-505385626098770887641334128169218399845}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-344309417346599605936811589522900888493},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-344309417346599608017365034325292792615}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":137075707859414072139912148121309715099},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":68537853929707035173810836671523744573}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":163115988438493510183096475868841989287},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":163115988438493508239654003054648244965}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":127120194407118813847241237065766615733},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":3972506075222462910864258732338722089}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-64953248884000234460709152941738314675},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-16238312221000058729175561383548514453}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-66750646305492155045186263973720579171},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-66750646305492156613006998656168401681}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":327663121026544889190741409995175297},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1310652484106178561873312602139646107}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":69812001697044414088618398607394711745},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":4363250106065275800792162261213171483}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":65324457259435963827186398205560690889},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1045191316150975419439532184607437355465}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-41105079509817540613149740996159371317},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-41105079509817542780584725551245974001}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2103184975772017355932661251759523686311},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1051592487886008679442447564902789166987}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":340359510324364416523897595492285084553},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":680719020648728830023417035605611890233}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":174201206616941620199802105680925990929},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":43550301654235404755631231611908174933}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":31279229299896467004679841534561633003},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":15639614649948232518415592292740899083}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-101453336061045421555299772998678285925},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-202906672122090844804920365585906230195}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":210421761592815755288649813052611916613},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":105210880796407876571567835417926738873}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":254167037092150290476244476292092596199},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":127083518546075144462726282957266305395}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-30551792183495105045313540531710161},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-488828674935922872098838796754362321}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-249182507898710810505988202873235273917},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-249182507898710811771058237358230436113}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":66883315156739152848769880686483741633},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":535066521253913222313174417061559195927}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-32165812308869919},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-504397242841717215}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":88303424956241437},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":47358551465463675}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-153578548893438137},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-101087481475926817}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3857200723670077},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-916721304313411}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":11957154211172023},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1722832707707101}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-167820815499505275},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-602049104367240737}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":27309010248011591},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-28578233765814485}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-284261030755257},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-496722995659683}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-292185061554027},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-784124123729815}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":401786013396359},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":208389565316907}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1576612802102195433},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":904196090477909075}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":59635528772014443},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":7817021883949731}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-367123584930049},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-50038796076697655}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":7901094513884755},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-23864470097698271}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":6935946706265479},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-185282495898211}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-8235429728487487},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-5215292361756091}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":546465366063383},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-11333935056527057}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":42674569722868125},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":13758150901866155}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-186801563947051},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-5960438040576637}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":536500920985137},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-115092318962197}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":3791937993826629},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1256353091232127}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":30780742469900285},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-25676983463533043}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":85070591730234615865843651857942052864,"numerator":229698659894657914587},{"denominator":85070591730234615865843651857942052864,"numerator":297744657282662909021},{"denominator":340282366920938463463374607431768211456,"numerator":1040151336712690817495},{"denominator":340282366920938463463374607431768211456,"numerator":896137713303190189255},{"denominator":170141183460469231731687303715884105728,"numerator":485858490331349496625},{"denominator":340282366920938463463374607431768211456,"numerator":699451753894243393791},{"denominator":340282366920938463463374607431768211456,"numerator":911930297940897660197},{"denominator":170141183460469231731687303715884105728,"numerator":391954261289878325075},{"denominator":170141183460469231731687303715884105728,"numerator":248722094243663787369},{"denominator":42535295865117307932921825928971026432,"numerator":79746100858852839097},{"denominator":42535295865117307932921825928971026432,"numerator":112173610623119338275},{"denominator":340282366920938463463374607431768211456,"numerator":1083691583024099268985},{"denominator":340282366920938463463374607431768211456,"numerator":1476092653872158835101},{"denominator":340282366920938463463374607431768211456,"numerator":1512169244359916405545},{"denominator":85070591730234615865843651857942052864,"numerator":294317537661334769153},{"denominator":340282366920938463463374607431768211456,"numerator":983918015604680648979},{"denominator":85070591730234615865843651857942052864,"numerator":211784162248357412073},{"denominator":21267647932558653966460912964485513216,"numerator":67046413306185544903},{"denominator":340282366920938463463374607431768211456,"numerator":775392983575762568883},{"denominator":340282366920938463463374607431768211456,"numerator":595686585277503526205},{"denominator":170141183460469231731687303715884105728,"numerator":316264344859800579983},{"denominator":21267647932558653966460912964485513216,"numerator":59620511844120186943},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":16,"numerator":129},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5985668420388672240088233013004766355},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":587959068608499981982108703573281845}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-126297727006031376866097153381212325759},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-63316124187810949689867642452423623785}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-339205550168114659887368816398839837173},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-344972384753181463361577306167255748521}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":34283809750941624055843697513764502005},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":34246668682390939793701719653864630779}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":163340835109098909578789225804567685611},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":161417956046320686314960030173467930597}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":127291850273410771838284203487438784687},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":251660706056924686434642929249568599371}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-257356721440999351630788619178909377721},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-65033959113027663357291552720974079307}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-64445755609169556404827457995505182903},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-4188619486080149493595491971804676219}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1324355284055487097152007698001028765},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":39775208055065926769078314817104387}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":70078199516049851949314112553543797421},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":67521484002395764787555970476416951619}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":523539866246539291986915119071035666147},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1044831908579068233359709909217187001071}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-40090801353908758182894338869164833651},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-10311229213028727353628491942460569939}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2089527784511870117532247825703132369441},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2104749443054293141754225083213166758267}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":340477647096828316198198168851263966869},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":679112409362248083877545210836802137271}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":348858295345697856441154555052914122963},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":172295176437870100299555768913773314285}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":7867610433637068939421628430953475389},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":14873040268484949468463950386406394335}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-101179961963398778049660003550954723645},"lo":{"denominator":1329227995784915872903807060280344576,"numerator":-793011949688951145340569272163474977}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":105248283516465599229070086636541267773},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":105073367002748274601131101855725545129}},{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":1986854361806226136624100860712569163},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":126553050798018308180105940811725788089}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-464711511965299928260254744573172955},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-256477052932171086341614037182547351}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-248198531772221998682859459550809783471},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-124662345022352392391018461258967841721}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1071004923447276871492496348908383425025},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":531218069738041006123665991436879522233}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1681350067693248392036992447637675325},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":6725400270772991663289352250977524609}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-504333005074110680222392861827239631591},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1008666010148221362876636718137204879799}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-348795859265978058291643656627648909097},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-174397929632989030198275515101121519091}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":137132437173138187884199445577423864777},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":137132437173138186049024793842678266439}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":82307122336255124674781075176840800131},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":20576780584063780919466706739208607565}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":128292387251210816059190050231592949669},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":64146193625605407670538923884989991431}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-131021159646831276177246491798133999607},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-65510579823415638556624936453608065133}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-17202181302519233819452002741762400403},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-68808725210076936888635972674592954129}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":335918369101523458939238843442805389},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1343673476406092811768862585631781729}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":35927314422290493726753738895920967757},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":35927314422290493070728290617044579707}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1043333281931045722119468425884890533373},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1043333281931045720269699581355118112661}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-41998787680256067104982396623813845177},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-20999393840128034665605986254801263515}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2115260557936869979778694755695311442947},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1057630278968434991397895709631551033907}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":682058217830979206296395694871749101613},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":85257277228872400401158807868452010051}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":351811076030428883397820197380766799807},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":351811076030428880985894077292622203321}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":32654800737097788335647084304081377177},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":8163700184274446577731022513229873791}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-203344167724377394642340666220221442433},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-101672083862188698191273907953900887947}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":13163584589738563308990578503113261659},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":105308676717908505371905551066746103345}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":255092414102825158759041102993588523171},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":255092414102825157163215127366818839857}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":-7684525890953614826978443668107035},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-491809657021032576870915343293935875}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-125020486420444764775139808196306587681},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-250040972840889530852773689211589487825}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2153895513655109180676125306714842579245},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1076947756827554589358190349736036755777}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-275740777126014091},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-264767390215163371}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":340679270370509491},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":47739957884323967}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-113419251347306763},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-88162121600626605}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":6841334032093325},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8180967865626971}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12702491733454713},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":254548621001049}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":-4403839908931431},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-549514109888874365}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":32908703571157921},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-37537610396064823}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":49970956676271},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-441297774107689}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-293819197693037},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1550332007232733}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":1554548219511919},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":1546529276318943}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1529807293125320817},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":105381370410758213}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":47701418079675121},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5242609549883661}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3995319705478875},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-43323888149658707}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":1225046275843413},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-28345276971834733}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":15474928314152485},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1882845551850695}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-5087743336850285},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-1137415933108719}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-5017345073330135},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-58082105694886169}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":21699688895221917},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":237120991464335}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-6004918226102075},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11773816022810505}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":467001977004551},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-184896534151471}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":18628766304366917},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":5932937393660993}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":27841070590502653},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-14328266569819687}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":952302411768134432019},{"denominator":170141183460469231731687303715884105728,"numerator":607889513792559857773},{"denominator":340282366920938463463374607431768211456,"numerator":1052334072169769464713},{"denominator":85070591730234615865843651857942052864,"numerator":229394953679105984755},{"denominator":170141183460469231731687303715884105728,"numerator":498454966681553825453},{"denominator":42535295865117307932921825928971026432,"numerator":89747296035469291927},{"denominator":340282366920938463463374607431768211456,"numerator":935949389146900486875},{"denominator":340282366920938463463374607431768211456,"numerator":805412165691718569231},{"denominator":21267647932558653966460912964485513216,"numerator":31999588633604059379},{"denominator":340282366920938463463374607431768211456,"numerator":656022323144550978259},{"denominator":170141183460469231731687303715884105728,"numerator":462270522049983291399},{"denominator":340282366920938463463374607431768211456,"numerator":1113088315929079561535},{"denominator":340282366920938463463374607431768211456,"numerator":1508524672179967743641},{"denominator":340282366920938463463374607431768211456,"numerator":1543543543138477219583},{"denominator":340282366920938463463374607431768211456,"numerator":1205956264002691147347},{"denominator":85070591730234615865843651857942052864,"numerator":253088735417446124099},{"denominator":85070591730234615865843651857942052864,"numerator":217519887784004013445},{"denominator":340282366920938463463374607431768211456,"numerator":1100004965140991626729},{"denominator":340282366920938463463374607431768211456,"numerator":797910103364486487441},{"denominator":340282366920938463463374607431768211456,"numerator":613971821525011964805},{"denominator":340282366920938463463374607431768211456,"numerator":651240688495032803269},{"denominator":340282366920938463463374607431768211456,"numerator":979830134284224211505},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":519},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":6949833001635567725303974893869748055},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":704088895311367273035099867771790211}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1008266888875140267699937396782579496395},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1011049514788919720569638352088979084007}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-85934486391469482842646278778808765903},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-174726331686547338516424928496435028435}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":137189677970232911106820491430115513785},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":68531522256883766242744235544518673451}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":164838410488884618735665934909840569323},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":81462304105336136870048560746534368043}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":256934398733191709188562098045335670937},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":253941054378798283751618165383602578941}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-129764404778131780053890003832821605771},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-65592667338409334364586511619930106891}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-33246086640696765626183234340363406985},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-69076903522379769180564419411641210427}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1357266773455543505311786098210312049},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":652736559311457895190074318009049637}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":36060714723640393080329987348901208479},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":69555398613684815774009553877475751641}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1045440316432903176089911956988106956429},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1042950313613625627540616102195771189933}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-40990171837724107306000646481301489689},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-2633703034916152523593224339428565651}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2101670123155495256449875703104115126239},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2116818649320716251277731187459177471403}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":682284048308165168690160448614162357997},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":170136282171642309209555830701192591355}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":22016841668836746858050497395192212535},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":10874148144574459828894758918161650481}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":32847851753619477024874876247878055923},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":31104937916149463704826329711990741131}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-202846910051625112279281136043409217083},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-50861132689070605148116308345964877299}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":210687682982928732485015268930448324463},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":210392214771692088771815715247673688605}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":127620658264364924906247390730348813001},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":254047672710308115493558986165067247371}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-116895821411776706936398211718291929},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-258022078420097278527985737142452955}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-124535730248443412796449781720298208883},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-125090967257563337361892977783980861861}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2155635449253344620668646018394280435621},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2138558377878131585762036740207673793989}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1928494687980643525489049777116997451},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":7713978751922572128345471471151130463}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1006478334113167950276016678172000311515},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-503239167056583976379056121519247480301}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-353237689084798049156623257282415463389},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-353237689084798051286596408985478989533}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":137171231679711514434464740214920457015},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":68585615839855756277660016256104310205}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":41526233670221683444937267398364915781},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":83052467340443365867180700646608383309}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":258983760257026480284695569197577919363},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":258983760257026478810914073145073487113}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-132160360857996002667949747563167473225},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-264320721715992007256599978305262834765}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-35438670042228027946801660075921620831},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-70877340084456057548587727619900273253}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1377008151460852522883001637143513145},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1377008151460851468998853813255456771}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":73905197876595842658427463514716927833},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":18476299469148960327316323371141359813}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1041285081629507830193876810651227818147},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":130160635203688478536126980951169057625}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-5360793071055755632748123818440740281},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-10721586142111511837199184344840292659}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-132954721389867273981296989810621939335},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1063637771118938193392077893729131479997}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":683314429594657725527794395602203216055},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":85414303699332215297107326081673613273}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":177621304613069835718135680957984532845},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":355242609226139668965761431866614898943}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":34045041578785220514633762481183164507},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":17022520789392609215722550649866574879}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-101867762669229547626825821493675340279},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-203735525338459097040996705772974947453}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":105383550874333774188529668341445118241},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":105383550874333773060562884171844788243}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":256003572901888269340967627087267313705},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":128001786450944133849438338688927175723}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-494170607169282950959888461122948741},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-247085303584642108256484877811508689}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-250886843912713754953409680561926832371},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-62721710978178439073593082753478804767}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1083735413406291564293507049003417779675},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2167470826812583126573860699634808737765}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-284222610965436057},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-544596951462633851}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":10147563692125063},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":46047017612100093}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-74081754724283353},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-300758482231592877}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":756272649661507},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8866620351551245}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":6635808260259675},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":4542537370628813}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-220852071540414821},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-488855843767792637}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":13104502652009581},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-90701746293190217}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":490059799025389},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-383669025665159}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-70057090401627},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-757508331800851}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":11830744048850769},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":1382441438512055}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1457472558333137039},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":757417489940489163}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":8960836073904939},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-4506477547919527}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":9235737944033125},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-18317579076504069}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4396184742653343},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-4007139156970807}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":2088904176797431},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1823303022165249}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1851913956878621},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-7701362362366287}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-21076773359372853},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-69443044471372591}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":21763077650463911},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":16113635615690795}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-5895402399439691},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11468457755013243}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":397616700677263},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-63180357219315}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":10818440051844499},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":8957585329110433}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":19759840318861239},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-3582057280418403}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":85070591730234615865843651857942052864,"numerator":246668794162102457693},{"denominator":340282366920938463463374607431768211456,"numerator":1240908444922979373581},{"denominator":340282366920938463463374607431768211456,"numerator":1064873237487778108309},{"denominator":340282366920938463463374607431768211456,"numerator":939564895450581496651},{"denominator":42535295865117307932921825928971026432,"numerator":127836183701318312873},{"denominator":21267647932558653966460912964485513216,"numerator":46047296633758657951},{"denominator":170141183460469231731687303715884105728,"numerator":480149169232495672129},{"denominator":5316911983139663491615228241121378304,"numerator":12929537875437911601},{"denominator":340282366920938463463374607431768211456,"numerator":526941456517793030589},{"denominator":340282366920938463463374607431768211456,"numerator":674577934525928343015},{"denominator":340282366920938463463374607431768211456,"numerator":952080453986741354635},{"denominator":340282366920938463463374607431768211456,"numerator":1143378938788673975261},{"denominator":85070591730234615865843651857942052864,"numerator":385419759949026861171},{"denominator":340282366920938463463374607431768211456,"numerator":1575449666825407945035},{"denominator":170141183460469231731687303715884105728,"numerator":617624216355496029449},{"denominator":340282366920938463463374607431768211456,"numerator":1041587555185341080397},{"denominator":340282366920938463463374607431768211456,"numerator":893648348257256133577},{"denominator":85070591730234615865843651857942052864,"numerator":281988269477439427871},{"denominator":340282366920938463463374607431768211456,"numerator":821042688327028694353},{"denominator":10633823966279326983230456482242756608,"numerator":19774256733693289283},{"denominator":340282366920938463463374607431768211456,"numerator":670474985578606904065},{"denominator":170141183460469231731687303715884105728,"numerator":503266798724047634955},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":32,"numerator":261},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":7941468128984620119789683419892685219},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":6590281619860588501455981876762145035}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1006070010325818130413958938637180800675},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-504477227286466416575133791385216180715}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-174115041917453733062079688811870887671},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-353887838145613387799002165463789857339}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":68613402532307760352468976049196675579},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":68557910138237538412842495046623453445}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":20791050002495896142218323544146406129},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":82211891483618628023310552699138561145}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":129669679101129405836122859856981818189},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":256278709646884166127701248165179196145}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-65438024259560425803846607927186854117},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-264654319592450194606451948384929988371}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-17137244707427609001584432824698286029},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-35573221316687714360520262891167231759}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1390492440951592336115342580610584239},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":669235684617185321198515615371332083}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":37086306999960680041463572051217958745},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":71597074938432055703515407337714713455}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1043605964733329412087529580591849666451},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1040879136710492512406918035721281591225}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-41884512008081873795246896378555787781},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-43027268729823806892601896632113106187}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-528438292431537913787382848788694494931},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-532206762958333725360291249590272339099}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":21360305362934334581874634942843122835},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":340947355927549629192928683839230978767}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":355703416223887035829068152353879939197},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":87844648446677827056385350510369967735}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":34239899864795032130120316635515451969},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":32478678611798092331013397966072916013}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-203290012023139125993557894321707184419},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-101915784517760906240692805553913254503}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":210832741120374934737092790184613950255},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":210593421470866130300113136550142762343}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":256151075007268866856817921346934578613},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":254974785113442522752814816680247840489}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-58729199095952147502459823627634253},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-518515592862033627400436786661501649}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-15620716085041202510268256563480388045},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-251026612162962134024167216585932619587}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2169206439008646437346605726182235353039},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2152194299726938372201911251815497389661}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":8729248410883156911702048053080914403},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":2182312102720788716893847428764826735}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1004211909384266892220135526172835524321},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-502105954692133447376555964104326135961}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-178815601292548555435545857676223166971},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-357631202585097113026874502629575775123}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":68595798990670671345928880741167103475},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":68595798990670670383812659620495245699}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":83793993617006868168358082779170602135},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":167587987234013734238572502741524981013}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":130717425050128598194030100170720693471},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":65358712525064298719059035969667786495}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-266646261891068125229113055462629145269},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-33330782736383515899893942500621266909}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-36478318006855891470593639951322726089},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-4559789750856986540094149370694727833}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":705319785097550402948039038172284983},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":705319785097549860648677338031031919}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":75963888372407102725777115966258762355},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":75963888372407101338472978801714652143}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":519525642102867962240476629109527235649},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":519525642102867961260137466274552326355}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-43766773457676467973185011470670373861},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-43766773457676470322405324845367315759}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2139228853121009592065989857531908741209},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-534807213280252398804292703121451374179}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":684487883829843434927837598250271276077},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":684487883829843431712003841527464707067}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":11209264109941846163971844694812364587},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":358696451518139074716762524393423154143}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":35449771454063693105981683583983360737},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":1107805357939490342584284770958428753}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-204078814864838031188589510489997808861},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-102039407432419016512171677737269080243}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":210869675195562552602252070235043543817},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":105434837597781275144515259436238777227}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":128450355940283492307483728611433271611},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":256900711880566982925352376516568009011}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-495887742897172311585698209808114883},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-247943871448586807907103342622174757}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-125860200828823581531751425553835898291},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-125860200828823582222001742220553821845}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1090494310044936733910249777948171571971},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1090494310044936732876153492467198260723}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-141045527133795467},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-549494369275656929}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":153485524458815295},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":41829740837905579}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-18029150984365517},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-125252561269213791}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2689033207143139},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-9414793901605981}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":13664352661773235},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":4813746243546171}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-77197121356571641},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-52767876531017089}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-1085494230869007},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-26059407048888923}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":878665961000443},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2612682109799227}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-251166781863715},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-183114169042827}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":345973370080707},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":591499082303157}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1362253515460519131},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":649367734212672127}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":12179477150872375},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-30355492468967231}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":1780252418311413},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-944011834784307}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-266831421066625},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-35067298481505393}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":17616813043141425},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":316826512059065}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1426116034172813},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-3137085078144681}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-30709873142222661},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-4954627717185869}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":21566368515152267},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":4137489617706741}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-2830353004348183},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-5516333632412969}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":330577912715667},"lo":{"denominator":2658455991569831745807614120560689152,"numerator":-2479757119055}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":24150483435678903},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":11518657624854677}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":100512386681704281},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":395786607798137}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":1021929627511506770733},{"denominator":170141183460469231731687303715884105728,"numerator":633177815181934255647},{"denominator":85070591730234615865843651857942052864,"numerator":269446042557069968079},{"denominator":340282366920938463463374607431768211456,"numerator":962108824690513911645},{"denominator":21267647932558653966460912964485513216,"numerator":65566712881574937381},{"denominator":340282366920938463463374607431768211456,"numerator":755778153846617623765},{"denominator":2658455991569831745807614120560689152,"numerator":7695072612855737931},{"denominator":340282366920938463463374607431768211456,"numerator":850157809340199696739},{"denominator":340282366920938463463374607431768211456,"numerator":542298754826856013613},{"denominator":340282366920938463463374607431768211456,"numerator":693648899004679976421},{"denominator":340282366920938463463374607431768211456,"numerator":979982719944350985791},{"denominator":170141183460469231731687303715884105728,"numerator":587291399731981557479},{"denominator":340282366920938463463374607431768211456,"numerator":1575568252277918583189},{"denominator":10633823966279326983230456482242756608,"numerator":50246858691496033285},{"denominator":340282366920938463463374607431768211456,"numerator":1265161979125861158127},{"denominator":340282366920938463463374607431768211456,"numerator":1071635298228483444551},{"denominator":170141183460469231731687303715884105728,"numerator":458926320203551900095},{"denominator":42535295865117307932921825928971026432,"numerator":144574685536500406987},{"denominator":170141183460469231731687303715884105728,"numerator":422402427186260601159},{"denominator":340282366920938463463374607431768211456,"numerator":652113930244306139961},{"denominator":21267647932558653966460912964485513216,"numerator":43140250047113281965},{"denominator":170141183460469231731687303715884105728,"numerator":517026180936678614649},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":525},"tube":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":4479826681404374718114054500044150309},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":7575570461824107983025178168044416495}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1003794863603996132001483263376535744333},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1006776497503075932842182129911937457471}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-88169518444604205420301508585809407565},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-179137113421114548217689130767996352997}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":34311759178888917441288013050343721339},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":137136321401836567927610544787026041371}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":41952683325091107385175488138948936751},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":41478850375236191327858668282704129545}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":65449018099774124515798288036187280175},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":129335640565064905002552643172609027493}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-66006177142197823594416076750681905401},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-266984840040798403960016186039777614507}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-4413518922797367302389033735047759261},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-73226675961739667392012341472531827479}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1424015087054447348062640157206573297},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":171473144827139824193415219115621373}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":76231935237771044043521364711746196895},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":73646671503131929894347951992764993341}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":520790434937503467739557106336793174591},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1038622987420015882626740194649024294387}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-42772827233778151995718361711933270685},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-21954000290228541329192323934418265381}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1062887879853724856678283176456934706187},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-535193396252929104199605297818915581669}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":342346352342242619160545213325071215185},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":170790321979502555151319323824575649331}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":179579789534310334146698812946430021949},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":88701847588688222815672685849285158055}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":17823203204822134642502844686454473499},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":33867112153134212781049480158377699447}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-203687222584863271297451322467834574877},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-204170250120821510859454525463972376131}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":210930416671113178503727613855520586341},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":105374477823086793483751670410130662387}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":257046829912964903749687737782949418739},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":127943827728106542957726612988698380009}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-117859617352420498715176667210657021},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-260172406688078642454652509252307745}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-250778826505743359394494994979096056349},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-251859000575447314983641848608380561017}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2182719418539941913021673055260145067447},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2165776538842876594746325993209879894961}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":9770216677069712047110912886320073893},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":1221277084633713741361698789335456723}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-250467601926171004325550334364723478961},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-500935203852342009943335902953983757441}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-361972862721668366980657289623664182873},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-180986431360834184581512887891861198179}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":137193036993763981780615534501739007983},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":137193036993763979810145123146021860229}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":169063337468119781953966901307882475035},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":84531668734059889900923381930103871193}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":131967732443923747029519523812912852417},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":263935464887847492508709804528289620357}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-269016947031099681439462343879359208321},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-269016947031099683459467320975581320455}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-4690423145109829840271828413839286835},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-75046770321757279191210860294402470857}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1444550237531618303909314408088634609},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":90284389845726074234756201634253817}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":78030897765359606753461939947256370509},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":78030897765359605326958232548897586195}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1036636769953542711900181374385866103055},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1036636769953542709883352253995829523917}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-22319558352233366483116310644426910815},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-22319558352233367689861490443890684577}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2151119492987561444243271338054461338153},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2151119492987561447463723165652959421391}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":685578893600704283314268975187021079275},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":342789446800352140016212747198616981569}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":181086003847269068475907431180265870921},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":362172007694538134360377469291130211955}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":18434409890293678507533654161891725999},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":36868819780587354810018136801336591845}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-102186089155336228286304731719447365911},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-102186089155336229229030034391701691529}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":210923803472001263626271824400146585485},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":26365475434000157656793621494151631331}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":32223001578012024300129836820875866469},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":32223001578012024082826449313900012973}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-124234454260619549537485522810151481},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-124234454260619885537393368567051131}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-252541904739211042220691183493359497835},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-252541904739211043641824322013815025813}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":548611396413094154685571788930906021719},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2194445585652376616617403592539306815165}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-135052681223298531},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-533987696098486615}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":286682793723136333},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":36344615879301067}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-564045329730543},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-202686955934769545}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2399900850285379},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-1221886299193197}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":6821296919710325},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":2457166871669857}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-42997024705237953},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-173748196211820005}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-19479452743149949},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-57486814804654443}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":624481112844019},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-538301226496455}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-211205854009795},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1391975965107825}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":2528667950694361},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1920090458446935}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":613613310943973423},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":525073117290073869}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12435385801152273},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-20699074695736259}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":18749555102458249},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-23820567501586755}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-2120953331878091},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-18630137118626733}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":9072376864527167},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":6177082083849317}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1127695373647201},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-9344457218564067}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-9803275596162667},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-43454997403342983}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":21058610730784069},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":4132873422388571}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-1326751904973945},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-654574236806989}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":32888541565917},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-187738225060073}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":26007527019848947},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":6815561085388925}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":29664613886692413},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":31871716645579667}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":1057976720118992265277},{"denominator":340282366920938463463374607431768211456,"numerator":1292110065135614881885},{"denominator":10633823966279326983230456482242756608,"numerator":34096358238980982891},{"denominator":340282366920938463463374607431768211456,"numerator":985227918231811515709},{"denominator":340282366920938463463374607431768211456,"numerator":1076055704593789325855},{"denominator":170141183460469231731687303715884105728,"numerator":387516935188630730093},{"denominator":340282366920938463463374607431768211456,"numerator":1009954741459677976597},{"denominator":340282366920938463463374607431768211456,"numerator":873429101752921103819},{"denominator":340282366920938463463374607431768211456,"numerator":558076017205914737753},{"denominator":340282366920938463463374607431768211456,"numerator":713248716453736450369},{"denominator":42535295865117307932921825928971026432,"numerator":126007935430339919135},{"denominator":170141183460469231731687303715884105728,"numerator":603359131515933730683},{"denominator":85070591730234615865843651857942052864,"numerator":402551157184486754779},{"denominator":170141183460469231731687303715884105728,"numerator":820452615605553404713},{"denominator":170141183460469231731687303715884105728,"numerator":647856356349439081217},{"denominator":42535295865117307932921825928971026432,"numerator":137814707267733356705},{"denominator":5316911983139663491615228241121378304,"numerator":14729710222281926687},{"denominator":170141183460469231731687303715884105728,"numerator":592974316679790380245},{"denominator":340282366920938463463374607431768211456,"numerator":869210966937818905961},{"denominator":170141183460469231731687303715884105728,"numerator":335999748199561237779},{"denominator":42535295865117307932921825928971026432,"numerator":88820047632225403555},{"denominator":170141183460469231731687303715884105728,"numerator":531199194111354020431},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":4,"numerator":33},"tube":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":2500846658083411219283652076785976467},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":8587677497388655977624365182713989775}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-500722558653698482651314242748267255507},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-251129832681535332839680299966361429549}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-357078190148659812850642033727720059351},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-90652078628258198263784711943989887427}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":137248334806201507697972582761803312147},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":137137901341652842575219898916069102749}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":169285346276137736729022768422803062061},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":5231230993277776408530216169421609349}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":264301952981595681633247630063340501357},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":261116283113441807458790422947149744765}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-266344709597211494749753202629299520063},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-269360232535777799543351728763572516569}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-36347144312583722814370719764327757337},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-75317762510610818753199841069531634161}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":728908476542260053123837119727810863},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":351349409690735475186829731170604475}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":9787449122552404460102029194491570405},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":75704365638183530855990394695798966959}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":519684781026533268150486832665588066119},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1036186783579760418100769596408982778395}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-2728383664291916965236614693528990203},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-22390243459364318368888798319752946913}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2137736807776433257119303880531758145657},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-538164315305549151646540912083560211405}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":342886586506830823368803248781391416219},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":684345073920530296709159101723648998075}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":181318678315195107756383294599270834071},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":179129286586166696203047702918703700985}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":4633400204089777817914661740620857905},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":4408757123721092876161858758093153919}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-102018301430232412505306015760017610435},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-204458722904196886790386819020637845221}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":26372430773170443935124813242492038671},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":210857478418917994601034075620646219957}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":257928760559202562436104993708762606843},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":256786484249607474090824307695321580857}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-118093623859376325502182076799290443},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-521508744751278394119676105699217225}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-251613851243065574510608981120840248577},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-63169838847220365009886919697533118267}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":549042771968237734986122092555355046299},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2179301679225087079730953497435946863745}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10835813313645186892443189331225529829},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":10835813313645184702564123077234865789}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-999457479378966454006719729300796805769},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-124932184922370807080409860718195239921}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-91564824982150485287659842289685475169},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-366259299928601943360404432235592714597}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":68587522133226246341728112059606497605},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":68587522133226245332782050899896375043}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":170530926488898628978697498049260131455},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":85265463244449313385678159150589589839}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":266482952847650643111511624624765856163},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":266482952847650641522229592263165694865}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-135715369441029688815933132634839660123},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-271430738882059379702458126724692701721}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-38573955926696864889936190395472820261},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-19286977963348432893629087767711870999}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1478722141596332897274653292018026431},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":369680535399082937176277564696172089}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":80106440461942276235251431409437938351},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":5006652528871392173028943393063195829}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":517023353095646630108276498476683795657},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":517023353095646629071674499552633435963}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-22751219269005394933608257613865602687},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-45502438538010792346872210653170690171}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2162946540944133499166095303587391281063},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-270368317618016687807166973196091830221}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":343293927279143354635161881161583922179},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":686587854558286705921333699370546333527}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":365668649754705982738737994897021341021},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":365668649754705980084892864320552271077}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":38302026494447838876376411619181839945},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":19151013247223918303927587755477234805}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-204613832769015008718440635196594905637},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-204613832769015010654892456228986015715}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":105464139195042783088131715930921351301},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":210928278390085563744205275266081689641}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":258653639375429077584533131429652469441},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":258653639375429075795976850348319115421}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-497298167065455652681182796095242231},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-124324541766364259394362228237675463}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-253351589095970931959206519353764728197},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-63337897273992733355523096166728033525}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":275979814733972173956896829428260165211},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":551959629467944347367982327371568080361}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-249283610097358943},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-508385150553259319}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":265584962573917355},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":29371670394369381}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":15372099108737837},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-158700857675445037}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2166661464259101},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-10025615188631739}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":13417835984479809},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":2417458747675759}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-8427233684211809},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-16967279784436107}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-7989407808860627},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-61527740347418383}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":199969701256835},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-855506901442641}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-159215389044749},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-326383092376643}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":9055093291355845},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2867080802548339}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":33632591667965263},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":387891370018859093}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1423047635637241},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-51332653028798575}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":1425631980098499},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-1119381049398949}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-3728558374753115},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-38755644405085103}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":9183626099228525},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":3481607685076201}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1858160728092249},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6241382497065923}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-46010897329182517},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-11586473634517251}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":5082426520325515},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":16057589224084181}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-2429463279821555},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-9826621758236401}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":100071933290959},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-213961004078309}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":6826839558302113},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":7608675213871203}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":133962732813612469},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":48609831436470831}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":1094809982356767381831},{"denominator":85070591730234615865843651857942052864,"numerator":329540367894073195703},{"denominator":85070591730234615865843651857942052864,"numerator":276196952252619736651},{"denominator":340282366920938463463374607431768211456,"numerator":1008938881690651547591},{"denominator":170141183460469231731687303715884105728,"numerator":551833149207397955871},{"denominator":340282366920938463463374607431768211456,"numerator":794513705176208803601},{"denominator":42535295865117307932921825928971026432,"numerator":129406297725347124201},{"denominator":340282366920938463463374607431768211456,"numerator":897320329754244451755},{"denominator":340282366920938463463374607431768211456,"numerator":574284198358126438125},{"denominator":170141183460469231731687303715884105728,"numerator":366695537276984499395},{"denominator":42535295865117307932921825928971026432,"numerator":129532227892796543129},{"denominator":170141183460469231731687303715884105728,"numerator":619900734931193762245},{"denominator":10633823966279326983230456482242756608,"numerator":51424996277701115649},{"denominator":170141183460469231731687303715884105728,"numerator":837239691106241482989},{"denominator":340282366920938463463374607431768211456,"numerator":1326916863269820382647},{"denominator":340282366920938463463374607431768211456,"numerator":1134253781041408967707},{"denominator":340282366920938463463374607431768211456,"numerator":968202570070322077293},{"denominator":170141183460469231731687303715884105728,"numerator":608008388693205623255},{"denominator":85070591730234615865843651857942052864,"numerator":223568914173266845091},{"denominator":170141183460469231731687303715884105728,"numerator":346223909512745180271},{"denominator":42535295865117307932921825928971026432,"numerator":91429610956583871241},{"denominator":170141183460469231731687303715884105728,"numerator":545789993259607964651},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":531},"tube":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":2767897204907095740878596067244898205},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":9625619772340968482824612964314854385}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-999024417616099590557076080661773081957},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-62636664301602365335483624865395314739}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-361426874835903156127778018831187397775},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-183443376846777632328285362278465996601}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":68615097522038753952403932003879011941},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":68560027742311633248662552741374935179}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":170752180841705620989813584445634497991},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":168875688204388019669850450217491074479}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":16678396272417978168660709970970607381},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":8237848293471483591626828762320636215}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-268710112893516500083036284669192981429},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-271778454269348313647296874571831994797}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-37391546139065520283853335793776354197},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-38709936357196704667066249863644131249}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1491879761394490557856468737596429273},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":22488928149169585624487016188994663}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":80375803917198232186966758724539358437},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":77770352637377535675846173840601471995}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1036976885848094974029876887425795138397},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1033575726902572352732921759225528040533}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-44527486012301193963321312549431719243},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-22821896466978291996217198872314743777}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2149635306708049438637338890985001374851},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2164477169503169494696663359480577752317}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":85846458794356122643432374421500849175},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":685446362850243757686310660711256620269}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":366136289555785640858109597167128322639},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":361731531932177300305073899282794504595}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":38502212356387924250579433079993492417},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":36687331716609513761066881414927685609}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-51084071421008445757333632880954242065},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-102347605975210259231041924237785674161}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":210983553168110504008412769511670485193},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":13179586914971710659876194102063695885}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":258797028876930040909025100479864774257},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":257671455262670209524121204714790334225}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-29538677755751269763074489003245907},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-521984889281268759992130939215519995}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-126218396552048526805226328201747697581},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-253487909455236939712837925103113166337}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1104779125138278655657441024268204300557},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2192766400694134317206572652739737366109}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":11924895391113894964015239248188034657},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":1490611923889236587363578994059965729}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-996976745983330920647040739915907683669},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-498488372991665461668131400939573681035}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-370487311698844975038034877379765417739},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-185243655849422488638021468080466727461}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":34284277582983723691738328527844579871},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":68568555165967446350210700923466348039}},{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":1343677351243765944612438425560632095},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":85995350479601019323280518960349464817}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":134537300040468609100017913587248699503},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":269074600080937216571369395936998554151}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-136942779988303610966658227848631895659},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-273885559976607224055104030878834178247}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-4953765015127686678668678309837534587},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-39630120121021494351198239290761856121}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1513136794656726081900491329403479513},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1513136794656724900030334205497841289}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":82190746928513448050533103394508856479},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":20547686732128361635586782796295370759}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":515643261138501857080423253449244278755},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":515643261138501856015578142254475692595}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-5794478462720397194482795764549555307},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-46355827701763180103611966734185451459}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1087354575715915997197676103321935322423},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-271838643928978999719865360568762422419}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":687515242295108329515556651998005675861},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":171878810573777081524564351780140595191}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":92296429509272548546257126059691766111},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":46148214754636273933429412650408927011}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":19874621368033516123355649613510384639},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":19874621368033514956485585096894502577}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-204802073082358508846282267176381306987},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-102401036541179255417527826604887323653}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":105440977387803642940910054917618863267},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":105440977387803641694086039691450517055}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":129754869278360812228874246849355904969},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":259509738556721622617716023747658067009}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-496946762467994892747771252666479193},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-248473381233998159848387912049422585}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-63537416797185515589710838878745133303},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-127074833594371031932314184108482233507}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2221164318486742484757714656393994989919},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":555291079621685620628604873951445703425}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-220871569911787511},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-237035565226287367}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":243951462021197545},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":10337127134521323}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":29504235691654289},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-118690129200333225}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3959890438187809},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-636232492111721}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":6501949986793675},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":2293969926750159}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":25920963116320557},"lo":{"denominator":1329227995784915872903807060280344576,"numerator":-766154168691751}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-10293732093487033},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-128542969664161167}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1924980799528741},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-648622778199737}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-47043244271091},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1207259781090995}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3964742271415133},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1829834531989911}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":457143039823949869},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":60357623581584611}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-4228726309668779},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-60009430879558705}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":3294595772788525},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12581983747453989}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-4973524987251647},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-39592268064665757}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":18312424313488541},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":932560593475373}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":316499271444375},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3313896619641731}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-51062299690014577},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-96701516672810439}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":38874594715363535},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":15190770553114833}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-2171628233317827},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-4564574717074939}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":71610909223661},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-474579264435499}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":14043936774989593},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":8137651493240351}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":146347267208630253},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":31315738375282937}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":10633823966279326983230456482242756608,"numerator":35388334495861992525},{"denominator":170141183460469231731687303715884105728,"numerator":672249696188871880875},{"denominator":340282366920938463463374607431768211456,"numerator":1118915180090292197689},{"denominator":170141183460469231731687303715884105728,"numerator":516629443163533412015},{"denominator":170141183460469231731687303715884105728,"numerator":565955666147735472873},{"denominator":170141183460469231731687303715884105728,"numerator":407104613461020278871},{"denominator":170141183460469231731687303715884105728,"numerator":530425051785070043473},{"denominator":340282366920938463463374607431768211456,"numerator":921847201698883615317},{"denominator":5316911983139663491615228241121378304,"numerator":9233351905864164761},{"denominator":340282366920938463463374607431768211456,"numerator":754089936279658266543},{"denominator":42535295865117307932921825928971026432,"numerator":133063585425263475689},{"denominator":340282366920938463463374607431768211456,"numerator":1273849024319764393927},{"denominator":340282366920938463463374607431768211456,"numerator":1681765869578149486157},{"denominator":85070591730234615865843651857942052864,"numerator":427158699957419141579},{"denominator":340282366920938463463374607431768211456,"numerator":1358791175547964981399},{"denominator":340282366920938463463374607431768211456,"numerator":1166863343579962951195},{"denominator":85070591730234615865843651857942052864,"numerator":248590968352051318057},{"denominator":85070591730234615865843651857942052864,"numerator":311703043328521805465},{"denominator":21267647932558653966460912964485513216,"numerator":57500865126815194647},{"denominator":340282366920938463463374607431768211456,"numerator":713474193385174741577},{"denominator":170141183460469231731687303715884105728,"numerator":376443300032855108829},{"denominator":340282366920938463463374607431768211456,"numerator":1121605722398877055919},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":32,"numerator":267},"tube":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":1520388598213764401534680944354045755},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":10688336038971303534818197890943670699}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-249134059007914737517841622199253327521},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-999782061973111735151269152317514348795}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-365720737265994664705595564184031547765},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-371106363892067429156033611732111821317}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":68596054060828430660119056703149399513},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":34270568550109864006858222691418378137}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":172211184424342510908188354099145008581},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":42586057790684548800149300742045098129}},{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":2105083275239948830335617569799798039},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":266153207693976996104370763499806616011}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-271118836628275969895036877309541606157},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-274237859166110047263330754711895491495}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-4805178564274959518839923203465435687},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-79533405278343127085774864411410410735}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":47693273665476163023648616675509201},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1473448517629786696699371628356370397}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":82460800689161395862911403572712684311},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":19961211220285037550603320475510427577}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1034407975999790131525802089583264304643},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":515397638957410709216655582741660213455}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-22695965364248057625955021227145590511},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-46497008823642861404974767989668168989}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2161470326141096504743442779792019777225},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2176232474171466448969968015546711560047}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":343844359396974590125372210545603300029},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":686465536309879764329176952268359275517}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":369655784340600784706631230813234876933},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":365225634800717668460255267799251619809}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":39951325399860215775503447180134926877},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":38118771060513127811449811747820723741}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-25573059827324629331436962390691160139},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-204878020122776775320945057637162270805}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":105469826098803388280025457138187255199},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":210825914122394672722176092330079687991}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":259651778942512021725015270454898164763},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":64635683744771631562076478634146381497}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-472149329674568548867775546710799349},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-521751372335276227471843836129729935}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-253247890984337928496106849374810202159},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-254284872100667963127103546965332206985}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2222877817373126288178586912651467561641},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1103083742296924867030039232222901799847}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":814765791180134575057229715023621491},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":13036252658882150859022294905353413733}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-994431793673107723752938703085340843697},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-497215896836553863247689106436259329271}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-374653861495278434093707516003171196233},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-93663465373819609090210889348164007231}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":34269680271442620033237188516300022045},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":137078721085770478016523838870827473015}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":86721306336514275520132939726601533511},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":173442612673028548718651576011704343331}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":135853820476017951911273956940892906115},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":271707640952035902154083611880037237225}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-138189649851934196548972817471087365389},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-276379299703868395271527956734717408385}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-81383945165191751392997607795094371801},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-40691972582595876643527425486860070845}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1547775275558644407463113100369210385},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1547775275558643191385066150103489633}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":42142031374539995834171930091605967865},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":84284062749079990117618848090914363963}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1028361884144711926254639302711715822729},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":257090471036177981017117747130720790447}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-47198399924929239485883980938226607451},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-47198399924929242103688710134797818709}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1093203276375013597603828177148015653221},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2186406552750027198645122494730630365929}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":86045201207026421337336033444141320015},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":688361609656211367211890618813628606525}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":186361261174968930634023797190301257339},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":93180630587484464621332858975051411895}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":41210331488491803542862796454660389821},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":20605165744245900571058491947229966661}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-102467637094715661254303064607552243307},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-102467637094715662275518199313440311323}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":52695937795687137605780712941494540909},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":210783751182748547866410008566631010055}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":65088109586876935718105737385980566111},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":260352438347507740979536857601517301933}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-247931125088528022302897006281673181},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-495862250177057514795027632772281823}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-254936327339925153445724137751896205681},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-63734081834981288748895328663286868647}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2234420001270412257211774426064231007529},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1117210000635206127453363077628807066787}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-186267090611185135},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-216458242763592467}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":55562346538721045},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":9941685668499717}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":85518759177717495},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-20694992400718243}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1846455134426623},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-640776326448445}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":3106611812282811},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":4193112031138427}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":116340138963722585},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-30837292742845365}},{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":-373850281094985},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-131705632230838771}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2223441474805769},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-915951997422211}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-20872815369429},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-550226760686757}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":844642442642579},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":761903233093477}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":746677048152019529},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":93158914832776273}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-17071960090295755},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-67312848178852279}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":1847604109671673},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-3918700845846605}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-5885998907896359},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-40066218931570905}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":18101402135544979},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":3847806895433033}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12557875417914433},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-621993507017469}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-54387243197195019},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-98758725560988837}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":9184370241170861},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":13929685144056975}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-943439396737257},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8389200515033567}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":11618581454579},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-514112487525355}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":28298265207647639},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":16826609471403273}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":155466873986968461},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":18451678116303607}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":1170823365570054265161},{"denominator":170141183460469231731687303715884105728,"numerator":685556800521672857595},{"denominator":340282366920938463463374607431768211456,"numerator":1133483871330352121111},{"denominator":340282366920938463463374607431768211456,"numerator":1058205484931440293399},{"denominator":85070591730234615865843651857942052864,"numerator":290200758763285091359},{"denominator":340282366920938463463374607431768211456,"numerator":834112306345906735479},{"denominator":340282366920938463463374607431768211456,"numerator":1086749234498145998457},{"denominator":170141183460469231731687303715884105728,"numerator":473513525946288385477},{"denominator":340282366920938463463374607431768211456,"numerator":608038483684779858333},{"denominator":340282366920938463463374607431768211456,"numerator":775359508427994762305},{"denominator":170141183460469231731687303715884105728,"numerator":546378699013878354421},{"denominator":170141183460469231731687303715884105728,"numerator":654438622077120663683},{"denominator":170141183460469231731687303715884105728,"numerator":859357185341788154877},{"denominator":340282366920938463463374607431768211456,"numerator":1743384677259193087703},{"denominator":85070591730234615865843651857942052864,"numerator":347838219086506523523},{"denominator":170141183460469231731687303715884105728,"numerator":600183158172818881149},{"denominator":170141183460469231731687303715884105728,"numerator":510596474482353085553},{"denominator":340282366920938463463374607431768211456,"numerator":1278345017701763263555},{"denominator":340282366920938463463374607431768211456,"numerator":946440738249738438985},{"denominator":21267647932558653966460912964485513216,"numerator":45943394579970930421},{"denominator":170141183460469231731687303715884105728,"numerator":387461426311378756135},{"denominator":42535295865117307932921825928971026432,"numerator":144060413165318444995},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":537},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":13276728788116831756494367819071925757},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":11774691680335788359176883278522453001}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-993984083812322459373715201298593199897},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-124663658000291482972068233606831995505}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-369956554063607424781738162470582063149},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-187632065207991463672352654681696176747}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":34287468689986739991871665207367258279},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":137022230479826307962153195847585152353}},{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":1356736793399388946112700781394182343},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":85902483335383255631288037610528372271}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":272088207909177449449760212251377360373},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":16796234672918018862943984339719339761}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-136784392166110015460659965431553969795},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-138368270388045970520642588502821600657}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-19748437224114072125936300838201722019},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-40829331176161636026640848599860142841}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1560727743451435338051152451861503817},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":376962227864328157284782983447045931}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":42277419219021875032654467713121505493},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":81928070094121190595351374914060951535}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":515834116240508940092838264403710462895},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":64240695652554763746086019494820031159}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-46246558307772173854558338618177298073},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-47339252247682210867598611401345486345}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1086620505610729849924854290530975849005},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-546980603331295661326536208670529477703}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":688524767521826746601497407666645664147},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":687403072825472946042341851259994987549}},{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":2915585292276745736417901819269622399},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":368740251439942051156984619663019915361}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":41414289690677527376657542423592665241},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":39564237518888085750339350812808236749}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-204779466659245825070115806536397646081},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-102502765445186331415890205368605499791}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":105449954087355788338894013589727098295},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":105360187091834334359054427968156375793}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":260493136562007345673468320251507033901},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":129700236055844937805760661945891687813}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":-7358507080709221383844215143109619},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-65098373437672557018985822788016079}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-127023680189536266952494439515749556577},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-3985475444933872163180213151051407159}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2236126813751500052844049660966536783835},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":554875454753220132563892924858118558267}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":7084306631005542203157308888123231469},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":14168613262011081986081539837243632885}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-495913083540177675879361799479608290783},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-991826167080355354554912675272310565405}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-378756077052381883311497021037882488069},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-47344509631547735701085472830399689677}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":136999358198489790620492310153589895045},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":34249839549622447113221319507270732657}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":87443309059062187108817847115401529373},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":21860827264765546479615023129862016583}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":137189634148169433841454337907954403129},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":68594817074084716493562340753614470837}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-278909820172647156052407490904153484175},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-278909820172647158278370167981665661599}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-41759612794762291407714002734128637609},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-20879806397381146190295736041751014917}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1582618273422354720826077886106893137},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":197827284177794183701165118461712337}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":86386647657574012840606928440775971261},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":86386647657574011246172607213202749287}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":512639334277433542959082350448798125271},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1025278668554867083675644433193523386925}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-48029300213396243000511949776981837889},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-6003662526674530711295648506414409359}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2198038045489537035997312333886265252345},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2198038045489537039510262563342790433561}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":689127584020408294996128528841262116753},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":689127584020408291438616182234858301333}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":47034792887588942600885891670619747987},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":188139171550355768978918838139418648839}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":21342584082448067368004352535581089111},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":21342584082448066133214913353854982291}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-205011893156371461587897523913013248815},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-102505946578185731842667226985950794173}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":52658162608233927165175433811868825541},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":210632650432935706039428980360196589625}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":32647731039783451013821175303199865529},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":261181848318267606163421254411363859521}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-123505999438242408711506280981122851},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-494023997752971149495175049639162993}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-255711733164292077927487367180919450039},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-127855866582146039761308432205427297055}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2247602696197315033142097525958428585325},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":280950337024664378846697392809131512873}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-145789382193206013},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-193614048806655953}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":200941870841709781},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-610024982133131}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":27084534081995799},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-25517973440079395}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3503018809710301},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-5114976895716583}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":11710048950172789},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3659031185137259}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":87572433161240139},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-28403222869094429}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-52365883247616999},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-33180531863662051}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2487177073239287},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-567597695994807}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":55444223883273},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-990381827826435}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5584642968659189},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-293629491695257}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":291020035388432633},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-54192187057969831}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-24241190094016605},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-36631188111036011}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":32291898310096585},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3649304129913921}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-13046627371013889},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-5005795431877247}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":8846565623506423},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":7720507335741187}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":14721748539463869},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1780443615996153}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-55832905716148891},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-98993939433566829}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":34279652802684463},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":3079128440989187}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-3169578882858333},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-951932104835019}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":50098480980645},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-34099784630353}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":27977517600169439},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":2103893915046613}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":80750854894771197},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":20446197812711817}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":1209995819611791362079},{"denominator":340282366920938463463374607431768211456,"numerator":1397993457196144003897},{"denominator":340282366920938463463374607431768211456,"numerator":1148513693761053443679},{"denominator":170141183460469231731687303715884105728,"numerator":541898324787976455237},{"denominator":340282366920938463463374607431768211456,"numerator":1190353729087070945275},{"denominator":170141183460469231731687303715884105728,"numerator":427106840372347563443},{"denominator":85070591730234615865843651857942052864,"numerator":278235290104163143277},{"denominator":340282366920938463463374607431768211456,"numerator":972875941961988775177},{"denominator":170141183460469231731687303715884105728,"numerator":312803927778090371183},{"denominator":340282366920938463463374607431768211456,"numerator":797214221477556433763},{"denominator":340282366920938463463374607431768211456,"numerator":1120942017723119014259},{"denominator":170141183460469231731687303715884105728,"numerator":672451054272051345391},{"denominator":170141183460469231731687303715884105728,"numerator":878228572063521292677},{"denominator":340282366920938463463374607431768211456,"numerator":1778742673435159905665},{"denominator":340282366920938463463374607431768211456,"numerator":1424619742231104707279},{"denominator":340282366920938463463374607431768211456,"numerator":1234782968529264372961},{"denominator":85070591730234615865843651857942052864,"numerator":262174221128146365199},{"denominator":340282366920938463463374607431768211456,"numerator":1310625395874119992411},{"denominator":340282366920938463463374607431768211456,"numerator":973571851068139621445},{"denominator":340282366920938463463374607431768211456,"numerator":757324277115339802647},{"denominator":340282366920938463463374607431768211456,"numerator":797559175431827673767},{"denominator":170141183460469231731687303715884105728,"numerator":592109666641709446803},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":16,"numerator":135},"tube":[{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":225174534951413932175975937284368011},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":6441742019551723162831138159350629393}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-991371705753155661255811022740516479999},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-994771803441991289299774567575965928997}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-374131268039588173059424112570496639231},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-379357202596490783402258144698218953697}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":68547045427977923448817963892103655781},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":68470196577051089625382096396579166649}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":43776378357161446327654736650566070363},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":173257845922404411319544090146195099589}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":137381984345104193035646564214931709813},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":271368048981127848385504776463498410785}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-34507239699278268296946018536662476065},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-139635869345324306799671506291512887771}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-40557995820443878077771240978047899511},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-20948881720981927132523434536764567815}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1595474761830166718700511043132464259},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":385618833159896255420837451635532681}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":43329085826658689377174613539442836819},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":84020272870831391380204361292359412271}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":257190823767252160057048268595158096867},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1024749185826041500492655359890489995637}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-47090480961088027525927976066395617173},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-48169670599500147125488022585682264397}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2184946581138053235590654062819326339347},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2199546297257792831760676975387352754743}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":689280455196687587873414622703295799913},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":344129757853634782458082864624109278321}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":47094120805048940140814650756776292167},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":11633584225899260637940267884544523899}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":42890981942112803354464741738839555689},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":41023592549200578674078343889637391331}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-204919614619537809012074416296450923699},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-51269052579618235994347885820990824323}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":52702101614612575702438565292185345835},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":210561853701432778943440169340132441855}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":261321208910562386454719232271907008849},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":260244797173835002593405482393804750547}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-468983445637871430362347228941862431},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-8110488118501159620808477212997651}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-127417696355689515294994161309552380265},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-31980592374605032393418308968499494561}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1124651190537906824641390803619097102927},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2232766403514256544420497771459880430481}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":7660324874328264563537486390732471029},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":7660324874328263313479531845943681513}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-494581681895550580051527018712999772381},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-989163363791101162953502529070797916557}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-47848906015937646798233768746655571087},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-191395624063750588357034804477078574759}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":8556156222534624504561160949715775123},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":17112312445069248731607949933558015421}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":176322678029575087356772470234937585255},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":176322678029575084915612924645258046467}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":69271660845430605768225949001412661053},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":277086643381722421323663833107714509571}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-140737480923845600862289689035059972145},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-17592185115480700250218602522770743561}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-85666289007658021750701675169423642625},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-85666289007658023749525050643871911509}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":808823066178392200717578193786000361},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":808823066178391557062377006809426109}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":5531173409252911032988390192790602057},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":88498774548046574888469636843756162609}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1022042937245839189164821239105037229599},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1022042937245839186866197942483444368395}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-6105963118930540621098541884514328765},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-12211926237861081933178702170736964351}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1104801500444755803696989708335252794247},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2209603000889511610984025537902026463467}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":689813864564494910203737936578713784737},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":344906932282247453287133391658609530931}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":379852432420435241908308029661079910771},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":379852432420435238991078438519637929387}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":5521705142815390646618680997698710457},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":44173641142523122632668977840391147221}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-102515235447743701184513558551337858181},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-205030470895487404522834118880835053419}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":210427699985015792228336852506168795017},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":52606924996253947385247274663214008061}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":16374878694868830502453752354050674083},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":32749757389737660754551226796271045551}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-491412134297880589465062412773636497},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-245706067148941074913416290836789403}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-128238011544992097736749684527630475473},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-128238011544992098557564487951628716561}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":141294353319129302578313214480447504507},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2260709653106068838819294417066315582817}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-102176594440143937},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-337956538059378721}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":180795584060353675},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-194927859740545}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":3976635927166481},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-24144684829898919}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3385015604758471},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-10127072231999821}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10873831481540109},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1496962311718653}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":227395875854833989},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3352091945498709}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-54822876179778105},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-131966604965586133}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2717305341726401},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-64199620932781}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":8447054423611},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-27446061948317}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4431347313617173},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1318171095313923}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":422009505837115357},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-195291764907616949}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-7477893781600033},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-38839243723691691}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":8622262323906137},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-8392516072737}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-6873276585989943},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-39577690784766111}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":17115732413295975},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":3771435982330185}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":16535790907546853},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3844349074778279}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-6955972774609353},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-97534385985054739}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":15805991627713299},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":10435570113314805}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-317635357085439},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-106738743791331}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":14628579396937},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-71220255590697}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":13593963245822657},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":4094571957979479}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":82200045387953027},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":86801552944418947}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":1249940064572979172123},{"denominator":340282366920938463463374607431768211456,"numerator":1425127610338857311619},{"denominator":170141183460469231731687303715884105728,"numerator":582012015486603338627},{"denominator":340282366920938463463374607431768211456,"numerator":1110050731819575760153},{"denominator":42535295865117307932921825928971026432,"numerator":152571979105176339749},{"denominator":2658455991569831745807614120560689152,"numerator":6832093434039167185},{"denominator":42535295865117307932921825928971026432,"numerator":142427569910339134041},{"denominator":340282366920938463463374607431768211456,"numerator":999410200685311405679},{"denominator":340282366920938463463374607431768211456,"numerator":643654694473550012291},{"denominator":340282366920938463463374607431768211456,"numerator":819669428361242269603},{"denominator":5316911983139663491615228241121378304,"numerator":17953171838678501007},{"denominator":10633823966279326983230456482242756608,"numerator":43185604792101753813},{"denominator":85070591730234615865843651857942052864,"numerator":448751437237746010829},{"denominator":85070591730234615865843651857942052864,"numerator":453680665265485242081},{"denominator":340282366920938463463374607431768211456,"numerator":1458610009140496672889},{"denominator":170141183460469231731687303715884105728,"numerator":635066944674841441965},{"denominator":170141183460469231731687303715884105728,"numerator":538441278793592789285},{"denominator":340282366920938463463374607431768211456,"numerator":1343663288720085325489},{"denominator":340282366920938463463374607431768211456,"numerator":1001422966548948229623},{"denominator":340282366920938463463374607431768211456,"numerator":780180592889137909897},{"denominator":85070591730234615865843651857942052864,"numerator":205202349651167094347},{"denominator":340282366920938463463374607431768211456,"numerator":1216819708041506501093},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":543},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":15565099734281831936770274578892705503},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":14013448098425443102671680177168929755}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-988702592624000602741972604814146081067},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-496086615454419607933730786117110157141}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-378241986561489869623202997687325723981},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-191691445735205003253071614496935054653}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":68508699024194869953291479767273182443},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":8552312471836890440354779245250307627}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":176540757453965381196685898744702108125},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":87351412429293240954028663858068664609}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":277475099893540428818672376365158600979},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":274035287007760914547091250175599664105}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-278584101248526241897235407274889263765},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-281841290489735383448956241368508212309}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-83249783231841609020545145417546821973},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-5371512925541959185585858982851756179}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1630405706286993700271281506425847241},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1577308558659615666202436196831987129}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":22192768740606958575875683269224945747},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":86121711290368030906469259650678272703}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1025699017607155146095153414557978640053},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1021495527084274544325266280153178000497}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-47922839894251833034780638930159459733},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-24493721542847966346046872599679992869}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2196586327566396584527703237708623256683},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-138193969174862568701487137330376247359}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":344978245968957168578332946437427480967},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":344517741570342698734971995959705821991}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":190164590473587419245885483105507821835},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":375828250006660060120733977153148230839}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":11095322980654917879160419143941715381},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":42496709969593516794184065366923280971}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-204968976795891239108742029341205234371},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-102546215061933826879977723234034593331}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":210664121765229528800671477930197180993},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":52587352110572831850243513325500412065}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":262136084225423537578562744879477055179},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":65268955526590347890434716584309396791}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-29140394334020493434728051425097845},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-516584385330398500965951271242009443}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-255612154751779868781684601686590856021},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-128303969438450980119856127215426770321}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2262401781687033791909575486984182056493},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1122979176682562028657011996419295317655}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":16490985312729269337235227517693915767},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":16490985312729266755705423655540593937}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-246611707347124955038124346632177372475},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-493223414694249911528846313993027923039}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-386756823760110410682830587153508058999},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-48344602970013801630489223753390210207}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":34193904940283522043469147920773221465},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":68387809880567042949945153556404342249}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":177750756936806002620274046027961266487},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":88875378468403000058651300022242967661}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":69956726390999007852828674407544035323},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":139913452781998014810559796024624482379}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-284072548941634836765597915487896432485},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-284072548941634839098037109292851733569}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-87825350668318206276057020083722900895},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-10978168833539776041169098758938775441}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":826419448475593125561734503119093723},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1652838896951184926739785995370246983}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":90620728466152730235701258818415989307},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":22655182116538182137553538444750182493}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1018660911166090963221966731486238175549},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":509330455583045480433808284375613469331}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-24826411903691245185797685011420660799},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-24826411903691246605825149613889066405}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2221100859131641516833994954198187492633},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1110550429565820760251386923237440745711}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":690421219522232052327417580628046604823},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":172605304880558012156177118115526945209}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":383444015279639804241587172472091460587},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":95861003819909950313722454863405721237}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":11418913060184712106476461570141875637},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":5709456530092355726626697274900343163}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-102494816788382541196889479466997895191},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-102494816788382542302666178898168544541}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":210168012144464403431205857238118514417},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":210168012144464400676248203932765523739}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":131400571106726318464884002326141197245},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":131400571106726317434871754954984744733}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-488007588954556428288450527366628357},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-488007588954558035649402645088006171}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-64307327491992391269182225754844798761},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-128614654983984783383057297237729752723}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2273738244857847826018954262073626955853},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":71054320151807744484946896648765044867}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-57520983784174161},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-143284425808629813}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":162179036208924703},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-23407938010587951}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":142509611443023001},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1274194462357987}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":416171623640073},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-9964359434582613}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":2486936849085665},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1107538171431945}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":136056062293001645},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":56463777370260719}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-27722024578385903},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-129512812907739905}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2912313021165483},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":1112864407487}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":54019873578177},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-766247472968833}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3319842507773169},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1147072559153577}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":67457770281786297},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-163081444430892475}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-34131899923881059},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-40261868416310977}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":36135258421408293},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":337784377788871}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-6933555959316425},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-38722222603314023}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":4100833606183537},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":895067539829999}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":17966102749065389},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":5569075062665801}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-54014015950367413},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-94525225751969229}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":28793032837152207},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":8367441043739049}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":-29802188787409},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6049136368939013}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-6613587039585},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-293276893712971}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":25983706161492547},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":7765277561743479}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":164271960040755119},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":89055624755288929}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":170141183460469231731687303715884105728,"numerator":645325188998580059091},{"denominator":340282366920938463463374607431768211456,"numerator":1452504827241563421761},{"denominator":21267647932558653966460912964485513216,"numerator":73779317027288933865},{"denominator":170141183460469231731687303715884105728,"numerator":568493247709465124541},{"denominator":340282366920938463463374607431768211456,"numerator":1251481856656210926197},{"denominator":85070591730234615865843651857942052864,"numerator":223747432154213929245},{"denominator":85070591730234615865843651857942052864,"numerator":291545640630150541623},{"denominator":85070591730234615865843651857942052864,"numerator":256661607765777970887},{"denominator":85070591730234615865843651857942052864,"numerator":165547837585487582365},{"denominator":340282366920938463463374607431768211456,"numerator":842740745525894589505},{"denominator":170141183460469231731687303715884105728,"numerator":588438542191255576687},{"denominator":170141183460469231731687303715884105728,"numerator":710002134342007017579},{"denominator":340282366920938463463374607431768211456,"numerator":1834372729646647450731},{"denominator":170141183460469231731687303715884105728,"numerator":925671063263813535703},{"denominator":340282366920938463463374607431768211456,"numerator":1493344055112181240741},{"denominator":340282366920938463463374607431768211456,"numerator":1306439935526839178827},{"denominator":340282366920938463463374607431768211456,"numerator":1105756443826269848441},{"denominator":340282366920938463463374607431768211456,"numerator":1377468613856779788759},{"denominator":340282366920938463463374607431768211456,"numerator":1030010176473013180093},{"denominator":10633823966279326983230456482242756608,"numerator":25115005918611062985},{"denominator":170141183460469231731687303715884105728,"numerator":422343809576260576203},{"denominator":170141183460469231731687303715884105728,"numerator":625144588244465013479},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":32,"numerator":273},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":16737135342623333714779848081322512999},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":15163262460437992506090087404280873523}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-61623761412188339776291915308642905717},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-989517050590666465901594960885412881073}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-191142989683191609985696857411872542977},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-387338666977562764116158064119716657815}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":136919274657012022628964976785009207109},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":136711523692431717069100963088464411255}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":88984003399564126091492161358180123227},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":88069931860923477609619162307622053481}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":280218968039547954389552966418283988563},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":69184651827157673856863482290551051433}},{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":-2196446635428126095193121944703326721},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-142221547231855377791658649101971902375}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-21348832563189678263604210648496355421},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-88104917801751800017265166149344375541}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1665500342428738957544775060849611349},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1612328997904343575966973652923961697}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":90893949543541377886174251304337565955},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":22058160998247899194403392081505577905}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":511240727430372572656639378410128675533},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":63631017419480348989293973866692461997}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-6092850929261893831955037710257293003},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-49791782607586893787120633423597949425}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2208159613034179166555350580557411814325},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-277824186448437946867704867436165787557}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":690553656575929043856153576206730089779},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":172432916363028333941292062632401035369}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":191961391705332626661425441953721601211},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":379400171199298570731992611009990315099}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":22942561463969571317632638419144835775},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":43983476499699120410158277707399838345}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-204926976496348626965783044776042650129},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-205052727069276472841556858299332969763}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":26308261679359527595540769208120149961},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":52520539734067983851108286069015102133}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":131468915775454064316182532911996275637},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":261893639958678303525748119519851981917}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-462713856364176237737103042754767985},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-513307471774369574101987255049021791}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-64094447032089376090645832198848608649},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-257360137744624415471743729195036342537}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":284427800212218345430648353114910326749},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2259074903262549069416417482616094439847}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":8839100108044564963789014348881687713},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":17678200216089127263115282775538854887}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-30739998532669670902420180377531144049},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-491839976522714735918925882764442968125}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-12207825284260368752103050673827761993},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-390650409096331802463442193796529658879}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":34157547650312950445932977510633726707},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":68315095300625899727236250056598870951}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":179170822706425447464593362960299300785},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":44792705676606361224604239516092879255}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":8831161924467953072010652819105157957},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":282597181582974496472828154402103403139}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-143350197274106406293106014092515897867},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-143350197274106407486363261038666124571}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-89996632801730349477095869842865600571},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-89996632801730351586301742503334209379}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":844088179152925179778155708184569951},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":211022044788231124636801576911876075}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":46376402792618969976323808412275214241},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":92752805585237938219752293171867388779}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":507569472478650704735719942280109698559},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":253784736239325351765467238329855560675}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-6305487679755370396457734953005703965},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-12610975359510741522482576128166418951}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2232531127584601930255023840907787381999},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2232531127584601934004199939411643355825}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":345475241724457825766655548428571668437},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":345475241724457823878020399239445260997}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":96763072648250161326696326445654112075},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":387052290593000642249086526016579178627}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":11797779285329088218205004700066814555},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":47191117141316350185363445955159979607}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-204888093739088710578530306594785738983},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-204888093739088712849218700432002285409}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":52463191029946327373573344366548408793},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":209852764119785306670171313999561086365}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":65897787420071198484256006061169777705},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":263591149680284791818320284481368751331}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-483792126900831778403220632333348003},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-241896063450416717042319125996382753}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-32246460095966575148410686459521939887},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-257971680767732602925712015297365669527}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2286685969994038448706109938366971647643},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2286685969994038446136774346899954090941}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-12726864128445771},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-235616598901085565}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":36057347029777545},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-34142778011404149}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":38702139996641767},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":7623809923381941}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1668900996386667},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-9759749662845765}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":8960297056271073},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":171797136812679}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":308319234618027413},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":101362973983018825}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-54500896712600869},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-62734073083229323}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":95853158660963},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":110189692415931}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":73897560846569},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-328314093560991}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1139254657410215},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3202230238101777}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":16372203317964517},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-111033480913238729}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-18420556252057873},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-81888492950064231}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":4653541095868343},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":4956798149632583}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-6801076779081129},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-9379052172298579}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":15579272215223005},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":3325673127049279}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":19021778563118361},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":3452746181611237}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-25527550011941245},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-45079634407684835}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":12925977204960779},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":1546547049303069}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1286506432040671},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1319666203736479}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-8436495993079},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-298027365788423}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":6105827926203417},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":896366448174383}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":161401416027626191},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":88569911065578401}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":85070591730234615865843651857942052864,"numerator":333029982023431485093},{"denominator":10633823966279326983230456482242756608,"numerator":46253556582527481443},{"denominator":340282366920938463463374607431768211456,"numerator":1198002505646950735957},{"denominator":340282366920938463463374607431768211456,"numerator":1164623156188840772913},{"denominator":340282366920938463463374607431768211456,"numerator":1283084409487983007061},{"denominator":42535295865117307932921825928971026432,"numerator":114456611221789165181},{"denominator":340282366920938463463374607431768211456,"numerator":1193221763321423297815},{"denominator":170141183460469231731687303715884105728,"numerator":527300756434694072463},{"denominator":340282366920938463463374607431768211456,"numerator":681230473291321811521},{"denominator":340282366920938463463374607431768211456,"numerator":866444921456565058747},{"denominator":170141183460469231731687303715884105728,"numerator":602248954922650120841},{"denominator":340282366920938463463374607431768211456,"numerator":1459111688754087047799},{"denominator":340282366920938463463374607431768211456,"numerator":1874571913486619329831},{"denominator":170141183460469231731687303715884105728,"numerator":944311596080780445705},{"denominator":85070591730234615865843651857942052864,"numerator":382211231480009518153},{"denominator":170141183460469231731687303715884105728,"numerator":671861114139726845681},{"denominator":170141183460469231731687303715884105728,"numerator":567662322417106264811},{"denominator":170141183460469231731687303715884105728,"numerator":706025599425104959881},{"denominator":340282366920938463463374607431768211456,"numerator":1059349873802463727121},{"denominator":170141183460469231731687303715884105728,"numerator":413920213827727953243},{"denominator":340282366920938463463374607431768211456,"numerator":869208221086328063445},{"denominator":340282366920938463463374607431768211456,"numerator":1284631379981027754455},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":549},"tube":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":8962926512345169964745764734099208641},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":8165777783477907090420150271565792585}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-491603928449441629665986119450591509735},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-493403357610339720624719669064355483159}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-193130337937240700462866432379286685641},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-97805538682692874624177521627224248225}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":136799195636112437012639473305098464761},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":17070429610791118578126332410508241413}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":89693614965904215324038163070624565931},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":88784463302013976140274981783588164767}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":282993502073274220864938185376494986795},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":139737530753704781963680985162053966957}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-17733682359092528683376813128748952655},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-143537614853512118624859031070045943489}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-10944105892553048325541587981221113753},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-11284735302420322915196982998785695397}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1700738184728344452726140789068538279},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":411879188466208467074214360155852111}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":93027494502958120612199291847886748775},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":90353310017618796098882471527010810599}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1019116855882196968662735861994142141297},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1014557408721136914255044559114125739371}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-49549588959330687746627371997433041233},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-25290968719924356998153675026246294665}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1109832934611260781315024551445710164901},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2234015768313721104669507613760068702559}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":10798012404838751728246610178746196859},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":690348822368071152848811296775810883759}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":96883242592326887141859848796642242325},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":191494843468171692443414377619479812479}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":47402392194930599535715724538932284777},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":22741896122914325477467780847448439595}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-204818067614498488532893240191567517999},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-205008696461461373057825593330091847597}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":210213425658312202630248163388833308261},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":6554977828744819082494534502522144543}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":263726500533532177863441813022815745999},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":262698324622332685648221475986428432567}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-57295968090064402721473062334364215},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-127305593026067134979059858660050349}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-32141551115704676151594242532505096999},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-258101419348958967852503565654401710959}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1144180876792086777774755927092491170381},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2272113410554922742181499452357867640125}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":18880838335070953892620610805405969995},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":18880838335070951143720589858983567341}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-122608257955957233615265914956595423333},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-245216515911914467984546063692428720705}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-394469761834408271012496941082432409117},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-394469761834408273445892804705304671097}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":34115420410391010251506206310786705083},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":68230840820782019310025564526208134579}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":180582846083338911496252535802593559533},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":180582846083338908865452742153344812751}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":71348648613013898738003731251728331775},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":285394594452055593078835999726746938999}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-289356305505220788793703086819502148643},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-18084769094076299452177290042688723895}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-46090181920955690253398159434436041501},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-92180363841911382673384292981097736433}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1723638100367819245469516229862882599},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":430909525091954460974637301267031045}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":23723828042563694414871749065158825915},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":94895312170254775877885975496412283607}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1011483501848014585415281275000523838623},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1011483501848014582951131755688823666309}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-12805054747204081190461828713233010877},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-51220218988816327760443137801224836167}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-70121668094090226861447304335655267833},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-560973344752721815849394843404066132819}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":345701277250688303234049071949950697099},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":691402554501376602614896795954064174515}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":390676432310170459755526585562147681883},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":48834554038771307078155588261568867867}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":48719965749515382264559039597841031457},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":12179991437378844875135706383568306237}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-102362325554897424956298262016993003823},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-102362325554897426121909994345436320705}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":104740598967313000501229949254125792307},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":209481197934625998107599460541521250219}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":66092028510196974270891996502491734175},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":264368114040787894904646626017646952687}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-478748382759982827827656363543994817},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-478748382759984533186424387109315687}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-129351598178272023962369750604609844883},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-8084474886142001553547529761178850525}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2299550454899762353110385591769652161485},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2299550454899762350470617311909265409927}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":15131333689247239},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-92936015906354019}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":127176263653888915},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-43956744506883669}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":163452895348417003},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":29520872593886825}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":844761279741637},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-9507308106060075}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":7930602090914577},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":251466929962261}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":167712138612188211},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":4297299500919135}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-52187404714182345},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-120115757029230809}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3185087690848225},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":396531929744765}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":371145797051109},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-551983298386741}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":330806125245221},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4013131681093325}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":7254262623405607},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-545611459803350835}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-19089536741583331},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-40896498998015415}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":37775542278028925},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":6629843626089389}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-3244128435040995},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-9002927824680069}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":916668440116245},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":6033432270267463}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":19686269055628427},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":3940211138566665}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-23501242580825419},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-84614995538066347}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":11434274845060973},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3955345662059243}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-345104538799167},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4537912473067945}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-47061354748351},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-598467963746983}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":22567107868053263},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":12878952877575981}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":155975646399963841},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":42856878250743203}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":85070591730234615865843651857942052864,"numerator":343585485780903900017},{"denominator":340282366920938463463374607431768211456,"numerator":1507942901054395361785},{"denominator":85070591730234615865843651857942052864,"numerator":304157741450014716475},{"denominator":340282366920938463463374607431768211456,"numerator":1192980404918752762275},{"denominator":170141183460469231731687303715884105728,"numerator":657698091495254439181},{"denominator":170141183460469231731687303715884105728,"numerator":468245253646742855999},{"denominator":170141183460469231731687303715884105728,"numerator":610266406377800596303},{"denominator":340282366920938463463374607431768211456,"numerator":1083292592778232274985},{"denominator":85070591730234615865843651857942052864,"numerator":175196255486962415071},{"denominator":340282366920938463463374607431768211456,"numerator":890797842204020472921},{"denominator":340282366920938463463374607431768211456,"numerator":1231798326794636707935},{"denominator":340282366920938463463374607431768211456,"numerator":1499276104511889964245},{"denominator":340282366920938463463374607431768211456,"numerator":1915617244588322010541},{"denominator":340282366920938463463374607431768211456,"numerator":1926589156374139331693},{"denominator":85070591730234615865843651857942052864,"numerator":391284155775853143311},{"denominator":340282366920938463463374607431768211456,"numerator":1382002204108394655705},{"denominator":340282366920938463463374607431768211456,"numerator":1165592926073255109127},{"denominator":340282366920938463463374607431768211456,"numerator":1447420762381351135845},{"denominator":21267647932558653966460912964485513216,"numerator":68091172259028891075},{"denominator":170141183460469231731687303715884105728,"numerator":426339554154239080559},{"denominator":340282366920938463463374607431768211456,"numerator":894385881496756524875},{"denominator":340282366920938463463374607431768211456,"numerator":1319849008985244137061},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":8,"numerator":69},"tube":[{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":597806037545083337314187000981182999},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":8758456053302700324283268973609302075}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-490194468010552179894190431080957881995},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-61502851350230488601320394411985880931}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-97540915515259909257669320783839327885},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-49378891551745158424610083150955597293}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":136656633083272571998239406737036974251},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":136392208263064869853164441991039555579}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":180798398158460354033112782892240296343},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":89494990494766338608392044197358423239}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":285794820117391270071763048401607874405},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":70560472103120935962681069261677858373}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-35795399702243140852705846147962710377},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-289735166920621984467299356997979554641}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-44861277705298706670491940721600896445},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-46231664660963387351051881620408307073}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":54253079488432425090475829869444007},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":841425835523814020447160966561367901}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":95171514796282514349224940123703646031},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":92484060117344096427588665488438554023}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1015611506104032937140764151817581579863},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1010885894636717660447521481442983007965}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-6292803078850384306847480157788366121},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-6419649087900245202950027835083837617}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-557776148803984060773611964373628665279},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1122684959451296557350103844714109307197}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":691514811981471508502282498846786573687},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":86360972534828957903585076163098547093}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":391158913507621286871377344886212476247},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":193297999579021396423304884060030891915}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":48933031255751740487173772730455859713},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":46997571128601306818495631624680075645}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-51161488716660289096813570116897297229},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-204914998058249552456103636227939657859}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":209905287551325924235265399381202746283},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":209380053235919776825545182430134890725}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":132251060632687600111552726502117314835},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":32936241326909343305001352633478189279}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-226595255943129439064128892489581561},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-31519488685767591739398025350626221}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-128938053685030849030376240188278175529},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-258831841346770729326082591173724775883}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2301217478282639057217301822999672037689},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2285071357961971711572271293755649512907}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":10048706888640315395294085325073080419},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":10048706888640313977881623369666740055}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-978008426426695497876905928280093540457},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-978008426426695500949030248378899627065}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-99553197086219057241145658111306286563},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-398212788344876231437430112756906252015}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":136269560784813558530236480967787512483},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":136269560784813556086067081851412687177}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":181986800232533979236327564238392324341},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":22748350029066747067432551611262131993}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":72054067975166652611090736871264903177},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":144108135950333304264591369548334540573}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-292038086978478563678785718620220713323},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-292038086978478566175072165367978616959}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-94376777647477855428252780242336474097},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-94376777647477857653729692225080439533}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":219900443292962082665869229249046065},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1759203546343695219589514925794816803}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":97048563532642339826582538797040078835},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":97048563532642337994946689500682112805}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1007701129105453060978562894759599341383},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1007701129105453058460616698623421623697}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-51981095387601255816158632144296286881},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-25990547693800629448611831186931614027}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2255187249747400522225193789120874637605},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-563796812436850131535067181696039902191}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":691778391742285337239778491977154037095},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":345889195871142666654614675086111896551}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":98578897622675539736816264012595363273},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":394315590490702155742769540280872788177}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":50262142494966268042822694266824195549},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":3141383905935391575013008297482459341}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-204498193142664695458631447830637415827},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-25562274142833087231475096786605503555}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":209052620204412031939314942367053825987},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":209052620204412028972122877164733270987}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":33141506018700146210792603514938496667},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":265132048149601167445629437635436467483}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-472859891362188124150962383149600657},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-29553743210136867536278306995834699}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-259423891359282519049140921993105813423},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-259423891359282520889621323905736024219}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":578082363870742863532270435973073011443},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2312329455482971451417127205561844853237}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":70363846497574187},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-68947372470504469}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":3471580615244523},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-52762338742969129}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":21076768945385379},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":20287837449642949}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3427046715174453},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-4607970536399319}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3438453259091741},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-45971074487407}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":354322560255211731},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":165434247624942403}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-48694020255168415},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-113670332255541945}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3272266920308069},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":535665722480451}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":13790177302935},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-453139517108371}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":233308748531413},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2360219291312567}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-25336511829881247},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-630390977227612687}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-38307338737076359},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-80350724939841007}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":18920456941366735},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":122160510683515}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-1513882442092273},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-34300476056378621}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":1712753664599783},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":5356779098699697}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":2496671555259107},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":8529217093460225}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-21011034191983295},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-39040744421703119}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":19881645185692973},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1710168597627471}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-128826558420079},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1917990351488603}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-13335008261239},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-297010631633793}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":10236226383571371},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":11184271900991973}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":148279460302102819},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":20198013015323759}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":1417308332659687048801},{"denominator":340282366920938463463374607431768211456,"numerator":1535980233590187646371},{"denominator":170141183460469231731687303715884105728,"numerator":618179860458754327157},{"denominator":340282366920938463463374607431768211456,"numerator":1222078378064293426107},{"denominator":340282366920938463463374607431768211456,"numerator":1348429953336590592829},{"denominator":85070591730234615865843651857942052864,"numerator":239373915009470032779},{"denominator":85070591730234615865843651857942052864,"numerator":312027683804469691263},{"denominator":85070591730234615865843651857942052864,"numerator":278184271922693267227},{"denominator":42535295865117307932921825928971026432,"numerator":90108534030187921839},{"denominator":170141183460469231731687303715884105728,"numerator":457907665560069569517},{"denominator":340282366920938463463374607431768211456,"numerator":1258708575603134814993},{"denominator":340282366920938463463374607431768211456,"numerator":1540511493421682088261},{"denominator":85070591730234615865843651857942052864,"numerator":489380614377760747831},{"denominator":340282366920938463463374607431768211456,"numerator":1965263476194205301777},{"denominator":340282366920938463463374607431768211456,"numerator":1602243585259645283173},{"denominator":170141183460469231731687303715884105728,"numerator":710650779337939058365},{"denominator":170141183460469231731687303715884105728,"numerator":598283316760436793241},{"denominator":85070591730234615865843651857942052864,"numerator":370896736715716561187},{"denominator":170141183460469231731687303715884105728,"numerator":560176920832481737181},{"denominator":85070591730234615865843651857942052864,"numerator":219553618730944191487},{"denominator":340282366920938463463374607431768211456,"numerator":920235556865882030013},{"denominator":340282366920938463463374607431768211456,"numerator":1355943525461103192375},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":555},"tube":[{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":1271716710828790949785159171462034621},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":18717879553049872915627038849713318213}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-977526676397174876013591370016999911077},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-122654638334436164491225710831655169065}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-393992676942469886310220601289345794069},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-199381762930926866666491998510594344497}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":136491056782774202438684071093274063607},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":136197305370672588112091614791024886411}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":182201485164409510415146907077335484357},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":90201498648276643235521139569838299311}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":288620049747828653394381089946448909455},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":285036210530303030821553211680221913887}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-289015816088113700444716723476070720773},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-146210355129592291967290177355680871959}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-91904682880347971245770922432997060741},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-47330746247991031928012442296362013897}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1771560572677063074170574725395157253},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":26848646581599158619470338760872967}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":97326326128371584484931820158415505645},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":47312599754120898571884885144815781937}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1011971858378082388832963740106093734763},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":251772073269351088664034772812354507229}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-51120590917597102719440262722122247073},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-13029217907447330785877695457799238967}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2242475355713238575337339201523139450783},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1128327794344862708813542285751203696979}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":21621271230558785564148404095981393999},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":691349429515098320899579891807801542403}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":98699940181712941808449319942884015295},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":97554571177079244417184716082081947573}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":25238493115728869169830443971148829443},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":48524741251521784073974151689045703893}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-204410747173827265400823249988105114521},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-204759529324902361893041848791071617237}},{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":1637038383460450333562236714245348853},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":208943761599821225760902292470897223041}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":265264704173666154949776999818408942005},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":264268492914912532677409917573226369923}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-447165605615913051926697356473036899},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-498559435180751993350331172658515381}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-258608947599444724254253093642261592237},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-129775717585218980479558583556409655987}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1156993673400370469397518238938217498333},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2297946355799653618434570737668577316339}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":21326417516338479348901495092826229045},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":5331604379084619106670263738850811511}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-975110240079794165652439916864900107589},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-487555120039897084390512537637614188799}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-401877539516919912080988313960946553069},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-401877539516919914595497325550840733363}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":68026647446355738454701679917238684313},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":136053294892711474405515641248660026025}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":91691330141943580018462055049733729263},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":5730708133871473664766246979219586749}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":72764838583877812910071801816550562651},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":145529677167755624841391371961260843689}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-147371773380353481074699876730312286523},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-73685886690176741175340947629857374779}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-96586112722500812239079037115453217387},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-96586112722500814524987097611306836017}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1794852004969408860877342541996595349},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":897426002484703688944412375600863761}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":99212882979191510103124205928604566451},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":99212882979191508220092251256860646455}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1003798434180230584356633370125481563613},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1003798434180230581785812995146309693309}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-26362944216329793281590631880118987253},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-13181472108164897432221095975665494695}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1133206218935173619236908531369950838823},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1133206218935173621237224041679438518397}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":692079012476689073352783853482816479153},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":173019753119172267335855755768153498905}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":397968892361330724249800557026540155401},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":99492223090332680242352783424156360321}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":51817606571799894722076481952656019207},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":25908803285899945899390451899614796151}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-204207695285771543253346772133711772835},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-51051923821442886427470693488344753577}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":26070800223312365933548900090009814707},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":208566401786498924427255108215443282201}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":265882945123254507602807707025387187601},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":16617684070203406581168699391077818641}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-466111115806818254752268052251654151},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-466111115806820063683240156979001831}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-130066887047726277507193420818935609083},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-130066887047726278453970372556679691287}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":290627607297700544196921652267106809451},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1162510429190802175394739036440182147365}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":3348785459091581},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-23297342560311921}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":48288697044616063},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-7570677298049271}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":170781311520463647},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":24016421350336457}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":217502890078789},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-1114050144511081}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5832426149154995},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1221635059261173}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":365508843828939211},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":92552933353587593}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-22176626395227943},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-106424910587299289}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3324682932317639},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":80032015697545}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":31535936398053},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-361052702129511}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-257932050074283},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1331862853912859}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":-3011689865108013},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-698497947871021277}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-9325671771338903},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-38878622401153889}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":18749414076009377},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":8579464246756571}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-11082103955965225},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-8113624369776569}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":6357126368743445},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":4649366765586003}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":19923539002861351},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":8855415876016259}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-18136500928589327},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-2212848736142605}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":8466055543538963},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-258702332761819}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":392138518805789},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-793865373106461}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-54173320374385},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-583293522235309}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":18213450535309905},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":1163880505838421}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":69370923191142291},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":74025117626662577}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":170141183460469231731687303715884105728,"numerator":730505022408122701181},{"denominator":340282366920938463463374607431768211456,"numerator":1564214007798927321857},{"denominator":340282366920938463463374607431768211456,"numerator":1257193131560537194779},{"denominator":42535295865117307932921825928971026432,"numerator":156492207883651249583},{"denominator":170141183460469231731687303715884105728,"numerator":691099288175808066597},{"denominator":21267647932558653966460912964485513216,"numerator":61166376886454962475},{"denominator":340282366920938463463374607431768211456,"numerator":1275950982700504041333},{"denominator":340282366920938463463374607431768211456,"numerator":1142952688034523440675},{"denominator":340282366920938463463374607431768211456,"numerator":741493826081555184733},{"denominator":340282366920938463463374607431768211456,"numerator":941513442576189171421},{"denominator":340282366920938463463374607431768211456,"numerator":1285157312591333880929},{"denominator":340282366920938463463374607431768211456,"numerator":1582831332792353526053},{"denominator":340282366920938463463374607431768211456,"numerator":2000301050627535048481},{"denominator":42535295865117307932921825928971026432,"numerator":250583716126042458905},{"denominator":170141183460469231731687303715884105728,"numerator":820095339610985703307},{"denominator":340282366920938463463374607431768211456,"numerator":1461642255015149790905},{"denominator":170141183460469231731687303715884105728,"numerator":614125365915491964191},{"denominator":340282366920938463463374607431768211456,"numerator":1520559321494441316945},{"denominator":340282366920938463463374607431768211456,"numerator":1152052474584065428855},{"denominator":340282366920938463463374607431768211456,"numerator":904465221492262743377},{"denominator":340282366920938463463374607431768211456,"numerator":946772500534499780935},{"denominator":340282366920938463463374607431768211456,"numerator":1392915214263867279435},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":32,"numerator":279},"tube":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":10788682376301309494209042786399870095},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":9966487390011314476067465534528433631}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-30457008362311926164258358250059075711},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-978384444074774819137115002442903233717}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-397745608730703177880153373263351978803},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-50302175609054211090555745360382549717}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":68150967391852682925162969773320638547},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":135978194794787292649431355957126886537}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":91798233278619901280447856309932372061},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":45451987104669443412047455946724515549}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":291466332217033514680292550733293259019},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":71963788521934238072542634389843730469}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-291694578083105820747494988219492270447},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-295129667036833250060402290027753443653}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-94099462888726904356065226823174720251},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-96872610476236415077940758815769003153}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":903551657722292488375136728550686951},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":109617584361058105688506066679330129}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":99492252064162569093944493381739873209},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":96777042584695645650613599936228666587}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1008204452580073341584605425356265430869},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":501585608916935267762090060794313895781}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-51883401917167589423640681918062138737},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-52860336621504253348820181981380364619}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1126888889605435593201446578059836321809},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2267872484576164544625899483932669327933}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":346085711282282736214769598877388971865},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":691734721650920873406972700196492970193}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":398454637198057235146785299496154548217},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":196927848206053573460050561172975004333}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":26017109032262565607830773188392583735},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":12516311302364931132956104972816251987}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-204111431160333627366829228214405149209},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-102270583348128519508398806495169910597}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":209119600867142804165930088998690490193},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":208449794239835081899778624881347103687}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":133007119977249841838122828137547601077},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":265034026837945776753338746431138468569}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-440277412053742298854858436008458225},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-245974880846910457598304801981517211}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-259330967513418995963745186108669745621},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-32532525746506778352212817844250896011}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1163334630678115686872146922995473032493},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2310736143719275904491886467492053245759}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":11283161997260930249283640953492191569},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":2820790499315232185964832897051387539}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-972174634353230629587795929245079802931},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-972174634353230632772990990667749526427}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-405462206379862215728459878937100264945},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-405462206379862218286847561233136448263}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":135812350436764434564254986443512704915},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":135812350436764431999084284969654367607}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":184770402882275401076429915490302185541},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":184770402882275398242993068221169217601}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":73480250573275484014560435802153424013},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":18370062643318870878631422858301045415}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-148735249640870450882861373708295908737},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-297470499281740904373880413319393457925}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-98808611438858412843402318290528623303},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-98808611438858415191319637258000184323}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1830562716426003278556429365009563873},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1830562716426001753204352641441224781}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":25347150189449726769318174787208315489},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":25347150189449726285362700664367355857}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":999782061665069805872963391557000070811},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":499891030832534901625167541432525956917}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-53453995675895243095778539005884026057},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-53453995675895246348312484701215735911}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-71174021917317389918895119399153330585},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2277568701354156481492601959877624554619}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":692305489627789751029458867024130515025},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":346152744813894873469887976357135813527}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":401635443354234753065990919106431205095},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":401635443354234749707976729951822153541}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":1668322878683909482849175010331106935},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":26693166058942550222535317494566845089}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-25481527623966874316975539170977961541},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-101926110495867498528568446602011699853}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":104010988656478691268424372783802654621},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":26002747164119672427517234054263575983}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":266620778312078089266443890580003475561},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":133310389156039043448647909054004147327}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-458487472789500210185333763196019995},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-229243736394751036543425765178379799}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-260832826589768637706819524391385096995},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-130416413294884319827426275335005583065}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":584405670428453614833660310817493183913},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2337622681713814456473053693672226029315}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":141206323814190035},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-51788827347221195}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":41371118093289325},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-33424121338289973}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":170103446935712659},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":52796717861010213}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3499537404624295},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8574905607683719}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4824459829053931},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-507916083319377}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":368115523020035907},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":197197165693577975}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-19760422673821675},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-49160634883542587}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3333697505495273},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":359297191544665}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":557986170847815},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-276991531427459}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-437545031730743},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5821299194172013}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-66866468760124677},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-93745213710386497}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-17742158157066323},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-74247878732709467}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":36767078350581015},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":4539592454824743}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-10004893316690225},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-15243025358871603}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":2928222675009053},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1973999977852101}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":1224484228128303},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":4460796389171751}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-7541716614292711},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-985063806979647}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":13999978611113313},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2622827769281079}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":431641530883235},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2541400590896405}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-50815271602143},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-567272699825959}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":3963140036239607},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":3690181386941713}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":15983404270105779},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":4130772371508629}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":1505327811789705935797},{"denominator":340282366920938463463374607431768211456,"numerator":1592522735471903282449},{"denominator":340282366920938463463374607431768211456,"numerator":1279135187783480740435},{"denominator":170141183460469231731687303715884105728,"numerator":641289656757711507323},{"denominator":170141183460469231731687303715884105728,"numerator":708357497786242659125},{"denominator":340282366920938463463374607431768211456,"numerator":999984029559235255739},{"denominator":340282366920938463463374607431768211456,"numerator":1304049432739191099313},{"denominator":170141183460469231731687303715884105728,"numerator":586978675966087288769},{"denominator":85070591730234615865843651857942052864,"numerator":190668905218233257977},{"denominator":10633823966279326983230456482242756608,"numerator":30247139848159892625},{"denominator":170141183460469231731687303715884105728,"numerator":655536453214326390927},{"denominator":85070591730234615865843651857942052864,"numerator":406561897766614141629},{"denominator":42535295865117307932921825928971026432,"numerator":255495653200704815273},{"denominator":170141183460469231731687303715884105728,"numerator":1022415608288114458747},{"denominator":340282366920938463463374607431768211456,"numerator":1679003212131932359771},{"denominator":340282366920938463463374607431768211456,"numerator":1503046147593295011197},{"denominator":170141183460469231731687303715884105728,"numerator":630324925654752545203},{"denominator":85070591730234615865843651857942052864,"numerator":389586781290889538373},{"denominator":340282366920938463463374607431768211456,"numerator":1184572333894171259015},{"denominator":340282366920938463463374607431768211456,"numerator":931450500654866257893},{"denominator":170141183460469231731687303715884105728,"numerator":487006138520313748533},{"denominator":85070591730234615865843651857942052864,"numerator":357690721840191249771},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":561},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":22817958858350785346582073481143610217},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":21160690700559330991136497097096177185}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-971684829951354557286972239037548804445},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-975490841205176347835919835101528691899}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-100355122676899692699235789040739871269},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-405990978800810183637394731943806909453}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":68044367006280803846409514325708034427},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":135734342814060299858662342681052322133}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":92491659707883148146524798345083621055},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":2862575144831779993805814990383814691}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":294330829844162040778306011853273628489},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":290695857056772272894391269463657776637}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-294397290655967301264403391451194015319},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-148929925851681955057183504673238168515}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-96307133517308309225304374633004292079},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-99096925569233339363050997258470289605}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1842705752058953177219238391895829941},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":894767460979728922314944828949899429}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":50834811488126953885439298478635526433},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":98939911868406797158893768156923572903}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":251078972912986283603590743572056770609},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":499570658467399816918533467429897574881}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-52630210469282239330066684741158119533},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-53586990103055711661212472732933413705}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2265011556169292565671667539125020405001},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2279020373179839293693162773074809875899}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":173097030815456519158782808516625111697},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":692044666833896068533233221606735139317}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":201061323198143596952572720226698203581},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":198753682067612223099386994128546375007}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":53604702690226335596770459551461468471},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":12904760084104793955306627117828088861}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-101873540639980165552366417664214127115},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-25532359327468821194362429255616460339}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":52160178456755998786026088377398648771},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":207897593421773318386972827813457076357}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":33343837443567131795563004909675750573},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":265786527964889777624720873455113524713}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-432511281083331701097827608856815241},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-484468282937372175222461403563623363}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-260042178701547096326346374043483101645},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-260958132640601683206751047788341011303}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":584815314014781088845963923775130896321},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2323438591972991016945658336833788456273}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":23815597646000621475038189509920100877},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":5953899411500154593605735796870100281}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-484602334032007347669238186501648881107},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-969204668064014698580333385802461802109}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-408965115546014165171816984513991569925},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-204482557773007083888153046813134373025}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":135546194182311731058271746122362410343},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":135546194182311728430210434532312578471}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":93075002872594335984736645706607083769},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":186150005745188669065482202517176264729}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":148399201681254440067850456772406244113},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":296798403362508878092626472591271192521}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-150108384664427690194469840468115000805},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-75054192332213845763449893014630325769}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-101044519261456755450346413174099881667},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-50522259630728378930943774353549399811}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1866314897701069745132889706113151695},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":933157448850534088138101787495933309}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":103576053002883262766265904959056721315},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":103576053002883260776227208131929673123}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":995658671174519367740879271916380164801},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":995658671174519365067654804303157393615}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-54164855104502339944650167067010169369},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-54164855104502343286227760360432844965}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-71520495507291269745743960293354520613},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1144327928116660318020441986938188341019}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":692458949158082743846329144796344556415},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":692458949158082739674768081595792671173}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":202657164062613887475098544057530641685},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":405314328125227771512775807416095457657}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":858879817709942471941615338913335707},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":6871038541679539389147933781447548377}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-203430921483889084581944694827342336897},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-203430921483889087169512369149786652427}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":25927355576893696201067993249071056121},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":103709422307574783207304959783144486901}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":267345501312191212989308603569605041081},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":267345501312191210553442504753003152033}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-224987677585814366495764452188001369},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-449975355171630651371898624751289961}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-130760502326224788470961666722298958025},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-130760502326224789472936441556264434285}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2350133075388526905831362709585872838293},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2350133075388526902892336595976599088771}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":84999767718849857},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-14635072194557757}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":8737768441914883},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-35913223094889033}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":167054635682874001},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":55394155763746761}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3495552156550797},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-1028067241571751}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":966036164875259},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-700017906185523}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":181827414100477239},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":12554342747278131}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-17156300031551689},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-44879327538104197}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":413520299141177},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":95729823795333}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":605246213719943},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-203925272588009}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1375019964384615},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-3105053611642591}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-161650248481371051},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-195803352222433061}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-8193712339046163},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-69893035798554789}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":35656608234902369},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":9244775027839227}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-8868108941546859},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-28417397036620223}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5353368548218889},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1628357274336785}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":9483653475956179},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":8698829294814023}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-11859278171065701},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-55100390131294463}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":11209832682051377},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-575297199953729}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1283783693120729},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1953191623777375}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-42631523393429},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-273554735402811}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":3375092184122783},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":1350651411950639}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":7251354530998299},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":28478705027710913}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":85070591730234615865843651857942052864,"numerator":387553826464350930285},{"denominator":170141183460469231731687303715884105728,"numerator":810428821051359735691},{"denominator":170141183460469231731687303715884105728,"numerator":651094362158089512221},{"denominator":340282366920938463463374607431768211456,"numerator":1314024795749980353533},{"denominator":21267647932558653966460912964485513216,"numerator":90749513271242301865},{"denominator":340282366920938463463374607431768211456,"numerator":1021455827804648395661},{"denominator":21267647932558653966460912964485513216,"numerator":83275138908352443639},{"denominator":340282366920938463463374607431768211456,"numerator":1205769296604598075601},{"denominator":170141183460469231731687303715884105728,"numerator":392213969239908744281},{"denominator":85070591730234615865843651857942052864,"numerator":248754232717483518453},{"denominator":340282366920938463463374607431768211456,"numerator":1336382277350647890521},{"denominator":340282366920938463463374607431768211456,"numerator":1670770237553490152729},{"denominator":340282366920938463463374607431768211456,"numerator":2088525416327912479639},{"denominator":170141183460469231731687303715884105728,"numerator":1042885378478114202969},{"denominator":10633823966279326983230456482242756608,"numerator":53709591104319032211},{"denominator":85070591730234615865843651857942052864,"numerator":386383705370151999987},{"denominator":170141183460469231731687303715884105728,"numerator":646884073122163788117},{"denominator":170141183460469231731687303715884105728,"numerator":798479553553999448489},{"denominator":340282366920938463463374607431768211456,"numerator":1217931430920642495471},{"denominator":170141183460469231731687303715884105728,"numerator":479594966310606968757},{"denominator":340282366920938463463374607431768211456,"numerator":1001970725952421131971},{"denominator":340282366920938463463374607431768211456,"numerator":1469483524673416599281},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":16,"numerator":141},"tube":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":12033857012455611919796857358037751937},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":22399502880034150115288101649890249299}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-484355706329407038752414142765037163223},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-486279718381860680568060090185913566299}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-202507748434349210470556558142574898847},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-102370647995084092203645185151407803663}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":33962730229971548957401076803229890947},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":67732608044334291588055550858937115305}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":23295252730849068695042793611944682439},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":184593556330662381429954259013012384549}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":297210732872744811591042913638724397793},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":293555476673141614332220526832268845895}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-148560883515948240016633305902616312119},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-75152272382585174339456991429950325261}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-98527936812066460381489391008870698271},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-101334683079985985000618661626426693037}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":939173422554781276881814729605019969},"lo":{"denominator":2658455991569831745807614120560689152,"numerator":14259791943706992168645741975849785}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":25964693748097327182705935458413608341},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":101114136953955526964853809171335171707}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":500156409222400875105404904892357251071},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":995005250647482306832345629706593444389}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-53360409065108783463755098278613072267},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-3393517198310836236499343959518709663}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1138088218586127165405521790226323098607},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-143131192436954737296690373841014172295}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":692531915866925997310179161895669697789},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":692280331156774608009731151449780368577}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":202901435557415832330902951932876741971},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":50146549478159942116916130464631177721}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":13797107786795536927298530762260263061},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":26593049446203825374528456924626255221}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-203316859561053604881637284570063188377},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-203911705595144040632192405518799340471}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":208103678740347808164263785817127744137},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":207286664466443551890113385520926650743}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":66868508539127639138430941124754907103},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":266525972107141145824359379375782229175}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-105963387224328528172992057516037989},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-476101449363887464804304412555525361}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-65185641611373375487784332375755489581},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-261645167888244859507959276187630089481}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2351761497154761497904408817740413221547},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":584012925555093974078503558799522883779}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":12536349648248260205597968157361651319},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":25072699296496517219743607829631381147}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-966203327534458770828549511895595246401},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-483101663767229387063525466789148877059}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-412384724518217381445961755754111396975},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-412384724518217384098779190578406719217}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":135254293904797422704707309444854431939},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":67627146952398710006051954790520268005}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":23440180903742143239830624463377774065},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":187521447229937142942551982093921176771}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":299688778563512666325195100611124633991},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":299688778563512664238893278103569265341}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-302980195478166983416271263193870944871},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-302980195478166986138335588957118972301}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-103294083977609855841546925661374261657},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-25823520994402464579590854948188900379}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":475521946801739059652550475560789961},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1902087787206954625078576100728417667}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":26443895170775522644922113791418482635},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":105775580683102088533972640554879949241}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":495717458119150397488599751138677202603},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":495717458119150396127369479406188323541}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-54857945625243227979059385901803272711},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-54857945625243231411911288720954618049}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2299673774775219151315697347971220616363},"lo":{"denominator":664613997892457936451903530140172288,"numerator":-4491550341357849913249423836470174051}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":173135141885281619012767161518445235113},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":173135141885281617949006976858248471033}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":102251152887783695890888012857248996133},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":204502305775567390022444500745812572169}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":56563539539634029017485850650022285723},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":14140884884908506459804033126330722011}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-50735758823162363429531236131847975127},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-202943035292649456373374014194462954059}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":103378282024613172658758777229688989491},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":206756564049226342044694771057523516717}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":268057048015362300526513707888584697943},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":134028524007681149011107177664005852253}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-220281075891582715942564488095239989},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-440562151783167407292852184403912063}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-262198238025192146738074097548873553857},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-262198238025192148799409961735457054431}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2362550320995545975031693042579179650585},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":590637580248886493003372708793474822539}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":193344230780324495},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":8790849994126627}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":58116362472893757},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-75612698501365215}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":162052321915966079},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":56219978098716285}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3470186842114069},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-7877279265812549}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2962434360209123},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3491896199805505}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":176359933063039609},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":49400390296354523}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-7223784833401745},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-80973240704703493}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1625198518871345},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":390821049795695}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":643009842281647},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-142622407190597}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1760614873353709},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6490693200894577}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-180775234400028139},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-798890358469447759}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-14676879941593805},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-64854713406299371}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":17114380558938845},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":9109157793638161}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-3848312543344541},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-26291347185399423}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":4856270897828677},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2586053944852061}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":4523526402897953},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":8223042859400001}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-17159241086846217},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-47110430995184035}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":8589980463944927},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6418992957964867}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1651911879151089},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1416361525168213}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-30316012346727},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-261521014859373}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5593368931482673},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":860775412903775}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":103483240024398225},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":47030814640723187}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":85070591730234615865843651857942052864,"numerator":398909570744287481281},{"denominator":340282366920938463463374607431768211456,"numerator":1649183846310864124371},{"denominator":340282366920938463463374607431768211456,"numerator":1326355801240239036223},{"denominator":340282366920938463463374607431768211456,"numerator":1346296026198852984655},{"denominator":340282366920938463463374607431768211456,"numerator":1488043279641270500559},{"denominator":340282366920938463463374607431768211456,"numerator":1043073352101307353761},{"denominator":170141183460469231731687303715884105728,"numerator":680503061915469232729},{"denominator":170141183460469231731687303715884105728,"numerator":619203506344110797139},{"denominator":340282366920938463463374607431768211456,"numerator":806765420084632634965},{"denominator":340282366920938463463374607431768211456,"numerator":1022855542266233220215},{"denominator":340282366920938463463374607431768211456,"numerator":1361011601787654183321},{"denominator":85070591730234615865843651857942052864,"numerator":429102050233203529197},{"denominator":340282366920938463463374607431768211456,"numerator":2133991268349092129109},{"denominator":340282366920938463463374607431768211456,"numerator":2127511071959344172989},{"denominator":340282366920938463463374607431768211456,"numerator":1759327961724760017449},{"denominator":340282366920938463463374607431768211456,"numerator":1589129923540973602933},{"denominator":170141183460469231731687303715884105728,"numerator":663804779619290678933},{"denominator":340282366920938463463374607431768211456,"numerator":1636403887214216276235},{"denominator":340282366920938463463374607431768211456,"numerator":1252148142143584337067},{"denominator":21267647932558653966460912964485513216,"numerator":61731475952568626877},{"denominator":340282366920938463463374607431768211456,"numerator":1030664060275186075163},{"denominator":340282366920938463463374607431768211456,"numerator":1509072877489948342695},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":567},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":25325091782318271874895270117726653831},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":5911969018824664218592615543279280607}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-965706992241869929304112486599577156855},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-60599581169432479559022370650167111943}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-408528937382910676992696874964724689133},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-51611339876743194847987246032296280187}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":135587962160244840012359057290122412951},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":135170282380913750471485947811545642427}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":187732552551745884734945147340668966303},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":23246770901390844526664956606000978131}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":300103265781799049644798181807782575113},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":296431196427032192364607393545100677171}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-299865830364474953115907059633435165845},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-303375220008279225846233270462360267943}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-50381059003983719921708828503643721571},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-103586130542860595912705216476388572833}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1914005584760423010511280787998259101},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1861015932472250972472305862544127947}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":106060048945458688534094311785763133711},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":51650026726854106623787653740806130109}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":996201893471300579615508756040508779331},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":495384835251744230434606958499122944793}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-54073430554217748760243810614813177665},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-54987676057063660604307372937759839147}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1143636115543980135429474040966709746533},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1150554241270781940453767277136823951505}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":346301992464147580439071579755322831471},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":173110708518125895440820490395784938701}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":102373593614705611959289514644707758581},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":12651558704143941900314583379802431551}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":14196352406949675158062717789266096799},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":54766408189618272277731536573301803045}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-50705003781018527026223630551754185289},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-203498799968312973732247685721097004297}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":51876996418953367017291270841396844895},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":103308287534587241731476855917210664507}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":33523021911541532113885522072893546215},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":66813078828599440239537246354107219307}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":-6473305590300423248651160982452551},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-233418348635975333947272596025376753}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-130716044895709532173730590400798658155},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-262321238401724190292082705032580058151}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2364168282847503005115471917505954500889},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1174286803946542556878216335558945173959}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":13168046199329261646623312790786289011},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":6584023099664630002489060088563714827}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-120396690676702241316843076053375293047},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-481586762706808966944902518802491499143}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-415719616902417933967179595462743976325},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-415719616902417936670561364951687096157}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":134936119137070137624065481421974252073},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":134936119137070134865217562955556762991}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":94442352956214451531165078393392179475},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":188884705912428900012561357222772692871}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":151294694085668737010982665434014214695},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":302589388171337471892152391664561731605}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-152879316620041580343688067286421779531},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-305758633240083163467142018075608359911}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-105557554931792112347876902103966828869},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-52778777465896057445828907222207077005}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":484465172119859269603918286032827417},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":484465172119858854752191463547018661}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":53993764276932885653230108764689164011},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":3374610267308305287611658692211322447}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":987117424286515760364164271959992247059},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":987117424286515757593976104959996571339}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-27766393678407092958539910947719931435},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-27766393678407094721726290602071441431}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1155311191835588679800728998312200000197},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1155311191835588681981112698887832904269}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":692551569288404306081119677889764206119},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":692551569288404301740952274576046900763}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":103176334926472529762525722120726743811},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":412705339705890115448310066814136130175}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":29086022589128037626340516095858309415},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":7271505647282008998120638492576834383}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-202387887576968422482660115824728917071},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-25298485947121053150880490137423699757}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":206034757731582135859365458012753673053},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":206034757731582132505971337848959535823}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":268755332694529477021606329512978412989},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":268755332694529474447120994745056057531}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-430236264462108341180003073055234867},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-215118132231055187602373905926977583}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-131432215294332595484622169112600704539},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-262864430588665193089469349045545836425}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":593718207824028522777527376370643040493},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":148429551956007130500687819897684068009}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":211197666491976059},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":43091525502992095}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":47579756571190171},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-78609205463634723}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":155670356515555511},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":13856222269100215}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1723368383299195},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-945513886068051}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2149235331131965},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2049853204595545}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":168032314502529367},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":188567525081138661}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-5813384521417943},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-36106402018159707}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":395787741839915},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":770101779396249}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":335395849644173},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-5746808655127}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2032790392636573},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6657746538335415}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-381480210311985359},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-49875639501500655}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-25469615053329373},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-14855147303037819}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":32596074658517841},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":1088050508155833}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-3243743341887623},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-24172087818421391}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":8750719054828851},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1932963645483545}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":17050730523802167},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":7559607868547593}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-10735579866410633},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-19652548276610583}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":773497361101353},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-4028809846486633}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1973476151722977},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-936247344975537}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-15161378396117},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-62020011866213}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":4483100343810855},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":783457529898747}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":90745166355254705},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":2300714257606533}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":170141183460469231731687303715884105728,"numerator":820780569771582183687},{"denominator":340282366920938463463374607431768211456,"numerator":1677467120107972914507},{"denominator":170141183460469231731687303715884105728,"numerator":675820381005375991295},{"denominator":340282366920938463463374607431768211456,"numerator":1379418453809281173141},{"denominator":340282366920938463463374607431768211456,"numerator":1524881275311135671511},{"denominator":340282366920938463463374607431768211456,"numerator":1064832721049771388855},{"denominator":340282366920938463463374607431768211456,"numerator":1389858462118407076603},{"denominator":170141183460469231731687303715884105728,"numerator":635944629035073000517},{"denominator":170141183460469231731687303715884105728,"numerator":414851536137326366161},{"denominator":340282366920938463463374607431768211456,"numerator":1051441257211235155437},{"denominator":340282366920938463463374607431768211456,"numerator":1384885818489141825299},{"denominator":85070591730234615865843651857942052864,"numerator":440792351041818024761},{"denominator":170141183460469231731687303715884105728,"numerator":1090185877370168134241},{"denominator":340282366920938463463374607431768211456,"numerator":2170074859356291329605},{"denominator":340282366920938463463374607431768211456,"numerator":1800893001956680749881},{"denominator":340282366920938463463374607431768211456,"numerator":1633853216564223344595},{"denominator":340282366920938463463374607431768211456,"numerator":1362177617878986935225},{"denominator":340282366920938463463374607431768211456,"numerator":1676689937282606176569},{"denominator":340282366920938463463374607431768211456,"numerator":1287241212522212828471},{"denominator":340282366920938463463374607431768211456,"numerator":1017012131870041093355},{"denominator":340282366920938463463374607431768211456,"numerator":1060108805767358301565},{"denominator":10633823966279326983230456482242756608,"numerator":48422663334084273807},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":32,"numerator":285},"tube":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":13294278533546421081253090748376387007},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":12452135327659573890829438588918765661}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-481337235715917958543340057536214986415},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-483297711328486212454657179050531712439}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-205979626955917863475739505936512788395},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-26013372498478266993519153030303782693}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":16912415663073621730381675123671145633},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":134849011306673462459592487743245089369}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":189094890405163534416371574979761503837},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":93673310105233771944952680208912611573}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":303005693042318468108832297007894356269},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":74830058127578004841113902273021528933}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-302627317202614560026361200536706040793},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-76539024989534698481365456227332956505}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-103009924757576176641630615218191173325},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-105851516957912968640793717450998801091}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":974830516443554615915427244144046555},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1896801871020270779883878257774758667}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":13534223666061237103350448720188554787},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":105498001944725665390324757065363088729}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":495994886830955771276859961145611170019},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":246610299856451016697128931087891561819}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-13692187163400574730894734521013639377},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-55660718370011589478383414062518453979}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-71821837601258521608828333541779540241},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2312048518589737289814413417480675318667}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":692610086387615679999172241729048481651},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":692492632454556673109797581506754363527}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":12912381275554504004701732273324775211},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":102134719852600102008289849443634316141}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":58395659469649162914690947758950921855},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":56359970658521232830830041677250522559}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-202255883486552388871525968414175959021},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-203019385493326908318023797303275204125}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":103426593664549882578825993526380682533},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":25735869316295695844538457914743844973}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":134440517435803356064432873887350168071},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":267965493920224029788141978145154828151}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-100953418275504405170535998032434605},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-228331232941334534580904657291189779}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-262110681688579526445458990711198853091},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-262986245054705729371610056888922605197}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2376480042726355581313130445439019212721},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1180501287068283563267876550227830579627}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":13802124533078724776869464116487764993},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":27604249066157446177683549527620926531}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-960118099859432674050680308252592050017},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-240029524964858169365536360713430358775}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-418968497562548807035802676010532955101},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-418968497562548809791996040025497511007}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":134591141946280635907712679176564134691},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":67295570973140316540432889788870288253}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":47559940044840891669352339901297385779},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":11889985011210222722022792278848745535}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":305497536984804861254791846962839834109},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":305497536984804859081191008095985677225}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-19284372370225002533449266104367386231},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-308549957923600043373148717482274580639}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-107835182266901136623676646614166951667},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-107835182266901139236149085502303460833}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1973613012793691404574753465072051711},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1973613012793689698061456680362196765}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":110212244117002451414269663940191499771},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":110212244117002449252682686213515413919}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":982712777790707526578225469140240985091},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":982712777790707523761970191755306330475}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-56188941736829309668036477382371159059},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-14047235434207328322547603489642100071}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1160750831126108149686304194012060949409},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2321501662252216303827981512927898698345}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":692493224534976101652307684923098955259},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":43280826533436006076582571870611229915}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":416415540815148435984122982642772180133},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":416415540815148432297258026176206805311}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":59793859753646025997383458798208273429},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":7474232469205752829740147001236419483}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-201764889246202021885328940279010338017},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-100882444623101012340153545201141448465}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":102626554346575877110528169502307495485},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":102626554346575875392695800438489610259}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":269440250122783974920062304029966127245},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":269440250122783972273600003363109695963}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-418987122345873909797613635334326205},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-209493561172938002035601726410363847}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-65879865156820871107717975917936093673},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-263519460627283486611522600130878048787}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1193549574668109328181753026262779822625},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2387099149336218653181787807131173530157}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":111781821211559113},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":15827723774462557}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":38208017221968881},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-80678891086470501}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":74097451378516295},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":53354043964856501}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3401556185314887},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1820455559991833}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1428275546999305},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4617562345224209}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":314689195827170305},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":174906483583473581}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-17630616585884965},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-31806734183446671}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3058463258153911},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":734026451637969}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":688791684621255},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-12581201177307}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2207851756678137},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1678239131006519}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-386913937535469075},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-782208491814040981}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-10646922405895971},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-3353864027514415}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":30784861111668197},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":4046876963408707}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-5279524702524599},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-22086310916230223}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1957802588318331},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1311779746452093}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":7926753501467159},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":3377944742083385}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-4580164622654177},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-3969146549839633}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4003290327997511},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2375213599787883}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2248044632675587},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-63861651579509}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":854624186893},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-466857909262397}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":6856741365282461},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-97133257626769}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":77948353904026813},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":26592550477815027}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":21267647932558653966460912964485513216,"numerator":105496722686188416733},{"denominator":170141183460469231731687303715884105728,"numerator":852836561923205236425},{"denominator":85070591730234615865843651857942052864,"numerator":344512315394521547477},{"denominator":170141183460469231731687303715884105728,"numerator":706709054055099568991},{"denominator":10633823966279326983230456482242756608,"numerator":48828728707901834235},{"denominator":340282366920938463463374607431768211456,"numerator":1086730528077305230079},{"denominator":170141183460469231731687303715884105728,"numerator":709478619240153848141},{"denominator":340282366920938463463374607431768211456,"numerator":1306235057225664996611},{"denominator":340282366920938463463374607431768211456,"numerator":853256278834110262231},{"denominator":85070591730234615865843651857942052864,"numerator":270197809077738592239},{"denominator":170141183460469231731687303715884105728,"numerator":703964995707664020677},{"denominator":340282366920938463463374607431768211456,"numerator":1811060784298284401263},{"denominator":340282366920938463463374607431768211456,"numerator":2227675216898295974371},{"denominator":340282366920938463463374607431768211456,"numerator":2213484864103552785497},{"denominator":170141183460469231731687303715884105728,"numerator":921714609258989638397},{"denominator":5316911983139663491615228241121378304,"numerator":26245728009146860547},{"denominator":85070591730234615865843651857942052864,"numerator":349368872139437062003},{"denominator":21267647932558653966460912964485513216,"numerator":107364101061965894419},{"denominator":340282366920938463463374607431768211456,"numerator":1323229770864505559811},{"denominator":85070591730234615865843651857942052864,"numerator":261784140156291095663},{"denominator":340282366920938463463374607431768211456,"numerator":1090321822725626569047},{"denominator":340282366920938463463374607431768211456,"numerator":1590833444795479951653},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":573},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":27856584227344478814517106118128235391},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":26167148862137857920560588358377455793}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-959616511325456197245316026584775550021},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-963568749201191460183637150184897520933}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-103826239785069718647100179516096347421},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-419451536761669468376189489848948000541}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":134984507428415551743879360998810827279},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":16812578064370176318217570928683541347}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":95224507023434705515586559506140528355},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":188710893897491065454937827890713624049}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":305915324316693332304694955132976984735},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":302219839710742376290758773257068563973}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-305404080670964660953017531672392210139},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-308949606362149658296603558477882443811}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-105271606364901580521917275628211756641},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-108131092033806898781513538186739223363}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":992646183038392177884206679276891561},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1932590502079729981591026998255967529}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":27625085814240610670776131296454247103},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":107708326920188361039180694902531437675}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":30865096631408147892290725812495269259},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":982026413019611010661913687800308179553}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-55445878264028811603378730231419599725},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-28157484595941277370194822336299487809}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-288657009199664424988329691985403774429},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2322919174335934996854842141095904989497}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":692564693917565240131655659343431038467},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":692433447625955899626295847005785970539}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":416907376816664354358125196615951948919},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":51529805836697733335069103740644251351}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":60019217089186657917086755701887250901},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":57966803854819340214729369056137360465}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-100811942835345504191364746970012594761},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-202472776677665915965301079916988227399}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":206138898267770850246416162854985031031},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":51274373226470926593977279157923676701}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":134782252666680543528682015121365715653},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":268665424623548184157093990556533987605}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-196204648779785920664573912281298101},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-445568211687133747814885446271017229}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-131389124594988120109029508330871258359},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-263640063176865747729912230097308184765}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1194347668407603621477644652322775661273},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1186668498674774090953042326488048683519}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":14437827936697611808813064866239465437},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":14437827936697610073977902145592283879}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-119629976756932102995211970613846195439},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-957039814055456827429342355899646418005}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-422130187751910507129721177114340168933},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-422130187751910509940991099806574206315}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":67109418869367465644224938622425415025},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":134218837738734928391800209035166879407}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":191586587835545727400832572643222702891},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":95793293917772862099442815757876122285}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":77102644760007705193483487034368547347},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":77102644760007704639068539251747663035}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-311352067225894650181954763077027453997},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-311352067225894653078600351846449939693}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-27531804043274030105032942310352919577},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-55063608086548061551530719739706688793}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2009324320548184056354703174815918845},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":251165540068522787684045210475297405}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":112450076589782117695858818572338865789},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":112450076589782115474008751358675813565}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":978227496610876134795165932892375992809},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":244556874152719032983664400018520180535}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-56826011450898810788118437192495890235},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-7103251431362351813540697269925666209}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1166155820367589524662917086431090549607},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2332311640735179053877674367430369523567}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":346183423343450022868116410086865392051},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":692366846686900041220689100380333962521}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":105033556547357725810875602067264342573},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":420134226189430899469567528873263784141}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":61429032718644494682866430979905246205},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":61429032718644491229313666264159965785}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-12567095993624194957195850839321158361},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-201073535897987122182171282708971550995}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":204411359961227047656933510030381644377},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":51102839990306761034320587208756854085}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":33763959465455676249610366797111997865},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":135055837861822703638306812491052879105}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-406805193440966260377776918300996855},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-406805193440968416575200474702878341}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-264163181146981816629224340893876290743},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-264163181146981818871871661198441848159}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2399227947206058848946484665391724036749},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1199613973603029422840229094584937211605}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":231113407377267359},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":78784456392848927}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":30033608092177685},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-41165249258184861}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":34985791552205341},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":50272452162795125}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":834606680312709},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-7032923652321193}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":49605399777227},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1261344944568351}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":36201188433933007},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":157878082324004865}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-11696214306609457},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-55348780734761635}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1466790608232587},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":663015024717721}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":349124153899919},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-2240129735485}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2292221940019813},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6667473871678481}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-23790934036862847},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-188499265829584121}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-2115180563474379},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-11926577395346551}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":903077210510491},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":7305353946571771}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-2045371065886629},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-20082990707506625}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3481695841580259},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":363623292208187}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":14534043272175879},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":5831730033767089}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1207844539556175},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-6136995843357703}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2047000026824295},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-10797458984335041}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":312663860986587},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-140829450660809}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":1251180986717},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-218403706637041}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4882492745937819},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1807577754195375}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":65289266628594289},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":4145309380541679}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":1734758998245154972341},{"denominator":170141183460469231731687303715884105728,"numerator":866883556720567076771},{"denominator":340282366920938463463374607431768211456,"numerator":1405590125989094005571},{"denominator":170141183460469231731687303715884105728,"numerator":724159824214827594653},{"denominator":170141183460469231731687303715884105728,"numerator":800485275515323937321},{"denominator":85070591730234615865843651857942052864,"numerator":277191007463167009757},{"denominator":170141183460469231731687303715884105728,"numerator":724150484050748583379},{"denominator":42535295865117307932921825928971026432,"numerator":167682962479488121989},{"denominator":340282366920938463463374607431768211456,"numerator":877440812660833927943},{"denominator":340282366920938463463374607431768211456,"numerator":1110922845980865696777},{"denominator":85070591730234615865843651857942052864,"numerator":357516873837445842467},{"denominator":340282366920938463463374607431768211456,"numerator":1860088178050917924131},{"denominator":340282366920938463463374607431768211456,"numerator":2275909300725699330205},{"denominator":170141183460469231731687303715884105728,"numerator":1128881931886205272053},{"denominator":340282366920938463463374607431768211456,"numerator":1886964321625347421003},{"denominator":170141183460469231731687303715884105728,"numerator":863386015600626717907},{"denominator":340282366920938463463374607431768211456,"numerator":1433505956725960015115},{"denominator":170141183460469231731687303715884105728,"numerator":879909579184085767175},{"denominator":170141183460469231731687303715884105728,"numerator":680066666813612917801},{"denominator":340282366920938463463374607431768211456,"numerator":1078098483365046409965},{"denominator":170141183460469231731687303715884105728,"numerator":560660157558516356055},{"denominator":170141183460469231731687303715884105728,"numerator":816494442048185796491},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":1,"numerator":9},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":29127662789518733717827691155248958497},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":6858745218668214668305772275609362535}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-956535718740035616275672122725879708337},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-960516142206032350927309145334484210913}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-418564694532882307580837231342735487829},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-211301362414773651065245837910843452495}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":4207593893302733430582242901339130809},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":134124378191619131069440838378994929477}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":191794901489537223705391300967847645317},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":190066966700455379090917273494325376081}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":308829519103848803805559173786364928709},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":305127316749355531889594544997163176443}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-9631062292761720936037569626557401449},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-155876819460312387886531261025613462047}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-26886853256406657291344766578835600647},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-27606276359592925937088716776141159455}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":252609864667913631195629047403518579},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1968361245621509770116614691707840385}},{"hi":{"denominator":664613997892457936451903530140172288,"numerator":220195428594981650134288832238067557},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":109931375747710431962007886425582254939}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":983288439536892638868627070901021918395},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":977531822075041515964611055492235840907}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-14026093900030153237068246051930866779},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-56950036967207580145907913755177130989}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2320144014984024660909501279115406481825},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1166860243832970522770286183001768698099}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":173128695772837896722918279719090360399},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":692299197527596734498018781542759833781}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":420626912246219729602964904521166697683},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":415947610656140510374401706115764233319}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":61656133859471669731877130317226033959},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":29793470204277142035963034865703570507}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-200923527129131755580196989683521376031},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-201858373925876499024763768504258983203}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":102682397046977604276041144289534966719},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":51061985021480166310455698758385941079}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":135117229896416873179310599421519145197},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":16834500287743097058176241892979412595}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-380068882658768274324094278478178571},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-54193052511272738075453117427642809}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-263434673710820129691066050479919463355},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-264282542875453677089124580199145321169}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1200406427135707922385278485950076628743},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2385575404343418965227480121912506532059}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":15074409695864137771440886703380535785},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":30148819391728271978827922890063480871}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-238485339009076631077854857087600625043},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-953941356036306527834948495493829490279}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-106300905063039889146619206192127348169},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-106300905063039889863771997721999680285}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":133818686090860120591098246128068363437},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":33454671522715029405698618557827166099}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":48231291431967828223691070109507829717},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":96462582863935654807131216685636885367}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":311325921776650678355327540683057133643},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":311325921776650676093344867504133515695}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-39270360444389900229100672388263663685},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-314162883555119204788624807677415979237}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-112433906145207307825166348358149217767},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-56216953072603655290179029945178284949}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2044974361281137533998359629574834639},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2044974361281135729451978589829392047}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":57350687942681722826368584236073652131},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":57350687942681721684512846221600180615}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":486834010792576664786935914167582809263},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":973668021585153326671084949186722755019}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-57443640192095189746008420128712191271},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-28721820096047596783275007712905823329}},{"hi":{"denominator":664613997892457936451903530140172288,"numerator":-4576274215828472751438221820944426357},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2343052398504178053386551987764111269077}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":692173790132737071371274748673667537081},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":692173790132737066765390306615762514707}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":211930195568017088629282986076913345903},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":423860391136034173395506990306116641589}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":63077628306378628199045459011567441327},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":63077628306378624649014016186607799669}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-200313406587848775408970872824755226119},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-200313406587848778349537653890308904657}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":101754656788608455344464943431900246591},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":101754656788608453541780180610608807005}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":270769465750497324984950127327461932249},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":33846183218812165273625491832032965491}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-393681993507682730292250560512131965},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-393681993507684950132682111698828487}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-132397710120855539237021015022447853971},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-264795420241711080780291889339696904195}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1205629012234964618401565708482478055599},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2411258024469929233451123291568914317019}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":232746858803127383},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":89814615053115959}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":11424661262424967},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-83165361361243555}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":131012445132037745},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":23224523109132637}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":808211637088141},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6810624363408715}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":124634763091975},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5342476562264405}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":64770794511698831},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":17336129019554877}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-5933719448095893},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-47347331314280983}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":695488406709283},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":569832969316167}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":691232664742611},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":9427003927121}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1155460865903481},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6455488807095555}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-364774296663274687},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-354703568626436509}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-1577333688207031},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-41500977436048481}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":26876390259660619},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":1602494564522331}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2953674177815685},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-18136994855587307}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3070165079147491},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":191150029428461}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":13083697299781135},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":2422528615431103}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3121334051803143},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-2200490782296851}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":281009534959313},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11815551225597613}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":677119657892811},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":90367025112209}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":9070156995401},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-402643650957031}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1506341160104771},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1579358381182325}},{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":411365153330529},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":7392496876105783}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":1781955459136473789637},{"denominator":85070591730234615865843651857942052864,"numerator":440427881557442612077},{"denominator":85070591730234615865843651857942052864,"numerator":358565825340071944499},{"denominator":21267647932558653966460912964485513216,"numerator":92759179013307748055},{"denominator":2658455991569831745807614120560689152,"numerator":12814438497346363671},{"denominator":340282366920938463463374607431768211456,"numerator":1130931139516516630819},{"denominator":340282366920938463463374607431768211456,"numerator":1477889007479720242333},{"denominator":170141183460469231731687303715884105728,"numerator":688797374852887457791},{"denominator":170141183460469231731687303715884105728,"numerator":451136424808521156775},{"denominator":340282366920938463463374607431768211456,"numerator":1141853665730935827219},{"denominator":340282366920938463463374607431768211456,"numerator":1451221123153926632587},{"denominator":42535295865117307932921825928971026432,"numerator":238782044561823066447},{"denominator":170141183460469231731687303715884105728,"numerator":1162540487257140850749},{"denominator":340282366920938463463374607431768211456,"numerator":2302934629368613625375},{"denominator":340282366920938463463374607431768211456,"numerator":1931526516333790591847},{"denominator":85070591730234615865843651857942052864,"numerator":443752900523111340341},{"denominator":340282366920938463463374607431768211456,"numerator":1470271467235595848721},{"denominator":170141183460469231731687303715884105728,"numerator":901339357270455580561},{"denominator":340282366920938463463374607431768211456,"numerator":1397971832463308430747},{"denominator":340282366920938463463374607431768211456,"numerator":1109919996313453878943},{"denominator":170141183460469231731687303715884105728,"numerator":576560921973929655515},{"denominator":85070591730234615865843651857942052864,"numerator":418995357894161449031},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":579},"tube":[{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":1900018934887943314773983624164715033},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":3588281330218682061710754204530374743}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-476717547212094962269937603319144644217},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-957440338458930927750394261617466460797}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-421737374913430876982225993405087481453},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-106416375824556794614294457074647775175}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":33568559471476906067693736234358465261},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":133720236414180694447524270210626806663}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":96566264871591355580130392113905731225},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":191414816512474947869843947636743080855}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":311737253221424741973622965571468306761},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":154020474287715746866062144572189719949}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-38874368748834738671733929112778563699},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-314566122342845317454704732451194698083}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-54918797537398560239558390486386362191},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-56366903028893559944633330730069504045}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2056400216423883440150777630393656311},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":250511708181360271869067180675095563}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":3593540223965620708671214798856307403},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":56083748818384516225700479879129613511}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":978810939263048629038832411298813137191},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":243244128185330921650541907358366237231}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":-886622470961548751491306237595125619},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-28782785617568013511095988435571645127}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-582740662831106378166867861084949260561},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1172226272715980439625549363682307178195}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":346198333616590330212622832683845249769},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":692098461770374513535117215627116600733}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":212176900485797827762043764569754410623},"lo":{"denominator":1329227995784915872903807060280344576,"numerator":1639317908386594331237668297480080627}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":63306475933863340946772811178187667721},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":3826276744809594245460860064336032879}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-200154396504515459019044835590891746193},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-100587831248630875711259332983213723295}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":204530610533511324056770333109600255265},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":203338104810668560058402104516437401943}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":270890752223202372768241752458479459905},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":135012555834069538888771916397975270369}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-91695984377476538409818689708090473},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-210291307193057806116163007258646775}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-264079811340526336738828232533069928795},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-264913509405081135642789313942110292719}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1206415705878651298366813050470018067391},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2397716451144809540007883976506631649085}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":15711135718578869461418079902925669815},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":7855567859289433815928408033184651561}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-950825338796399523102579801415252679261},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-237706334699099881670403789650995072993}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-428187834547973048465843741469372931713},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-107046958636993262848514873610968562181}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":133390171604251856257947679886890135247},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":2084221431316435206501407940836316275}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":48563867346845527953241987799415997383},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":97127734693691054226116115021297273541}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":314241029667966793549624109303065674575},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":9820032177123962226345538686948715127}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-316980356095585796398198194173761529345},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-316980356095585799413679565987189948711}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-114755500249645964281587942990132470797},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-114755500249645967110886142165361336749}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":520135778049645036321416516239615163},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":520135778049644572436768086388676231}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":29241622901645978567181075862753205989},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":29241622901645977980379383001777316309}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":484520349693043027341484614898083718225},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":484520349693043025870017048601107833031}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-58041512259790247651698930720341304779},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-58041512259790251574863394764295033997}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1176862031215800341289347907984124244949},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2353724062431600687329107895548690783151}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":691915448020831911961262178320719012361},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":172978862005207976815802047875703675305}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":427593015850110483970048623010936988327},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":213796507925055240007877025672625171707}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":32369862655021733186740484930689089093},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":32369862655021731362269203319730215939}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-49871040611559534464339732698328727413},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-99742081223119070436464250037182567211}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":202546829558477690785342786225996437749},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":202546829558477687092506961488761776863}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":271413457493101878939362361850499323675},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":271413457493101876065828753860409136471}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-189805046153099438622625625611217103},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-94902523076550290623275390355702907}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-265415981504416303145883977371456627889},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-265415981504416305517378120859472219797}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2423188306291361849904681130612768446881},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":75724634571605057702032542633471365405}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":114852111034004285},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":6049109829558331}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":16839294032936225},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-41568559431257709}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":60838009355295515},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":5247928685827437}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1554286679922959},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6611414307827347}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-54124833794547},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5549834260418441}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":113448178492793767},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":7390775378783739}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-82633849909017},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-4993300191958645}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2614005863200581},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":115746960844443}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":675256891389467},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":7495485996123}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1125281974062039},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6151338788586931}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-170618028940071939},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-163908678353138249}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-4235932652426329},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-4419882311386103}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":6195169600835481},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":2709204158142515}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-930941751097689},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-8134610263529127}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5371511815778845},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-149349649633275}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":724273738877853},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3840417836993521}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10611186505009511},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2805986970932391}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-610192240263309},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12572521040714407}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":357704979321015},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":221327243580987}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":52699226182351},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-183756494044431}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1327887095848719},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4296645847007841}},{"hi":{"denominator":664613997892457936451903530140172288,"numerator":79369647376153},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-972231447139221}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":1829494804604158829055},{"denominator":340282366920938463463374607431768211456,"numerator":1789467690387916080533},{"denominator":170141183460469231731687303715884105728,"numerator":732034015096319336369},{"denominator":170141183460469231731687303715884105728,"numerator":760461962921424555095},{"denominator":170141183460469231731687303715884105728,"numerator":840182596955036050549},{"denominator":42535295865117307932921825928971026432,"numerator":144153639210611358925},{"denominator":170141183460469231731687303715884105728,"numerator":753860521620673005585},{"denominator":170141183460469231731687303715884105728,"numerator":707324012039302260785},{"denominator":21267647932558653966460912964485513216,"numerator":57985560888889260961},{"denominator":340282366920938463463374607431768211456,"numerator":1173601435334531547933},{"denominator":170141183460469231731687303715884105728,"numerator":735655183484604840317},{"denominator":340282366920938463463374607431768211456,"numerator":1961568788425383746525},{"denominator":170141183460469231731687303715884105728,"numerator":1187598179327588809089},{"denominator":85070591730234615865843651857942052864,"numerator":587254947435109931033},{"denominator":170141183460469231731687303715884105728,"numerator":988572225363642899879},{"denominator":170141183460469231731687303715884105728,"numerator":912233703814983173545},{"denominator":340282366920938463463374607431768211456,"numerator":1507773867073330742847},{"denominator":85070591730234615865843651857942052864,"numerator":461603059075084309137},{"denominator":5316911983139663491615228241121378304,"numerator":22449462414099552977},{"denominator":21267647932558653966460912964485513216,"numerator":71413982190562065819},{"denominator":340282366920938463463374607431768211456,"numerator":1185744259477536367673},{"denominator":340282366920938463463374607431768211456,"numerator":1719799078425390512181},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":32,"numerator":291},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":31673040824493159804968922268702483305},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":14989730727377197776850572468494948325}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-950317241666399716180771293800007970847},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-477172017705370309009372981296517232639}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-212410959877086910208999042460362432375},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-428638924734031182102785481199546888457}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":33469421561150484869143419501809486377},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":133287684707183750621819361414565380353}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":194461874457967783828775700127633192123},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":192754420313416145812649847931786806629}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":314641819645998940127349218885560093781},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":310957488680056424534011050439639089735}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-39225608710691996241722388244520446373},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-79346252095342072231010458814149425097}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-56071201121486365510536280867882859101},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-115057441265318499062010425760577458295}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2091836028538260935347428749841718767},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1019883754681838686620686386079385897}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":117260375297658893444378699892022729195},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":114417042617330615582875358037884180839}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":974258014468939854715609805509693240139},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":60522380351942162706139377247715017473}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-57363904413460108471468056944026279877},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-7270157774976365152108960823982767283}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2341712055918665952475212793630939792105},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2355115481773786915086780578357981563343}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":692211696056332848148034976507698709347},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":345916318410187540190216350183205121123}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":214043510910458053389171983160243151341},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":211695382752190312620929218585647603203}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":8121290502232354164264903014895940799},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":62867328782880823686224548394209690527}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-49829041059607844698717150833218403481},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-100212105646669800261139329876068816011}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":203636142460143994604940248826867889167},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":202367853630873155444836631395217184871}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":67883304416045903697556090533139161965},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":67671151106688600197217082839751592663}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-176273517481462297844174550802454071},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-406675362111652073995294040959318223}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-264713493203953941831092860141192205491},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-66383190895381327065146139244800993611}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2424749951509645769860317163801612168387},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1204879460732758142480606430538250430347}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":8173643502120547776567281354509865155},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":8173643502120546837869437593089582999}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-947694300657143894477337055326254040463},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-29615446895535746815981991150353991117}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-215540986031240167899493631083116768667},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-26942623253905021174316776456718986719}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":132932784782597485751422185226588251193},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":132932784782597482634061953895313865835}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":195577472690620319038649714329155484233},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":195577472690620315595974791115075671893}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":317153427330352684187905273757192071423},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":19822089208147042614780740349097147763}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-319802462625633538699748262295625931033},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-319802462625633541775380361116590126085}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-117092244401681712615476153185817439347},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-117092244401681715520765474271567947209}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1058005407553650218100382363189871305},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2116010815107298528307742616892093941}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":119245772054873465478648599105510648337},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":59622886027436731533138305995697372437}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":964351768655469638829025471544208375535},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":964351768655469635848223756710279576157}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-29309676003704973258881045482072048729},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-58619352007409950545842941376854999209}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1182163402621119983827882545021396011415},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1182163402621119986254152503399697757861}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":691593250103496460034559348633275335367},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":691593250103496455242461953929125952075}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":431331066285483962378293994271469524429},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":431331066285483958330594122658988953923}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":66415416813016043729001179228917761953},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":33207708406508019989335314115045403945}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-198585545158550782807631345746158295801},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-198585545158550785899681153424044958615}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":201523824812008188687688884656860238417},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":201523824812008184905622969820326335023}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":272043469509172787582833142241211215415},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":272043469509172784629760079295833186841}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-364583117259179096824954787244258829},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-364583117259181449290941311111164599}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-266024644478328158674640418851644431633},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-133012322239164080556528643136700270115}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":152188615079919179389657761180244063703},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2435017841278706866705628634664887612367}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":55842518147524689},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":99831728835445331}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":11888840985694925},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-82349466792269703}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":14024193334676103},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":18562291799887815}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2982144433755263},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6444647529423031}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-591833219826619},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5689045842820383}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":195431005656034009},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":48506599693195203}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2054231286873201},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-8298849282726491}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2453437822951001},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":172456632073785}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":327936440055133},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":5285025715029}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-264172899099345},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2906073610024703}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-311004826309797039},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-299144282362754395}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-558873980039629},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-14753682455064773}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":5670277595768055},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":2183755913136845}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-416506397939883},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-3624989590576599}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2330626769004147},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-46472622822247}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10113964385984277},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2828337754177553}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":14455643050702217},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2789734941382109}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2452872470114221},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-6562569529663791}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1485021729843935},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":650258248862879}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":70566963963637},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-167166855387643}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-128807855298571},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5271423621575939}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":29628934278093583},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-4332450481939737}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":1877333918350963237599},{"denominator":340282366920938463463374607431768211456,"numerator":1816996211588647855325},{"denominator":340282366920938463463374607431768211456,"numerator":1495003046089096308487},{"denominator":340282366920938463463374607431768211456,"numerator":1558675402269655603531},{"denominator":340282366920938463463374607431768211456,"numerator":1721334913000728409287},{"denominator":340282366920938463463374607431768211456,"numerator":1175657505182684031805},{"denominator":170141183460469231731687303715884105728,"numerator":768898698740314885671},{"denominator":340282366920938463463374607431768211456,"numerator":1452643606280595852215},{"denominator":340282366920938463463374607431768211456,"numerator":953946204258406629317},{"denominator":42535295865117307932921825928971026432,"numerator":150773018021880540551},{"denominator":340282366920938463463374607431768211456,"numerator":1490257215547756543813},{"denominator":170141183460469231731687303715884105728,"numerator":1007013953509910272309},{"denominator":85070591730234615865843651857942052864,"numerator":606565200394755836795},{"denominator":170141183460469231731687303715884105728,"numerator":1198020931939645739165},{"denominator":340282366920938463463374607431768211456,"numerator":2023847233398488703129},{"denominator":340282366920938463463374607431768211456,"numerator":1875161632686097573669},{"denominator":340282366920938463463374607431768211456,"numerator":1546014886282476598189},{"denominator":42535295865117307932921825928971026432,"numerator":236378452660621543127},{"denominator":340282366920938463463374607431768211456,"numerator":1476535371580083601791},{"denominator":340282366920938463463374607431768211456,"numerator":1176232790811596083423},{"denominator":170141183460469231731687303715884105728,"numerator":609602931201497457807},{"denominator":340282366920938463463374607431768211456,"numerator":1764428625191887716911},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":585},"tube":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":16472221631173959339873671684219699303},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":3906642654294853249408180218887825115}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-947184689137908893730087005711960425309},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-475614927712560354060336921251492541665}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-427817355824037194945452572045557095439},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-431522143063395730149364264084692202627}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":8340802093436595054766097148358593911},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":16603276823456109336644851463035885605}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":195782909586534240373763248581865477357},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":194085753809698538238728783293895193101}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":317545521117087548742435805018721821393},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":156936931975698909093785365144769097983}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-158310849074203941947304818343454922781},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-160104138810093504465247604678201713919}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-28615520730444337368449972462298206911},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-117396256200463497551680419059566003619}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1063583195753084507562885690531493055},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1037681373915534104574719437525600421}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":59770835640665322718674518396968435747},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":58340180265806026320990348948785140295}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":484818410337808372571799912447838714829},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":60229725486269365033580867256225047071}},{"hi":{"denominator":664613997892457936451903530140172288,"numerator":-113211432822750680913895553126662145},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-7342105018833417358219824524591328509}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2352392349759129834735109260686088704215},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-147856842280239894573185925706791456593}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":691961258297124536041739445828367803113},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":691503155534198295236966772950903151147}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":53978192431701650307903844649524359807},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":427122735449721288632701083784142811125}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":33323886545734033669348551932691353801},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":64527720000996284434076328925577595069}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-99204290522597107042926190576995318989},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-99801835745399288591301812321593553433}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":101340621431321417294846411537030908873},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":201337109820991396546192456792431273331}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":136080836227748401513079932409028116107},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":16958145156080013594667553274909804701}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-337351815145594255258169904340183609},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-391816278830217429489091798733849615}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-16583470366727463448268950966877794003},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-266140082235408294908110832285140686905}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":609141884783141868620480973908610792861},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1210850862432280610564916096937631694589}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":16982161949444225954984013428974420937},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":4245540487361056007374380031711644535}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-236137676467114984362660695196216511841},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-944550705868459941139245766072205235895}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-433885271475662699400202062932070339341},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-216942635737831351227202883315504165351}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":66223011464054017314197671091620789735},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":132446022928108031433533691742908314865}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":196891147541348033576993978027394825645},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":196891147541348030050648172659100254165}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":320060702130703358197697554193175589269},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":160030351065351677900586100113336737807}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-322627211099402256071400662922127931459},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-80656802774850564801918620613134479531}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-59722190826947701366883143741197695293},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-119444381653895405716972071904914945389}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":268919751457536588475451643177019189},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2151358011660290746159017441242171701}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":121539563255935716920344189194322815453},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":121539563255935714441100613649489112635}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":959607347418503924139087920027302197711},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":959607347418503921122852134635036051165}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-59176923149096492291841015775273293199},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-59176923149096496427134608682134725665}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2374860843923486112702979493620172642293},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2374860843923486117659554572363330240289}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":691208660648702801768494529443035079313},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":345604330324351398440217536655385617597}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":27192093437868879272727509191959734981},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":108768373751475516055076532256007049167}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":17026202467954777499940065857920866643},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":68104809871819106145520306686165894149}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-197617375323406429314120569810480924555},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-197617375323406432484131355159130631003}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":100220136003720017168133749883343012829},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":100220136003720015231595983357220799677}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":68164825469763558730041472352670710413},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":272659301879054231885558941550674228283}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-174297877297034381679345215863563873},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-174297877297035592450461973633664697}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-133310582572250347345392227885845613043},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-266621165144500697197840008458488260653}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":611686449769110018174150350877867534995},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2446745799076440069076854618563399350283}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":214319028266294273},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":49626289892386383}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":4070909384666283},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-81015511772044757}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":102750921135663173},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":32071979885270869}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2836858319544165},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6302528040948417}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-885812699623271},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2882464991040415}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":82686734009030765},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":75485101605569589}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":8358076136865013},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-13678457361395449}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1144817381400131},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":108610336536383}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":633947148723457},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":46584204572909}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-957035754656349},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-682462765253675}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-275305529903231437},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-269525520500755835}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-334864364202763},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-12020199652494927}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":10305681458310213},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":810861122576223}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":75290455115441},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-6415783617638799}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2003788771078223},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-286553819121603}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":8689377176801315},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1831119986123291}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":8886992917223421},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-90622519802219}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-3390003064025157},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-1686622563880533}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3039564435127159},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":797388205121533}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":88569111912243},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-152185975905389}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1346866518752837},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-380447392130283}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":1235308351870327},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-15618983952720357}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":1925428960077887082043},{"denominator":340282366920938463463374607431768211456,"numerator":1844256913978398905603},{"denominator":42535295865117307932921825928971026432,"numerator":190883314047355474941},{"denominator":340282366920938463463374607431768211456,"numerator":1597426255526986386011},{"denominator":1329227995784915872903807060280344576,"numerator":6887384621584008035},{"denominator":42535295865117307932921825928971026432,"numerator":149777216600005601357},{"denominator":5316911983139663491615228241121378304,"numerator":24501860191715236959},{"denominator":340282366920938463463374607431768211456,"numerator":1491601856004214913653},{"denominator":170141183460469231731687303715884105728,"numerator":490411002085307457815},{"denominator":340282366920938463463374607431768211456,"numerator":1239620014957110493057},{"denominator":85070591730234615865843651857942052864,"numerator":376996504985145983289},{"denominator":85070591730234615865843651857942052864,"numerator":516908777779535606017},{"denominator":170141183460469231731687303715884105728,"numerator":1239139427706182820615},{"denominator":340282366920938463463374607431768211456,"numerator":2444023236992059167819},{"denominator":85070591730234615865843651857942052864,"numerator":517916108031813615021},{"denominator":170141183460469231731687303715884105728,"numerator":963558274622081723599},{"denominator":170141183460469231731687303715884105728,"numerator":792498071595664210463},{"denominator":170141183460469231731687303715884105728,"numerator":968266357518699351799},{"denominator":340282366920938463463374607431768211456,"numerator":1517302352841889303871},{"denominator":340282366920938463463374607431768211456,"numerator":1210770920287238239313},{"denominator":340282366920938463463374607431768211456,"numerator":1253525406197520851437},{"denominator":340282366920938463463374607431768211456,"numerator":1809855700515244072053},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":16,"numerator":147},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":34213112496556086159159324103820675093},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":32525847509807309706179797491193265479}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-118004986440446764351732608019431772151},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-948100346116429429588930700684094026199}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-430722812413721924345278841354299364035},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-108578602225326509720590761818654460367}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":132999169262355302604654159653207665247},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":66167662232388567036167208793018390133}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":197095607066916249221801876741164299773},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":48852197773313525187165167561404698989}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":320445870981447852816585755680945053779},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":316787600258008773949814744219508370305}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-159721704734902699066041642882089005665},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-323033941028086803808733048879633952807}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-58398441719861311988253734456645307215},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-59875246529656755183097154719767804021}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2162371651133034467774635839359677289},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2110859611104438979478087570059778507}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":3807422505680351128228356858399003009},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":118957800040773710506606522027350677433}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":964953598197456663291726763429757173867},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":958935302777586418664713846773292446105}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-58544605036813553773116851049845633337},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-59292074742777481219569247993807018993}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2363003699889274199946990568752112405691},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1188117376709465938517367889729942660763}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":691646779550571454832624450396252376253},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":691111485079821506851973434965505222949}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":54446038151184674211498566161559977083},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":430860261960595798845994743899820718557}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":68338932084682872154750498250338732925},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":66201692893941947514661753539060676713}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-24678934533201408296251682318156023179},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-198713775035544065847422008654913850697}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":201665821763085053680501664613831067465},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":100122926126158201876186933621573016271}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":272775914493253053668293572193012806975},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":271962086733163865847700802062921756209}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-321192986467829763244779777487639809},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-23500001838109135436282371044977421}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-8310802868338767294479773896396065457},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-66683804675429151484057326038838552289}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2448283361139274144813809001052587793075},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":76048246707110397646675268553462725955}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":17615078483912525808898328304924309145},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":35230156967825047670219542101370601757}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-941396945421357033781409618586078144889},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-470698472710678518761955987024655146537}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-436597064145137244895760562134686948169},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-54574633018142156002042381593883098915}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":131929391054946120597648148436086153341},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":32982347763736529330808922836325856637}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":198196463573527832238135867300193795845},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":198196463573527828626361176326935633251}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":322960506313693236419746201720319303949},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":322960506313693233977839512266635582177}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-325452641004504669003486653516625403181},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-325452641004504672200896450201029104309}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-121812151496560885604519620578458494217},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-121812151496560888667608445313958283527}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1093282788418158608688002720344485409},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2186565576836315200546847459326516405}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":61924104001854645376077710561054456179},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":15481026000463661025537130288470030291}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":954813421767786016959793638168857877057},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":954813421767786013910708196057905613803}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-14928506983898182186301945613531254945},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-59714027935592732990010896129054859825}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1192663219091962386674435307119150278175},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2385326438183924778411395615052752719937}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":86345397052428039187771589983411124715},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":690763176419424308516188084709165787971}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":438819242017532267235422282355479117081},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":54852405252191532874270653559160760451}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":17452006288649170904626897712815105799},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":34904012577298339828896082241246293097}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-98289775352047908091016969615977969595},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-196579550704095819431489119437632356053}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":199296198416365754533795984492556124301},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":6228006200511429705247367832157760679}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":273260736481629168803968619010323506639},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":273260736481629165685790085258147466285}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-331643748035446628294912831691666481},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-331643748035449120820003051167861137}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-66801319110413882537259751493488991865},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-133602638220827766363243765878057196669}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2458371467727379914166870384131044255715},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2458371467727379910454708611607767141587}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":202956480184671717},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":95706760883357983}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":647231729980501},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-79098115083623579}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":46734832135724055},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":27035631100825285}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2663151528663865},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6179720282002057}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1108445631532363},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2886380457020465}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":34176000509535059},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":27239184118477469}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":6031357378773699},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-5549365144144385}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2123362503100559},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":85514654485445}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":38074639910559},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":44917016620141}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1672802122936041},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2546902529342633}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-118139718235246509},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-478610371254495413}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2863351566258029},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-18953754472375549}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":9292508192714135},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2123353666260359}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1051756027943729},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11265528124295705}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":851956450674181},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-187608771859097}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":228875195055125},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":434631056332695}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":20548390533554663},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3438825276480897}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-1026795109633081},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-6842197209149137}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":768442240683121},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":903614004123425}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":26495536682927},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-276826685667915}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2359243330216723},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6741417103456897}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5476345170927905},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-10882716185083681}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":1973734932394588351399},{"denominator":170141183460469231731687303715884105728,"numerator":935604519873577170149},{"denominator":170141183460469231731687303715884105728,"numerator":780128014145801805081},{"denominator":170141183460469231731687303715884105728,"numerator":818600903554743015217},{"denominator":340282366920938463463374607431768211456,"numerator":1805885013328987827013},{"denominator":85070591730234615865843651857942052864,"numerator":305228057977485317059},{"denominator":170141183460469231731687303715884105728,"numerator":799343884127267394047},{"denominator":340282366920938463463374607431768211456,"numerator":1531543393443825587097},{"denominator":85070591730234615865843651857942052864,"numerator":252103574213017563201},{"denominator":170141183460469231731687303715884105728,"numerator":636963739452853230201},{"denominator":340282366920938463463374607431768211456,"numerator":1524421555588084130429},{"denominator":340282366920938463463374607431768211456,"numerator":2122390648284445603233},{"denominator":340282366920938463463374607431768211456,"numerator":2531254269575866497837},{"denominator":85070591730234615865843651857942052864,"numerator":623246539734246371289},{"denominator":170141183460469231731687303715884105728,"numerator":1060313036296553865993},{"denominator":340282366920938463463374607431768211456,"numerator":1980354485812319369195},{"denominator":85070591730234615865843651857942052864,"numerator":406179758830052417887},{"denominator":340282366920938463463374607431768211456,"numerator":1982935318324764008311},{"denominator":170141183460469231731687303715884105728,"numerator":779544090899304357823},{"denominator":85070591730234615865843651857942052864,"numerator":311565588426330474379},{"denominator":340282366920938463463374607431768211456,"numerator":1288722071804192592851},{"denominator":340282366920938463463374607431768211456,"numerator":1856064527200282545477},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":591},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":35477690329508216505829325597522518399},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":33796172073264029342680119415598420983}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-940885230360814737516586301204276296593},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-944957980924864963763985706857422146435}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-433537516641342569785224899798436797761},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-437015064984543865934996528935748958009}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":66258094929153990011433508829154627353},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":131814520556308526078150265106655757901}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":198399936526910687709685454076557047905},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":49180876080182489244355451953206173283}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":323340445523410094340043764464815621217},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":319696286198180384852408692844766208819}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-322268007744970714999333578786013492175},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-20366252580580382857500276121758414341}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-59573523674559721592064587015577204347},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-15265048799609879835062538293067621507}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":549358123697078753270200359781745003},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2146238624646065827612152308252386827}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":124148263725515498299880712015239122979},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":15156213456025578418210075309453177053}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":480107233887162260698066789214530714895},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":238535816054029637206419249152623091139}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-7388089685323505068962536365055987379},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-29913387073836278976553768634839292575}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-593386579452050184754925949641975025943},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-596672894740263618963115186722900558357}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":172817430043396224108518366072589120373},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":172664781231190987444571029504041428815}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":109828564484799514312453821760684385547},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":217301149562212365830735888944362287163}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":8755490438592555952010856982326369365},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":67889352801050068204346245422669414557}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-98192378057761284934114037964276630977},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-197754333013171306108120608651308478181}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":200589845093483874009860620717019632105},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":199094114233045477273929413412706823193}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":34171965438425850286664777818434662765},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":68144924868975986571174199743340047921}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-304066324163446324983529839445346167},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-89805581715854065711352357389605603}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-133271874894652989746046493004587469367},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-267317903341253131479007681435314556699}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1229948361133983511533445214272651029931},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2445284585388492629744628417209963131935}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":36490752063720287534229153664209332609},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":36490752063720283489718416982562926037}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-938235338049218753983932473332831260769},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-117279417256152344722454223664221569197}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-109804192411519421600244582710586739911},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-27451048102879855599386119676625142603}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":131382402817006177344019081510008685335},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":131382402817006173987955029183213380581}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":99746693938145743232535770801737429555},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":199493387876291482766083652742340827361}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":162925279336547909837686117547425662181},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":162925279336547908593904468446170586723}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-328276824508199925030286715801128701665},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-328276824508199928289331331651988946267}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-124195789170658197540746352548662023349},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-124195789170658200685726567444413846357}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":277701843823613717163243785760937661},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2221614750588907663822451243450160479}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":126172044923995906371893890653516288561},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":63086022461997951876820130207353648453}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":949975835798349587305497838182436297555},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":949975835798349584226298998745520238155}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-7528813276234885565115492125705314241},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-60230506209879088877531338420796216511}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1197861944481070053532879558130667500933},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-598930972240535028059038630896402014775}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":690258324720342533765976385069441718283},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":690258324720342528680059307429453949117}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":442567235583604537427530383900260710649},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":442567235583604533086000440356704891031}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":71525196537879178102433860409711289035},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":71525196537879174032632171443780004095}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-195472044387631908811738855944200507545},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-195472044387631912142124028060750835351}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":198091684724638669223448840660112077861},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":12380730295289916572684592507779903317}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":273847537289661907882444162234963410383},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":136923768644830952339306076717896438887}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-313723895124265615598528259667800375},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-19607743445266761316419439121111877}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-66944172203635613721649639554432616251},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-133888344407271228768116763564249581665}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2469894250830697235635827255181185999309},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":617473562707674307957430355727788568509}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":189702374430520829},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":89912824659076927}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2886232891129815},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-76714490724759359}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":42239072871287783},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":11054503997360269}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2498927090938251},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-760650937637021}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-628305128428847},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1429928619663205}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":13719011939617167},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":34416260284810183}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":3816281679926683},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-17664239167875319}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1960627296579087},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-47158533582965}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":291046173875773},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":38333834058123}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1401899333365433},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4711211744504673}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-97844626841633481},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-418090355689617113}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":6070601887321461},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-3567758136792823}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":16622908819217921},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":521152719270213}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1858249218091553},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-9813593485259951}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2868270385206001},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1806139674012369}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1507216148146511},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-38910254984457}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":22779280508937005},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":6934846798969123}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-4627716195868287},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-6856527551268249}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":769068429931367},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":60928232420791}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":15298096255703},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-7858516767663}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-3175885869328931},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-3619468443621479}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3191700100206849},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-27052865208315103}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":170141183460469231731687303715884105728,"numerator":1011102736782968740667},{"denominator":340282366920938463463374607431768211456,"numerator":1897810857628662701815},{"denominator":340282366920938463463374607431768211456,"numerator":1594568607422953733487},{"denominator":170141183460469231731687303715884105728,"numerator":839013867048050817583},{"denominator":340282366920938463463374607431768211456,"numerator":1849491712878456118311},{"denominator":340282366920938463463374607431768211456,"numerator":1243743981183639011881},{"denominator":340282366920938463463374607431768211456,"numerator":1629505843242486331275},{"denominator":340282366920938463463374607431768211456,"numerator":1572489103554960830477},{"denominator":85070591730234615865843651857942052864,"numerator":259185369410515455923},{"denominator":340282366920938463463374607431768211456,"numerator":1309125160463198926207},{"denominator":10633823966279326983230456482242756608,"numerator":48109006848982964207},{"denominator":170141183460469231731687303715884105728,"numerator":1089146764945179802457},{"denominator":85070591730234615865843651857942052864,"numerator":646297478340111547467},{"denominator":170141183460469231731687303715884105728,"numerator":1271476351449321104415},{"denominator":340282366920938463463374607431768211456,"numerator":2170762634566748300623},{"denominator":340282366920938463463374607431768211456,"numerator":2034897810595541857219},{"denominator":340282366920938463463374607431768211456,"numerator":1665184663841420179961},{"denominator":21267647932558653966460912964485513216,"numerator":126890196099897717393},{"denominator":170141183460469231731687303715884105728,"numerator":800957476844292384949},{"denominator":5316911983139663491615228241121378304,"numerator":20042686007101276397},{"denominator":340282366920938463463374607431768211456,"numerator":1324815452929875392149},{"denominator":85070591730234615865843651857942052864,"numerator":475759448463090400415},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":32,"numerator":297},"tube":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":9184215504472273249117585037706688763},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":35062745295595709300636119851539556329}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-468861507532218424518393139719017901173},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-941805159905459280689148162583787820439}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-218130394429177939240065205570567324035},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-109905885431542385659107979719408598377}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":132003399192287109548033240245233139483},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":131263317818877220044182324352786533617}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":49923966252653583325802129358050456587},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":49507465853462887582233423434392534739}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":326226886102434999277405552313782992801},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":80649393806513815013916376893154154817}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-162546764228944511975914906222319549747},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-328684653924045474468398220965478880811}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-60756407362418380634822343400729627507},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-31126545610519501154598505593107097873}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2232329983114575794518477622317709417},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2181480642805397356772221641324911009}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":126474239368743583935246938445101992171},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":123556426740927699789747053603719686173}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":14928522174781060195564127907103583847},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":474652722501984748476499354697968865125}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-59644388363406616520601341334780723019},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-15085196021316934691666437582300108769}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2384020457923376043003299425982035607583},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2397080260528863346459011306345661839695}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":172707893313972032162039021196207652137},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":345073802445624988594161218904218877913}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":221531162408646175521250388102020879011},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":109586947093278618858309764064716550625}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":35881441522995998423897318864357205301},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":69590818722219422192236333877465355087}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-195268401843425363505180833366781010865},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-49181308477709245300269732311349050145}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":24931666692247191096090780725180617709},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":98940991160929893209711817455790011759}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":136980430679244119385405800084931942661},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":136591472414322412115949402789588195665}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-35746083305885265704496916679135583},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-85369982207312135056704217763951625}},{"hi":{"denominator":664613997892457936451903530140172288,"numerator":-521737178890254186550639658209003083},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-133943922045132004932521256256725106289}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1235703521298450731400433796268403310351},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2456923070519655293527357613482426837735}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":4718104323954693555436074943719830983},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":18872417295818772150905061091557970383}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-467534065698227857189129108642154212803},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-233767032849113929556593307389880250059}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-441743891444494308207624513753102954097},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-55217986430561788933460577550981173475}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":65402290723644297225407409972666007801},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":32701145361822147752736567556529863399}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":200781884741456101585570019535215251575},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":100390942370728048898779170889183513367}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":164364322896722871955438747602125057253},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":328728645793445741377373968138583778119}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-165548933702567316067763994413546693905},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-82774466851283658864178045609149440213}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-31648881248543422584669469922136978385},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-126595524994173693567600142534882325601}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2256487167613460717191200631415136155},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1128243583806729292772905322522244139}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":128511407559022040936622536871459801507},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":64255703779511019123077779518023598223}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":945100282766640708106233449588490497747},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":945100282766640704999807475379305218873}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-15181558588301214604164586214146325671},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-60726234353204862887360384780649789349}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2406053536987015786710475092957993611077},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-150378346061688486999416588277355416717}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":689695661511263769311760389460617997121},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":689695661511263764123859770285337184393}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":446316393022170545931581085527628428357},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":446316393022170541487366504278648931867}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":36628235332251355928643379319352791947},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":73256470664502707675743205678314526473}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-194294902865293172536969828911590769505},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-97147451432646587974886207386451632395}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":196826863823855921650759808511319201263},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":6150839494495497421681984402049119905}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":274419450682866132803959201403141394973},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":274419450682866129512346692928571548355}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-294834041246505929408127230690538447},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-73708510311627142454603598264520595}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-268335090787194986718102999798295953467},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-268335090787194989441757979472850143575}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1240656832260062601469425665310650355841},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1240656832260062599518654918041702980327}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":43757839228060861},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":82342757689215803}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":593853495773639},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-4625073249251939}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":76004157642017491},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":17404755300707129}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":144961725090099},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6047191753215733}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":-20898327592299},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5617272381713955}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":42500705638201435},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":3816264490678299}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":8989863583894295},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13723217394048463}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":900346553261645},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-44981171552487}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":553943801385209},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":26887049808429}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-551976589278321},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4323871238763627}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-154160784088310179},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-179482388567976725}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":4478161259570357},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-10029320039562191}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":14763735821921509},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":5773489862055}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1286354573891237},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-4250600298249393}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2395572093619487},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-129060826740615}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4816537499188565},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-884476537472253}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":24555154803801905},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":9768254152898095}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-4961535808618239},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-851083368166739}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":381515075838047},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":126682154241253}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":138282016838775},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-114270547256221}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-3800640645356291},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-3805628353409767}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-3494680212188413},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-31573146385323261}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":21267647932558653966460912964485513216,"numerator":129424555898981864983},{"denominator":340282366920938463463374607431768211456,"numerator":1924019911698116498163},{"denominator":170141183460469231731687303715884105728,"numerator":815000376813101280835},{"denominator":42535295865117307932921825928971026432,"numerator":214991261446241119043},{"denominator":170141183460469231731687303715884105728,"numerator":947001849494358104505},{"denominator":85070591730234615865843651857942052864,"numerator":316679223839044080839},{"denominator":170141183460469231731687303715884105728,"numerator":830288122666235633997},{"denominator":340282366920938463463374607431768211456,"numerator":1614460141114270839411},{"denominator":340282366920938463463374607431768211456,"numerator":1065822431464809535547},{"denominator":340282366920938463463374607431768211456,"numerator":1345231878958676199037},{"denominator":340282366920938463463374607431768211456,"numerator":1553110585108068817801},{"denominator":340282366920938463463374607431768211456,"numerator":2235341527140752891879},{"denominator":340282366920938463463374607431768211456,"numerator":2640087783645425429497},{"denominator":340282366920938463463374607431768211456,"numerator":2593944772632768265733},{"denominator":340282366920938463463374607431768211456,"numerator":2222105060351829013581},{"denominator":340282366920938463463374607431768211456,"numerator":2090768925973177198301},{"denominator":340282366920938463463374607431768211456,"numerator":1706393899480330795737},{"denominator":170141183460469231731687303715884105728,"numerator":1039231912961916328679},{"denominator":85070591730234615865843651857942052864,"numerator":411451308726399634033},{"denominator":340282366920938463463374607431768211456,"numerator":1320204960169628096357},{"denominator":42535295865117307932921825928971026432,"numerator":170228198066155795429},{"denominator":340282366920938463463374607431768211456,"numerator":1950756708035860808089},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":597},"tube":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":18994679896899022113989927591912931649},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":18162120046855821703844684024598896751}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-116819435514515052451162628434350877979},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-469322105354225953232613159325663431527}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-438892038172847933490942245715761774577},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-442139352905145462591303094782590369691}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":131460309697830487918631972328711772781},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":65340620444793691086251533170352076939}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":200983356727668313103142160448003455077},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":6228994868177939286658660988806880427}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":329102900837640699912809548760449261543},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":325489187321479719107253313107104357485}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-40989754956522602762516729893713434967},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-20719118013273240712603912716556027717}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-61947210737807904051278403535015952491},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-63454049213019851242226129828654916547}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2267045579818822265061041920659355561},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":277070860084309088516159282150263801}},{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":1006373276447067608732264479453810965},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":62939148325263021312148486032108994999}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":950592301116570520031195828634310347141},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":944427647934361192774215926314593106835}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-30081726408398968533119105854819983225},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-15208496686902352903273865617660546419}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-598606604013340597167677692715035915135},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1203700572570569786310597111336516909123}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":86291732832301735368826292545350962777},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":344789241638850195552135394814085559221}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":446811422138388523076794168500166213929},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":110523914824934911327311395357440540023}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":18373989775317414205735411341905533109},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":71306222919724675944820007430128294773}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-97041233905471827843214852199571199609},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-24453305223130214801872369144547072359}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":24782045168405879827248554951483413827},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":196609595121163344672592452293338238625}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":274531072351921065693889331128335957927},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":136885794474705443394012900057253864681}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-66724477092412657780610664367252679},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-161385315885123004447590557503061905}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-133851231172820736428561600256052811675},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-16777795439665705821992298460583174021}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1241406927241531464807287078915406552293},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":308557342414220963731703334292801477503}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":38991179723276339680951883196720752553},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":19495589861638167720984652842549551013}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-931897503334249185063800385287780389373},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-58243593958390574310216043116611980285}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-444178012715707616070443181518367016547},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-111044503178926904850898702174217539025}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":130195460706011030467335032771331197601},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":130195460706011026941456325325080744803}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":101030957716990916020150984738597969179},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":101030957716990914080714843588279879719}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":5181134732654725686999694940508704305},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":165796311444951220693655262229464834099}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-333913909880042265247559243018317620725},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-333913909880042268631394550595777597163}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-64505791851149736564541321616815469879},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-129011583702299476444040439794552852961}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2291164885193760570492971888109119573},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1145582442596879189569676544862907751}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":130866623474087570009533262684456997101},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":130866623474087567244996755530093624459}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":940192297438994222558095514772717719825},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":940192297438994219426254397084386454593}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-15300281033042792569182324885145522815},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-7650140516521396857976552018391797645}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2416315761390364960989623160601475344041},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1208157880695182483190767510486337308225}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":86134596198282608239978722398104384913},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":689076769586260860627851147948067418543}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":450065621488001995739820878438362255723},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":14064550671500062224701472758160519245}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":18750501616401709468325633278419048829},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":75002006465606833577316653031024636731}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-193048244047928904044968480198335770383},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-193048244047928907541687263350512292123}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":97750959793901611437496147016047272687},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":97750959793901609309885881183480152391}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":274976205777078988360594645253263445159},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":137488102888539492489514270585523665169}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-274973071458731600522436186831074061},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-274973071458734317937784453180738293}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-268880149557643266854700711629625511861},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-134440074778821634827126871892996172099}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":623157333571536514007881460585892426269},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":155789333392884128252067806495508528387}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":39830490124068309},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":18386551438288105}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-310186242028655},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-70480372499771267}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":16922789985513919},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":13091165017050303}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":32944839775097},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6033666615025649}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-342022588360463},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1365929290940595}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":62387026214818975},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2953204332602947}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":1245508076043171},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-1267054713865637}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1630199349084337},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-300496799814321}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":130872796800615},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":780773459143}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-788041514346093},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3933766596922725}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-112347736244927769},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-150888071835757793}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":2873435361930117},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1551819520359489}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12914702081182895},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-462047445720201}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3173684502140633},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-7242889764985847}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":979369573650589},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2273789283055339}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3693527260162829},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-25794843749937}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":25901615934808735},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":3000359524706375}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-2577363962124913},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-6672561167373753}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":744844436269181},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":257942539926939}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":38181218867395},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-103298835276061}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-4255915585736055},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-246052053695275}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-9155123480716413},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-17675691841280509}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":2119448400878439264855},{"denominator":340282366920938463463374607431768211456,"numerator":1949793067195876776287},{"denominator":340282366920938463463374607431768211456,"numerator":1666548513591789067089},{"denominator":170141183460469231731687303715884105728,"numerator":881467641327472455235},{"denominator":340282366920938463463374607431768211456,"numerator":1939434093336912929195},{"denominator":340282366920938463463374607431768211456,"numerator":1290302305751539992699},{"denominator":170141183460469231731687303715884105728,"numerator":845951310752633090151},{"denominator":340282366920938463463374607431768211456,"numerator":1657477932932386507271},{"denominator":85070591730234615865843651857942052864,"numerator":273919138474946430987},{"denominator":85070591730234615865843651857942052864,"numerator":345566670178660099501},{"denominator":340282366920938463463374607431768211456,"numerator":1565825844640452338707},{"denominator":340282366920938463463374607431768211456,"numerator":2293532707793511565737},{"denominator":340282366920938463463374607431768211456,"numerator":2695949010787113324555},{"denominator":85070591730234615865843651857942052864,"numerator":661496026832812566785},{"denominator":170141183460469231731687303715884105728,"numerator":1137342379412198820841},{"denominator":340282366920938463463374607431768211456,"numerator":2147990267842695699893},{"denominator":340282366920938463463374607431768211456,"numerator":1748352441487170269251},{"denominator":340282366920938463463374607431768211456,"numerator":2127606170635361871455},{"denominator":170141183460469231731687303715884105728,"numerator":845391039118657686463},{"denominator":21267647932558653966460912964485513216,"numerator":84919218404493863829},{"denominator":340282366920938463463374607431768211456,"numerator":1399774707203117159795},{"denominator":340282366920938463463374607431768211456,"numerator":1999207371077615703139},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":8,"numerator":75},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":39233966028123537393861515541600873179},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":37579375543139100624915522676726142103}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-931390506768924518012596782428629675549},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-467738378177535148013951973075866865687}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-220715379052350276898452960917065621461},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-111140522875659524476022959706206274779}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":130886443270772031430407833540407580321},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":8129239064746103852154856236792199293}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":202262372825584525925334823595614576237},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":25077173258180228500697897110958783827}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":165983132932769377897139720986607301063},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":164184455114939925443303346511866662417}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-82685069069099645887456255815850790405},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-10447380861367470918964208646915067749}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-63146049334300133479480722801784570149},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-16165795240541812594515723031791702145}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2301561179510429271978238272176714633},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1125739472034675365748881443291384033}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":131173209976381697935730705778336020741},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":4006739116714717654603558619385807945}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":945720812242546957983842544176936246779},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":469757758741742229603875800245751006007}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-30330891328160386794952252681768851565},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-61306299625161621857442898094990443115}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2404764527981910663814813453573480786587},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-604413654508240473192857461304896443983}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":344889070559282244908120819607695646559},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":688953345045557284771429143866681588703}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":450560456097879722893561743025563394991},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":55730603807275356833056990243915314835}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":75243312317699911378130438723198542323},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":73035710480814129486589068428991496317}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-48206769877321539779085470420092503185},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-194457994349293955597931363138631765635}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":98499527565714495802719165177937028339},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":48819285513924573014663278527337189521}},{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":2149110027877495062616694691507445517},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":274345380362260214123170000730415466869}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-246852993460599679519148447776800635},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-303093262981769047686754626519721367}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-268262521207398241619327611587854422797},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-268988217005365692607081491493246473945}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2494116799348263165749375172118692313809},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2479891093983665424958191465168482670797}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":40228615249805860365767168521366890283},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":40228615249805856029443517991896216025}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-928725563404213183145096799375636636975},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-464362781702106593547670199872278241893}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-223259396158805880493281960025878170913},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-446518792317611764395029200717246267479}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":16194323229314831053854257032229575553},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":64777292917259322408343044736181578151}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":203333437985604129204736188072945223741},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":203333437985604125233140251654019836623}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":334440414275328479508091907298831730457},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":334440414275328476878745694024842058623}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-84180781774746953777056968698072469033},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-168361563549493909277617205748481854277}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-131444183802105019049961232813061214695},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-131444183802105022453091467743256408609}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":581407602275401125698694431561197191},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2325630409101602250146719492036018501}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":133238013387348094032739090513142056869},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":66619006693674045596119076750824039283}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":935257249588836618334818043486467366527},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":935257249588836615179165425212077182983}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-7706890182181316966313905854191675575},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-1926722545545329388633109143499044923}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2426510978372300299745820718740310603243},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1213255489186150152625690617762915911489}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":344201628408635167935568046885648180651},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":688403256817270330472941881325539968987}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":453813818739684900856236604270992009929},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":113453454684921224049791354871502152949}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":38380987324834463682877116209319216401},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":76761974649668922952580626836766219027}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-11983265951788918861804612474418528727},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-191732255228622705371031590537280014853}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":12132317852450106375145002341291286685},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":97058542819600848823475744208446125631}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":34439689346001767098721047765878382287},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":68879378692003533329007124949740701607}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-254140900202309629268247880047430695},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-127070450101156212900378011036382893}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-269411511610842429648705375434564375979},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-67352877902710608131521110915402979027}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":312980123958145527344684176063679744213},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":625960247916291053665170877841682605787}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":71597654100750793},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":15940023748230067}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-664658357910639},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-66649167411258003}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":59910916431072403},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":2240845170409185}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1881764056573333},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-3018377670390699}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1341066904979503},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1318556757411877}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":21318706598701573},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-19720873039282987}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":10670654859323533},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-439558381829869}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":731016130869821},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-103585017640009}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":15407546321865},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5769686294457}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-226530654569295},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1780815831335133}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-71503053384209015},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-7763249430540277}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":13691412742243775},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1445681237152441}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":11164014390610469},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-450829105867489}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":927526279622175},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6086448836678015}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1567854665347803},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1226303435564395}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1340783088578159},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2339451007401899}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":26826628286931611},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":13569124487519197}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-2592630919367267},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12954093164933163}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":719781157408955},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1027988906308941}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":166540130829413},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-187319971982307}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-141335764505137},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8025455598696011}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-854059717316319},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-38379916409448261}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":2168122107658131046469},{"denominator":170141183460469231731687303715884105728,"numerator":987544570129556102521},{"denominator":170141183460469231731687303715884105728,"numerator":852103583282435122497},{"denominator":340282366920938463463374607431768211456,"numerator":1807070024133038046695},{"denominator":85070591730234615865843651857942052864,"numerator":496449000407350089889},{"denominator":170141183460469231731687303715884105728,"numerator":657320963746938246425},{"denominator":340282366920938463463374607431768211456,"numerator":1723489081230422953725},{"denominator":340282366920938463463374607431768211456,"numerator":1701564179278931447117},{"denominator":170141183460469231731687303715884105728,"numerator":563161889855760044031},{"denominator":340282366920938463463374607431768211456,"numerator":1420248914220570223313},{"denominator":340282366920938463463374607431768211456,"numerator":1577737848672998551847},{"denominator":340282366920938463463374607431768211456,"numerator":2352865831491609742139},{"denominator":170141183460469231731687303715884105728,"numerator":1376386887363676784827},{"denominator":340282366920938463463374607431768211456,"numerator":2699092207945900612799},{"denominator":340282366920938463463374607431768211456,"numerator":2328533582161723460769},{"denominator":170141183460469231731687303715884105728,"numerator":1103292146141171913889},{"denominator":340282366920938463463374607431768211456,"numerator":1791072266721392071403},{"denominator":170141183460469231731687303715884105728,"numerator":1088840195053110534267},{"denominator":340282366920938463463374607431768211456,"numerator":1736869015596170462493},{"denominator":340282366920938463463374607431768211456,"numerator":1398266077140961261685},{"denominator":170141183460469231731687303715884105728,"numerator":719343891378978252125},{"denominator":340282366920938463463374607431768211456,"numerator":2048382591090887571699},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":603},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":40469516037041169763483605108285509065},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":4853365016607252564669575688106697995}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-928227575153586030967681470482518689905},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-233076318283025162740746817510400594757}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-221938261192375580275310041443093407663},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-27930714105894732234303191688060348249}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":130281332216551858369330430864535484317},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":32355654277785894837344113032878968179}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":6360402224542725353783846430737602077},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":201898475906050118921468198198107896929}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":20925926637423539968505149501838997975},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":41404325037503441310791984032789575817}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-333558084373294312771192492063651557809},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-84279084860193459383714999852822232853}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-64353035933849683025760797129895165297},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-131761190213700436827132081799173166679}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":145991195847638896566342101213991041},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2286198857597262382925783897645671423}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":8346678150282259610975424055354888715},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":130568820481817724297151196468470529955}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":940816493510405177362256874703553244807},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":233643633199073907330160819398555312635}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-7642410653825730228725768409594062175},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-1929927320195597696844927116125786889}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2415035168064299707673141246429087418633},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2427841101324952240837960385953943417155}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":10768218569084100393361213195214077611},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":43017112504385427038889937100254084041}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":454308323557997049252789433730617526791},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":449594210146891429183520205186858375117}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":38502557529970594475978952548353008649},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":9347429855501765928072341986312737423}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-191502431524163531269928617766183337551},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-96610000497506974674830223218775713291}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":195681592637357160066863049864048321067},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":193884862141817788148155493743533819693}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":275625605208249123477938639749922540483},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":274904050284726747368038529973503056371}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-225833903249467852638156458341106493},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-70611917624290887555895560486179765}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-268809281931629333216080371748431054173},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-134758979095884334801141884180676187749}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1252657812167831048546743982996700967131},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2491219746502866491470817896787659928011}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":41456024080842589141698844648427606699},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":41456024080842584708097584594683900247}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-925554354371934115274583380632573036333},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-925554354371934119277160266990299721617}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-28047872557889948871886653082462772913},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-224382980463119592718088796830321233221}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":128881514511990705079736111745844878061},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":128881514511990701375005663027269221339}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":51149101752929335954128210688443349189},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":204596407011717339750303950065803076809}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":337270013484351656089729629160007541667},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":168635006742175826705073769347835868171}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-10610116551338180314314921557311319767},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-169761864821410886784392863267203494131}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-133893536942217745415355969237312046137},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-133893536942217748908839585908386264717}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":73745834922956592262244875899066265},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2359866717534608636822123240194403965}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":67812945161838865033035791820057222819},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":135625890323677727147671914446179244071}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":930300338596471324958540876672655138681},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":116287542324558915222597346818564171801}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-31044102532288068714762062263808437037},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-62088205064576142256224653070221130477}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1218319819959688436367603371343090130821},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-304579954989922109794545317367396213111}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":343838377230315472390890640807146510329},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":42979797153789433704698801623124717171}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":457559873892984767823639264924609335977},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":114389968473246190764066930482200386837}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":78536557161543586483600432164813817869},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":39268278580771790975224342125848252127}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-190347191004591738733406666666772213263},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-190347191004591742402553273465208175597}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":192672644111657679476263175639638889517},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":192672644111657675018854600535407571563}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":276043073288160203682723864683990991859},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":276043073288160200114541892980564053363}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-58084614750413130756468772206183107},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-116169229500827700421002424542396969}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-269928803346779072695791269292972650363},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-134964401673389537826488200519498873275}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2514948470817791854714133686405426492327},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":314368558852223981314694778764483941637}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":31765304428487019},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":26317631752814221}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-59957417390391},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-31407099174419965}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":6592493782418619},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":652596423206311}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":51661869802409},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6041416101591817}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-316845461190203},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5065755818799037}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":25791066732465569},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-17256421782038107}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":22430000275849011},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2239359713436939}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":326050111579855},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-262951032289065}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":28988183422341},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-26160544789127}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-57185384827173},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3207206317758201}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-31933456390751387},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-199489987304483393}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":15667953748779365},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-53339128972219}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":9559609432181463},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2637616598748707}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4167872857370709},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5048259535956365}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1223125715373925},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1298131365484109}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1778313064151895},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1495704611113241}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":1711970740349227},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":7288396047593795}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-2541002579596381},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12495997052935763}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1385492369370225},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1003435493968155}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":89666392592267},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-85544156069037}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-2317495904943883},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8068820732638209}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-8586026600384725},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-10207643220758751}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":10633823966279326983230456482242756608,"numerator":69273856782805240419},{"denominator":85070591730234615865843651857942052864,"numerator":500314498849591792233},{"denominator":85070591730234615865843651857942052864,"numerator":435742953145295550171},{"denominator":85070591730234615865843651857942052864,"numerator":463090344265330048477},{"denominator":85070591730234615865843651857942052864,"numerator":508275636789249535215},{"denominator":170141183460469231731687303715884105728,"numerator":669880446638509815885},{"denominator":170141183460469231731687303715884105728,"numerator":877670331995185508207},{"denominator":170141183460469231731687303715884105728,"numerator":873370446642140830257},{"denominator":340282366920938463463374607431768211456,"numerator":1157784611408548084965},{"denominator":340282366920938463463374607431768211456,"numerator":1459198288179193548855},{"denominator":340282366920938463463374607431768211456,"numerator":1588797272796614016133},{"denominator":340282366920938463463374607431768211456,"numerator":2413342403624863252409},{"denominator":340282366920938463463374607431768211456,"numerator":2810571799513479256537},{"denominator":340282366920938463463374607431768211456,"numerator":2753295619755952109423},{"denominator":170141183460469231731687303715884105728,"numerator":1191841930901840361621},{"denominator":170141183460469231731687303715884105728,"numerator":1133286744547707733809},{"denominator":340282366920938463463374607431768211456,"numerator":1834566896029342781145},{"denominator":85070591730234615865843651857942052864,"numerator":557175145139042196869},{"denominator":85070591730234615865843651857942052864,"numerator":446022525519272770775},{"denominator":170141183460469231731687303715884105728,"numerator":719453944834790684725},{"denominator":340282366920938463463374607431768211456,"numerator":1478590848958551172871},{"denominator":170141183460469231731687303715884105728,"numerator":1049137949442468173419},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":32,"numerator":303},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":41694900535295269076105316146753232667},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":10016423665632313644953607265921824223}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-925064256768325077011739126334631108401},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-929132375252645199326851652589995220557}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-446228980907802688077368717332974158559},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-449127095005893417169320742321772735675}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":64822260101852281167208542851242657821},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":16093147063980677912323349181877682377}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":204794806240486572689734610224699392135},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":101585531867530815535648216895359762141}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":168823248107409031894371085350357571431},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":41760522868589815347204371768731697053}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-84092284614981142115698340995922199369},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-84977256212639258729284617467669082121}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-131136560486360878392108679065107295445},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-134212793643802284970634214345623232393}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2369922273982817373775929712205207611},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1160354545390733618205070167173984547}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":135937012150132315639127298505060904723},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":66469062317963810904625235239577590299}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":58492795097732423541774731961809225787},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":929610001814897193332619034563168407501}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-61595902192702093003592682465147855997},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-62188094840186520272778323949980086469}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2425238747886381425472947916018377221375},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2437961052745570168201675941038687784501}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":688499009635388793065241697990067633265},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":687541481454204221124185658001378169193}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":458053912800367424509575169447024216123},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":226671348588693418749004390178557702571}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":78781550867829152108224983399636832147},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":19134394323023891039377257854694502849}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-23763598182615017680985089940816475295},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-2998635011849491167122283312578631253}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":97152100757764224257002313513449699705},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":96216521376130491698579366781767265231}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":276149330950033040944116763810772314815},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":275447312970012032468463136886648054879}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-203841644762776736727562686874542809},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-16302169436644587488081522889113449}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-67335598370512991893925324583960714197},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-67508393692489147076435516781008698285}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2516410178858809385765352958832470883083},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2502444415310314751204609128070645565871}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":42672346395443124105715873942556736813},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":42672346395443119575003013739640336119}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-461192926936745861260761441483052060903},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-115298231734186465822271857265916040877}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-225459658669604725612334872910038355209},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-14091228666850295462199636388969899619}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":128175817811894072141990137886456402673},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":32043954452973517086077275272429740503}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":205850773551436431305822346956239248215},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":205850773551436427143084884831686420707}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":340079483084568270852412585076195973469},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":340079483084568268120984598699139643043}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-342313963796476001885866922510209213137},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-171156981898238002730409613587387315867}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-136359847298016572304623375656919891429},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-136359847298016575890686040499087283835}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1196928641544143914126856244010530303},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":149616080193017840505809535421211671}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":69015279396732986695953544895445245677},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":69015279396732985196817133743177730435}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":925326589100868080854810766734714591977},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":231331647275217019414185043319579855079}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-31250192563505503443727726004712236625},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-3906274070438188239837703652112667625}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-611675558143800620284080652437405765551},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-152918889535950155429691216865551931893}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":686898915524844624987140809238953328811},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":686898915524844619369880011836946447505}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":461302668161561228694801415916206625001},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":461302668161561223814460999586530757919}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":40162973307231834736541967292916232201},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":80325946614463664817118600798513106391}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-94446685584723814787992971365200981533},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-23611671396180954166712325057251084645}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":191168924411278939591873761703452389245},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":191168924411278935030497590283386881377}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":276552560775485253020828521224352468863},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":276552560775485249355886967216909417599}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-209567682244815617050162074359367065},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-209567682244818578371986366943995483}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-270431631720928716672579219441750478365},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-270431631720928719711603746895877166889}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1262975852508696025969879371247975346095},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1262975852508696023820988041871807222527}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":6943578103532843},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":40962183058924207}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2158187327476289},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-7373204386388965}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":11548674634794621},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1866405912902753}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1440636122231747},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6042786560499653}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-579989759836627},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-604271199816759}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":11537051327339099},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-47248623692494367}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":23190110564937315},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2425330633566883}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1157546629590529},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-317463766022473}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":217853314118325},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-11979573912573}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":3431822291471},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1438889939645659}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2560980764393729},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-154792257396503505}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":4328550336413189},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":144895807577941}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":8104788305519927},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-424250610920491}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":568858400913317},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4123783117140951}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":460995429579561},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-169278286468679}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":989327024384899},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3565664595894507}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":27588752378656675},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":7551791522495271}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-2436709654393849},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11980963790468733}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1328429800904747},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":962226940941213}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":190982767078961},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-79002381267747}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-4619547075777421},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2003218317827023}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-2470617791567205},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-1330965364879911}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":170141183460469231731687303715884105728,"numerator":1132660681284079699853},{"denominator":340282366920938463463374607431768211456,"numerator":2028297573856730284889},{"denominator":340282366920938463463374607431768211456,"numerator":1782837145167166900829},{"denominator":170141183460469231731687303715884105728,"numerator":949418388343513677315},{"denominator":21267647932558653966460912964485513216,"numerator":130085430872952311459},{"denominator":340282366920938463463374607431768211456,"numerator":1365684600351018248479},{"denominator":340282366920938463463374607431768211456,"numerator":1787463344611683457199},{"denominator":340282366920938463463374607431768211456,"numerator":1793030436184002878465},{"denominator":340282366920938463463374607431768211456,"numerator":1190080138148178893463},{"denominator":170141183460469231731687303715884105728,"numerator":749567431222007271255},{"denominator":85070591730234615865843651857942052864,"numerator":399738834904683735087},{"denominator":85070591730234615865843651857942052864,"numerator":618741601319494225381},{"denominator":170141183460469231731687303715884105728,"numerator":1434681340326503741057},{"denominator":340282366920938463463374607431768211456,"numerator":2808626061375841216909},{"denominator":340282366920938463463374607431768211456,"numerator":2440168392943116604547},{"denominator":340282366920938463463374607431768211456,"numerator":2327980389397849539301},{"denominator":85070591730234615865843651857942052864,"numerator":469712521569784130995},{"denominator":42535295865117307932921825928971026432,"numerator":285085566492223989177},{"denominator":340282366920938463463374607431768211456,"numerator":1832469929687391091491},{"denominator":340282366920938463463374607431768211456,"numerator":1480660737652527506981},{"denominator":340282366920938463463374607431768211456,"numerator":1519510567063965578925},{"denominator":340282366920938463463374607431768211456,"numerator":2148879916401496313811},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":609},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":42909067742449413412968696504042101259},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":41294574785108492629778571915974849517}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-460951285179251811818995136180772202561},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-231490027037801043587044788881679890739}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-28030490990452248454436607144815474061},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-225634453318634021031496531070796072869}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":16121945402566138472490322021278997251},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":32008769033786270194514483531346058523}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":206048128819111351208977129582218664961},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":204435104588673560699340263208532094175}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":340459259804229886948601757129541864709},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":336915652782142960794763736403128027017}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-339171650225937783804055664404192840245},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-10709138887336801448258559890714484615}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-66791888577647286485472697148520153497},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-68340687512263148707525570750367221433}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2403733935299167743076091727469126941},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":36796759097303678168654754297659127}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":2161624970222023352043645107256728761},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":135323878349174197438436206155370949383}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":930930703273946788577640509817829524157},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":924627056499192152386644180565108924949}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-62031608190184036689976346130375572259},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-15649394233526261021363531975941333713}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2435375714976407716117832375090527740941},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2448014964406099282291576048848029692397}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":171944708352899620109595657016509830627},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":686758043901923123872369165747599559567}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":461796104266124279952693394488766915975},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":457089181629302594512220424733358366883}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":40286406941698605982689205245207361965},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":78310306414670956393234269980836340339}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-47161616960221847398806438211867956065},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-2977127503828177143108171847228529839}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":48216789520437126337417242668447309615},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":23865252297605030826951377816413625573}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":138328469159635551659847065019408983715},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":137987433031240605434762488753766628369}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-180878236095216510775793782394863855},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-238256235744810342848716718602004577}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-269861484658282453408100553026744974383},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-8454208485726520196406491046562452457}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2527400411064293195322822465489672320255},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2513564921901513923316973314830002195017}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":43876581453272535731363859231195843293},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":21938290726636265551904725862184110251}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-229805494034802820556347741687883363511},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-919221976139211286337854710139096644363}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-452978724950873590057580241105039288155},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-452978724950873593705216791183780413721}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":127437081155105080528335214059493489575},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":127437081155105076635279848713471759141}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":103548242465310179692328920188853056975},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":51774121232655088780862447911118960603}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":42858369275637124834224720069575650537},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":342866954205096995888862626364232997621}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-345092111707603834128648210813825155935},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-86273027926900959442100106044125668999}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-138843310972812640566034159623063250829},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-69421655486406322123473497879020688919}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":606896523192136944766835939403950151},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1213793046384272666301322508927793183}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":70226156998557835207965186151804386797},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":70226156998557833667884528064445357437}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":230085211912334318432591607828321967155},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":460170423824668635256943371532523621977}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-62891701811422050073947196523621599895},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-62891701811422055149443169186676144259}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-76771852383215959495647872952209147897},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-307087409532863838714884278478348729059}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":686071413197671787757094604267464246077},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":343035706598835891013427855660722312207}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":232520537793050480455422106379238356445},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":232520537793050477957399937989241228789}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":82130345697927641940293521739238384475},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":82130345697927637158634102987267173849}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-23421397323271214404751039378666662341},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-187371178586169719085892182248952464329}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":189606301981989521067655479951496423349},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":47401575495497379100086986454834028527}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":138522820426350950773350171291134056245},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":138522820426350948891315722798610278003}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-92915745573578603535936966625708311},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-92915745573580127089177023589919059}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-67729896223612612319153793605079490743},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-67729896223612613099891756589962736653}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2536850723068964765994306818497763522899},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2536850723068964761593912192303824675955}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":95818734891653779},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":29398444235470559}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1036771762752407},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-27608786296766203}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":40305867143065407},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-562649264762823}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1234704112096629},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6037315783544837}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1018882022678023},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1145763830486843}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-234238868446507},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-29056157053263605}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":23641401607772943},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-208002175817207}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1020729657898399},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-741554729297313}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":408591992357705},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-35289648618129}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":273062476546643},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2566959159078827}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":4872114614150177},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-57290643016080539}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":18595734725277771},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":2107657883976793}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":6810820674130143},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2029533922241957}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":608434568589987},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1654250621627105}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":659871303032769},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1397170643970837}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":326893952743087},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4043296282898497}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":6864123904784073},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":7612769510121411}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-4586705951190641},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-357099699498097}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2539489049121599},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":454095315811863}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":100743016302073},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-147437047101603}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-2253003238458509},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-7875143456021747}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-5377410793285867},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-43665450991257439}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":2313743993608085719785},{"denominator":340282366920938463463374607431768211456,"numerator":2056205299679247581363},{"denominator":42535295865117307932921825928971026432,"numerator":227974694932066783407},{"denominator":340282366920938463463374607431768211456,"numerator":1946524046663063044483},{"denominator":170141183460469231731687303715884105728,"numerator":1065301121139982750547},{"denominator":340282366920938463463374607431768211456,"numerator":1392438745178001286239},{"denominator":42535295865117307932921825928971026432,"numerator":227482983747022904893},{"denominator":21267647932558653966460912964485513216,"numerator":115028471057830966603},{"denominator":340282366920938463463374607431768211456,"numerator":1223232109784235310137},{"denominator":340282366920938463463374607431768211456,"numerator":1540079101545302943303},{"denominator":340282366920938463463374607431768211456,"numerator":1608163065022647631085},{"denominator":340282366920938463463374607431768211456,"numerator":2537740796122048610089},{"denominator":340282366920938463463374607431768211456,"numerator":2929165711733789242855},{"denominator":170141183460469231731687303715884105728,"numerator":1432557679242056911889},{"denominator":170141183460469231731687303715884105728,"numerator":1249010220641850820217},{"denominator":42535295865117307932921825928971026432,"numerator":298853440535108473065},{"denominator":340282366920938463463374607431768211456,"numerator":1923935818131510136065},{"denominator":85070591730234615865843651857942052864,"numerator":583412586705965945097},{"denominator":340282366920938463463374607431768211456,"numerator":1882033632843315029305},{"denominator":340282366920938463463374607431768211456,"numerator":1523553065595424357873},{"denominator":340282366920938463463374607431768211456,"numerator":1561474241401276939455},{"denominator":170141183460469231731687303715884105728,"numerator":1100093117596530183243},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":16,"numerator":153},"tube":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":5513878143818120411673021642438647361},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":21256246600215901803146997892103940375}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-918744471501373762395720842369084956023},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-922790451914838167042891971233691285521}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-56331617242128628940798155769064168095},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-453316731958833228509230240629123745783}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":16034253816486833380506057009734404793},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":127291903331888718023465276362710137191}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":207292786009364341841787831380517518775},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":205690549944999992176562334970813714749}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":85812792552153728406678926988263862375},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":84931768351029660210642507689981047927}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-341963867044896592552211802191725757683},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-43183104320086335736095375397192132083}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-136047927105653485170523295139211173069},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-139167129029284356511524098117275101117}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2437277974458374108519845199127238283},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2389032761824942263601075363249263725}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":140768101726184373287639841428681725851},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":68863193678248629480483490624213868183}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":925959471324794111503325331503123201255},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":919630649085533805018179686018060364033}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-15611602371565569027774591553778600723},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-62986165893749583874669221959191850915}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1222723275784686181567087886963451082583},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2458003361627673543155644129955087879987}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":343503555172005547947581412810743496025},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":685925162152346386814942663995173615217}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":232766885642314169947431665349364174203},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":460832545592331544249971851440839552803}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":82379108254204050152384512212708345537},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":20024454385845349944966708154816651745}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-93557933989597562603724565963157087887},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-47272717880980033559153802079244329205}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":191370786077974112577469778394659663853},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":189352169411022382721509613681610173331}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":277148089068842607974014154821916295965},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":276486390965112209509428390572017180497}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-156868009426071712101481348162794465},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-107711600723450781756576917794467551}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-135183082367613056052046538105497502315},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-271020834592252157788954506319526486423}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1269143182114000541877900093613021790793},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2524581187327324376962662294223453068155}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":45067789076125323222985069326945540925},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":11266947269031329624741215451761654519}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-458032286890017123208867614272499126719},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-458032286890017125293735970345292468603}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-227472054200674580017007054887745892679},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-227472054200674581882671746472518282177}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":126664905256609677241943597090041156405},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":63332452628304836625516950010861537649}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":26041685580938165578995602548829066383},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":208333484647505320270317720021289566789}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":345630625812442183423287976616185883227},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":172815312906221090291566336291249972475}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-43482061428480911642846362081580617311},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-347856491427847296847893730261448094353}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-141344115415464237726781876495086117897},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-70672057707732120752431078239321546897}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":615259416515076514473362732231577315},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2461037666060303543367234580840240497}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":142891441055928956258772014157703229801},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":71445720527964476547332633447020310519}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":915347780288272511712531439616347476043},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":457673890144136254239820096711453037639}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-31631111892372289813533617672913780729},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-63262223784744584830415429241244176927}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1233315661579314807784167528443366384327},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-154164457697414351346771375873641633937}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":85649492416317282272059139655740402025},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":685195939330538252330878651590963225765}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":468773963752916121343277774564321576327},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":58596745469114514528591068846629833527}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":2623436455135882774071517770817994905},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":10493745820543530482501189276747307227}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-185781057050353108521493571353475112271},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-92890528525176556230591101166098090871}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":46996299269538038938180448095272125513},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":187985197078152150977482990186772265983}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":277521961715940697809998030013071586225},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":277521961715940693944382653092205754521}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-161133776000590354307685049561341759},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-40283444000148372383994221957935693}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-271392232891718807951989838575470422041},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-135696116445859405580506423579678004249}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2547645645677338824368574021758851123285},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1273822822838669409932090777804255916841}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":81232662361043585},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":9165581910156829}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2054576078031441},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-51172336823231595}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":34742483822178265},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-825941466306607}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":990536556515505},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5950792603446927}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-868290639222635},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4293625273717089}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-10421980957740909},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-33440169689294917}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":23689580980730793},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":188432415203515}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":890675553106281},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-418555088898217}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":95665803456265},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-46572678519233}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":215170406099923},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2270656466210031}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":4302058908057183},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-39367077524316825}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":9724622030534931},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":1422585461925713}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5637282037160501},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2267972805157023}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1253148568830935},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2565756698655581}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":420051106931943},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2808733045658967}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-225375015466397},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2202612850656561}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":13486337234619365},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":15009525320487443}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-4267295362654657},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-169045652628897}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2415663815300849},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":424177129597515}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":210143129311961},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-138879264560615}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-4314082187552075},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-7651763182306361}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-5626707766799075},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-21997758957508011}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":85070591730234615865843651857942052864,"numerator":590494663252669774115},{"denominator":170141183460469231731687303715884105728,"numerator":1042421898596210370903},{"denominator":340282366920938463463374607431768211456,"numerator":1865645668459928687151},{"denominator":340282366920938463463374607431768211456,"numerator":1995451377869579059337},{"denominator":170141183460469231731687303715884105728,"numerator":1090410918758677117455},{"denominator":340282366920938463463374607431768211456,"numerator":1420049422837632544675},{"denominator":170141183460469231731687303715884105728,"numerator":926274880223163208025},{"denominator":170141183460469231731687303715884105728,"numerator":944519638049456518295},{"denominator":170141183460469231731687303715884105728,"numerator":628631435134878801309},{"denominator":340282366920938463463374607431768211456,"numerator":1582051807962785999519},{"denominator":340282366920938463463374607431768211456,"numerator":1616371839547931926093},{"denominator":340282366920938463463374607431768211456,"numerator":2601667217496601624229},{"denominator":340282366920938463463374607431768211456,"numerator":2989998391931942949895},{"denominator":85070591730234615865843651857942052864,"numerator":730698360912998251389},{"denominator":42535295865117307932921825928971026432,"numerator":319659124687945644825},{"denominator":340282366920938463463374607431768211456,"numerator":2455137437300755766209},{"denominator":340282366920938463463374607431768211456,"numerator":1969838333914786159091},{"denominator":170141183460469231731687303715884105728,"numerator":1193808062641977660329},{"denominator":170141183460469231731687303715884105728,"numerator":966403452402827431471},{"denominator":170141183460469231731687303715884105728,"numerator":783806985703969132109},{"denominator":340282366920938463463374607431768211456,"numerator":1604509835451445416085},{"denominator":85070591730234615865843651857942052864,"numerator":563046372182936433735},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":615},"tube":[{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":2831099986864322428493895878298298055},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":43718690526988461353576908999098464509}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-915591854233182227387446422016619463011},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-919625323017658959554566742397041137353}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-113181020731299100244637695752355899335},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-455270503181968291768845361766557249933}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":31884876408276315096869757629182480921},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":63257630426551730898020434071694419073}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":208528721047229757177316809158888085759},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":103468673792165210780954505838158171267}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":173010174789132787144141146584040422969},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":171258288470705799144463553793068104151}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-86186018032255898910500932821218317197},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-348224467914825980508448524375368884699}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-138529207568150218001711295227587003981},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-17708780201846805455617492122915777113}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1235269394383581351716618232003220611},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2422813570990921180288134612836240765}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":143209606378326741876964361129128410085},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":140145948176981103497858466440083942567}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":920975507267413181269419960358793845659},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":457314455543327052939442336051378665413}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-62840342521861550770303281444328256769},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-63353935417466543806742430038238432475}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2455451773423297123080851261848773297391},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2467926801819432930879657985868944394963}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":686185511389703939129459412737650035393},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":685044529469382425405811330234815397785}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":469265780791833372502800100075328283363},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":232285831948287565924733258750581835381}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":42100323757923218370631065929162202003},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":81900312162603326093897655090591564325}},{"hi":{"denominator":41538374868278621028243970633760768,"numerator":-22646171368834765325646969915135077},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-187577150000911421479024649682640149785}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":47453863859109147068132666496753213553},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":11732745055747869763986175489429487571}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":69405607392061978029392357334159693025},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":276981553217641229523193891604060392489}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-131871887483823549477660017064180635},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-95913501332654388461437925208747561}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-135428012056242969883895226200930842385},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-271491631932131034856037670387401211231}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":318633521637982044618945794544124033779},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2535493228620643473220839507165136803751}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":46245090811723349921779089061196882645},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":23122545405861672550888496007706811243}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-912915439623013566021717696838249556353},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-228228859905753392562548100404621497459}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-456815450400178886134479012067513433685},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-456815450400178889951280272138481608829}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":31464726765674577268373481046129837715},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":31464726765674576245548206792992964391}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":26195214035058581480126844375797349233},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":52390428070117161844233408432456789375}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":87092190940776290591010127967606450299},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":348368763763105159466899780085514020929}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-350605456849715794551041743392260379571},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-175302728424857899161061184329194655237}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-143862438854848228873786327426003968785},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-143862438854848232751398196716962124467}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2494197071076480412619200252112734327},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2494197071076477828227928331412211031}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":72674107134996939175984035887644537835},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":145348214269993875101816652982763563859}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":455175935518116698509362847171870377333},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":227587967759058348442423513621973341375}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-15903011670559491283706809764078880927},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-31806023341118985234168280659548713069}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2476498956614851976816727988677090727669},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2476498956614851982920490225747128561011}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":42767137686132975724783741103970739771},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":171068550744531901408289044200894399347}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":472500194503023375163324958631147794187},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":472500194503023369927404407583012547159}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":85785030197271661933081015763256215217},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":42892515098635828445605883653875984969}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-46030877288125157602314657025602231327},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-184123509152500634442418931480096598247}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":186306073547695889646234503887912676775},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":186306073547695884761028336881088697777}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":34747644566471348412055942590477817349},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":277981156531770783326814019148852166031}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-8467461050766174614586674787795027},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-67739688406131009790087692942910239}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-271849128263005138393748515064567093913},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-67962282065751285422760935142931722299}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2558336681782466016208594895464853455609},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1279168340891233005799413139574341492285}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":8338679061348909},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":1051602377727603}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-117622463935389},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-2944892985006235}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":29755284387166779},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2546714570275743}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":47137821121005},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2923504790135771}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-721098149867327},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3949626683507041}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-4638654098698775},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-73315652016928379}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":23469964994013055},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":320047955745063}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":767489988973631},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-925221794498345}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":89070302712857},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-28604622615501}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":285936682294521},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1975976601396999}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":46668642216020747},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-22995175273908331}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":1233975255380395},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":1707871531320669}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4580158174343969},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1217463342005729}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5103571092421087},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1901324621783603}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":51246295077857},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1401763396366329}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-172665509718023},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-575743048663429}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":1628807110266005},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":14524353967156625}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1956969391630925},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-5081042136659199}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2291075796336429},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":785633254532861}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":54025512686873},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-131430234880311}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-4059401829499979},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-3664595565859257}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-22913944315718093},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-10839475389655093}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":170141183460469231731687303715884105728,"numerator":1204985950108078572427},{"denominator":340282366920938463463374607431768211456,"numerator":2114214734225949649973},{"denominator":340282366920938463463374607431768211456,"numerator":1908383205678720228439},{"denominator":85070591730234615865843651857942052864,"numerator":511411811974728660709},{"denominator":85070591730234615865843651857942052864,"numerator":558009736593502249581},{"denominator":340282366920938463463374607431768211456,"numerator":1448542985374644823493},{"denominator":340282366920938463463374607431768211456,"numerator":1885529217746478949049},{"denominator":85070591730234615865843651857942052864,"numerator":484701272072396835463},{"denominator":340282366920938463463374607431768211456,"numerator":1292195400610499604931},{"denominator":340282366920938463463374607431768211456,"numerator":1625074149534597468363},{"denominator":2658455991569831745807614120560689152,"numerator":12690985594612763793},{"denominator":21267647932558653966460912964485513216,"numerator":166671762817025659337},{"denominator":85070591730234615865843651857942052864,"numerator":762969098382311933307},{"denominator":42535295865117307932921825928971026432,"numerator":372711042247765002141},{"denominator":170141183460469231731687303715884105728,"numerator":1308979385634040550735},{"denominator":340282366920938463463374607431768211456,"numerator":2520932666586576904969},{"denominator":340282366920938463463374607431768211456,"numerator":2016574383408945286741},{"denominator":42535295865117307932921825928971026432,"numerator":305324994928833370153},{"denominator":85070591730234615865843651857942052864,"numerator":496204002016553571149},{"denominator":42535295865117307932921825928971026432,"numerator":201609152566062217015},{"denominator":340282366920938463463374607431768211456,"numerator":1648645977858928788373},{"denominator":340282366920938463463374607431768211456,"numerator":2304874086179463784379},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":32,"numerator":309},"tube":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":23230822251570469183753395785642596789},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":22456458125450680367896768016675429535}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-912446552735831095892241922815538786581},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-916466576118279045553608609587703760115}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-113675302050256680779961412080817905959},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-228565105102125546130765130323224991749}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":7923224199858274294974308173225117373},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":62852383893252636971567798077508958945}},{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":1638717759582927075197173007406969269},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":104087720736024363170996614059210019217}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":174382494139673637181686963279038467215},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":86320590829029848096332022140774979431}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-347510584566307063628828916766120891589},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-350969653181709358768248713432338105021}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-141027807188558062202933739781916841651},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-144190889457619817441415104714586348557}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2503501331896024593867895548217000699},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2456319480967445648867160895684683191}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":145668784487118482432342611829544725341},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":71291423670676169361906114161768790527}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":457991219953174209626818206702501775047},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":454817921862794671921293338858733032569}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-63213472428297652533097361794539577161},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-63700985992766923472796095108396164573}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2465391928686624605779346479407337528453},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1238892936703337351834616126001133337455}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":342657863173257325751325208627403720639},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":342058928093375359120438709682494223027}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":472990994039298982792718422812289495977},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":468305404832206908832729675857674881181}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":21509413489116606324017238041687358097},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":83718001298557334811558465308223543357}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-22981459996532155841075890287037581775},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-92997716140626326549067494623593578821}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":94100790525352962933613415396796878145},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":93018870662584112361088224433782234733}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":8689987225038714106118099687565501175},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":138730001442120449336002629928941014003}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-52958711218553251932734931332534189},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-83634463198268243971905623037534161}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-33916329371420476156641433617466973381},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-135973307087456898120857581549029440713}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1279873030121354493641376671050680036487},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1273150577585037733964392345099151944905}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":5925958849149877334256142643726559809},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":47407670793199013758656561583297309445}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-454888154291766469941545329187562625867},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-454888154291766472085897296739302222091}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-57324098590504119310650885563934796795},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-458592788724032958389297409870219760125}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":62509360337798074579315310490205776933},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":125018720675596144964343269746379386483}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":210781103417325757230254154207054836797},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":105390551708662876330858656089632314709}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":351079699661626131348728066473042172401},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":351079699661626128392782815379182902953}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-176668698775845734338870549462844533577},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-353337397551691472515384778447319453075}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-9149903109474224517167819435724714483},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-73199224875793798127120166791977091419}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1263524969409824488517471996251915799},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2527049938819646320927765126133800627}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":147822896403615963390696745044478485849},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":147822896403615960052358247108135842015}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":905357421179454245567534379365390374191},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":113169677647431780287562561981786925391}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-63941291545310073389040403755128321421},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-63941291545310078855033109016411388587}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1243151395066209324140753323145649027453},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-310787848766552331813893269354194376155}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":170826982247739521531956639790741569619},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":683307928990958080044162958697708267011}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":119054656158169312414472325425589011815},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":476218624632677244297664279049228610609}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":87635765763896507963664971998412106179},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":21908941440974125696797460744828372795}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-182399094147337747870128486214680532775},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-5699971692104304749952237108722554521}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":184569437628548391333002815744360637377},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":184569437628548386335756116708963878039}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":139211421920798038046770609445834280571},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":278422843841596072017364171714717397247}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-108874062437294073941775983913388323},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-13609257804662174083080563025333007}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-272289806750329192147099010621118635429},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-272289806750329195534926158462761679251}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":160557757804900982210335118809682232571},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1284462062439207855324408783563007845507}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":53631523298779069},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-658859414467235}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1471836526773559},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-43320362488692453}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":25365818797947853},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6664199501105555}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":68792787031713},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5740510967064225}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-278707965711327},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-904743982797267}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-12384632685245315},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-9743069371242299}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":23099285986142525},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":470249328742661}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":163490249306625},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1009212240842255}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":41415618040851},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-8429156467399}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1409034875298175},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1701723366521547}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":7106188938344979},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-9126496113621985}},{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":154515490670645},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":7613111082365577}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1834791635805469},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5149784200337055}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5174107365131947},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1326164978570761}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":4806042927453},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-349155596734837}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-65651969736829},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4733731251767793}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":12470857540213957},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":13799050990888967}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-3519312357321617},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2375201075828605}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2169377316894553},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":179101445407597}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":13798836659895},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-31456851878191}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-938179388764041},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-434796145244769}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-22754492963391553},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-42253860807286017}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":21267647932558653966460912964485513216,"numerator":153604321536993810085},{"denominator":42535295865117307932921825928971026432,"numerator":268041380411094829597},{"denominator":170141183460469231731687303715884105728,"numerator":976014573835110583089},{"denominator":170141183460469231731687303715884105728,"numerator":1048570265095192212363},{"denominator":170141183460469231731687303715884105728,"numerator":1142133445116947610241},{"denominator":170141183460469231731687303715884105728,"numerator":738973018951064955421},{"denominator":340282366920938463463374607431768211456,"numerator":1918811230616479607019},{"denominator":340282366920938463463374607431768211456,"numerator":1989776779719560341177},{"denominator":340282366920938463463374607431768211456,"numerator":1328053356337461112889},{"denominator":340282366920938463463374607431768211456,"numerator":1669167693589050412055},{"denominator":170141183460469231731687303715884105728,"numerator":816725482873963551857},{"denominator":340282366920938463463374607431768211456,"numerator":2732990270194779795091},{"denominator":170141183460469231731687303715884105728,"numerator":1557407672293696251585},{"denominator":170141183460469231731687303715884105728,"numerator":1520914275048228577189},{"denominator":340282366920938463463374607431768211456,"numerator":2680111105092090924071},{"denominator":170141183460469231731687303715884105728,"numerator":1294117861429840659117},{"denominator":170141183460469231731687303715884105728,"numerator":1032082989650087918237},{"denominator":340282366920938463463374607431768211456,"numerator":2498620358771725383267},{"denominator":42535295865117307932921825928971026432,"numerator":254760974637838493733},{"denominator":85070591730234615865843651857942052864,"numerator":414840315238936900581},{"denominator":664613997892457936451903530140172288,"numerator":3308421820137572445},{"denominator":85070591730234615865843651857942052864,"numerator":589565604307632016957},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":621},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":47612960421859544347465427690789425057},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":11523276324871497407508458062897876229}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-454655171535309072622493819558846874319},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-913316005906613061917437375474021045031}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-456584289597015309711920131849029759037},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-229447948814325536968754465917421624981}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":15746236252041126531402968604422504881},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":31215015120005495118481376131449103181}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":105487088915474460489889478960542533321},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":209404771663748616976617486353129250311}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":351481180583805791689726818884129022063},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":174011469835958100165515054431777107315}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-350261759252972438929848419711218951097},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-353698735220405995141781654322609980281}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-143543905460021723900841553659807144467},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-146729239408286773630289289122752132091}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2536151127982830623262155215302838125},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":622383877299498546083809052772111573}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":148145896882177908766742889602438551985},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":145037360646417871361269293114019314561}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":910986170088295988353431346738564581733},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":904643179567670075006374824989349566619}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-15891472874951212801716672699246389463},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-64027443324135990486472171191261960853}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2475267596815649291355422320782824329911},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2487581194807676145968478997526465051935}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":342199731193097163901076436751332522003},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":683146868305527165746022717310356222859}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":59588533411851335318985124184606421177},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":236016315429745723151231282230791713701}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":87890357965979084902415986190824574319},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":21387776222409374555825046796879774153}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-45529791312633830608494164456231262865},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-92173107015248390110567369954170232587}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":46632405389235479904426936683528191563},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":184294141464481619902975320471135127041}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":278519190770775328623404106120657895457},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":277921374949659167182748453685426723255}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-39505301080171128592460242508654993},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-35438421276729942739356543690670843}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-67947387984310199877636495934779996293},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-272385315194884188342571294794567817025}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2570320332297848408932312832377476604191},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1278502582529267317058663886495018332553}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":48554776308901562966305286481992855133},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":24277388154450778978111354732485509889}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-113331107445363675221278799271803442637},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-906648859562909406121016687556761370497}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-230138106693354011980850705389216334525},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-28767263336669251747183558404007931089}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":62071999131255562367301754832085334875},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":124143998262511120434676574719919472429}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":211991589605453168965359405290733919125},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":26498948700681645536289779189994128137}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":353761829551779664759347032181583699209},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":353761829551779661742724630376389739223}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-178025369281872870712755698758718975069},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-178025369281872872665380451548267120803}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-148952306267413677966594325309809630523},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-148952306267413682050553048135294467163}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2559582475595814364680408277559168593},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2559582475595811634957760454916464753}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":150315737998775746293817839645481513563},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":75157868999387871432552921137909041645}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":900368549329339051040724197490391841751},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":450184274664669523876898855406875278205}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-64250103237434846827986541962974095901},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-8031262904679356553600366321122644941}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2496043466379663903797871259052971082793},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2496043466379663910155545038724518924627}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":341149428329347461956750916190188488873},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":341149428329347458853504050828203826009}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":239964053293141144464381998911448240339},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":239964053293141141720616651767766491329}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":89502409954530337146525112026674696165},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":44751204977265165916191651256376043189}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-180608425837349879097260723675008539019},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-45152106459337470830637316502262382835}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":182775836760789928128670880640793528445},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":182775836760789923017268611309224645527}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":278846627972541577487688296285655936355},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":139423313986270786651192931163336115449}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-40662254155347312947985615905979395},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-81324508310698040114795449424974627}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-272713787954704872113475320168967213395},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-272713787954704875594154071589593154305}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":80606510916607953877578453246633420587},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":80606510916607953726804820252055829319}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":1302495778781827},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8468377224568333}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-449518396281877},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-19892833268353375}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":21515581020169989},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-4015521799795025}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":380145226522557},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2812945351135611}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-99207108801147},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3288320561410037}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-7353660433872945},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-9972172725221503}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":22603449275949829},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2253652707477979}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":136128718787137},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-271629620096831}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":304367872354703},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-75421194181391}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1618392959312715},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-354025907709997}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":32006679897093725},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":5318032036167131}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":19440409870166007},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":8112651525949625}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":719598906715543},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5364813870005581}},{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":40851291368769},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-413787232005517}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-141971741791699},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1389481512062555}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1324193510570781},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-595541196493963}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":2929961569805381},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":12917168797021473}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-3098457628273723},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-4395443413173583}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2046818215971661},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":20050443981367}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":110457264490871},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-119882615533807}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1710172940382703},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-3238469451697559}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-22178916335241537},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-10101609070224291}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":170141183460469231731687303715884105728,"numerator":1252508107193719062139},{"denominator":170141183460469231731687303715884105728,"numerator":1087686851688147421601},{"denominator":170141183460469231731687303715884105728,"numerator":998301494265268617083},{"denominator":170141183460469231731687303715884105728,"numerator":1074980232227080600885},{"denominator":340282366920938463463374607431768211456,"numerator":2337519140139327344289},{"denominator":170141183460469231731687303715884105728,"numerator":754143009766281919935},{"denominator":21267647932558653966460912964485513216,"numerator":122038411118203994363},{"denominator":340282366920938463463374607431768211456,"numerator":2041978545896064650383},{"denominator":42535295865117307932921825928971026432,"numerator":170607637038273874147},{"denominator":5316911983139663491615228241121378304,"numerator":26786788772445884981},{"denominator":340282366920938463463374607431768211456,"numerator":1643401888994544538785},{"denominator":170141183460469231731687303715884105728,"numerator":1400201265211915711811},{"denominator":5316911983139663491615228241121378304,"numerator":49669262003609773235},{"denominator":170141183460469231731687303715884105728,"numerator":1551621918546052528065},{"denominator":340282366920938463463374607431768211456,"numerator":2743764028648040582303},{"denominator":340282366920938463463374607431768211456,"numerator":2657069184688930614431},{"denominator":85070591730234615865843651857942052864,"numerator":528159752476284946343},{"denominator":340282366920938463463374607431768211456,"numerator":2555698288451185404737},{"denominator":340282366920938463463374607431768211456,"numerator":2092650514377487568769},{"denominator":340282366920938463463374607431768211456,"numerator":1707109241710234250143},{"denominator":170141183460469231731687303715884105728,"numerator":870168923706900827799},{"denominator":170141183460469231731687303715884105728,"numerator":1206184507076634316237},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":4,"numerator":39},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":48750745666949506184570270864633173925},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":23629220125835590633444185709406481387}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-906184944947578253383119877065920895785},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-910175348987527909814980673324349644621}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-57296669795632221035477646388752055633},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-230283830977404815148840151462806241235}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":125134045922960190946575544841932538625},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":3874399795291242908347697138304560831}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":106091783042799704119922490655388405507},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":210625274231962013153036459809205136401}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":88540045729548776842170458853626015109},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":87684355936057393793309619893841714265}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-352995986733957705863766874134463735761},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-178205047455647667001754559923846897067}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-146077672172579547590852855798746073315},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-4665170248833124825911731416506762559}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":642118570969450657328593520666027233},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2522447233813184508884808331072293531}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":150641192103208909236042939409078867109},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":9219359527312157578385691176897613177}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":113248727649173191750526403902268786769},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":449832910527036324818721357444787175047}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-31948858817373435857521670252087089465},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-64333456740378888455013970814692348283}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2485079387540720142106767388986901895633},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2497313413457705203854159959831840232809}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":683438442640834159243256299064906175127},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":341066653071036714044479451122265232085}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":480416452535517873826992289683515186287},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":475752199310139396572183388734416407139}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":89758997372652236786760721431082996831},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":10924981392587677653960245918930953603}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-45080127725071438608209885453910522399},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-182630047841454640616875148352733179187}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":23100009766022300245378014894156173657},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":45623418282969573915702771815846281505}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":69735207727607839759826035955034352153},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":278365289722836595681593063458668145367}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-51158324670041993859504781055758363},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-115286922189214659198549162221570861}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-272232312745332565664281750802780645727},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-272807252795298830492454346787137287191}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2580791376332379948667888413196794301327},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2567605541383530795313365250651593261473}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":49685718098151270286654234807818883501},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":49685718098151265182691303433872567983}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-112941839670132549688846855773169620039},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-903534717361060401926386696316725032319}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-461865863978649191527556735603570132833},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-230932931989324597805916706932740653601}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":123234410946141456001175661650845079619},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":15404301368267681449112076996596275791}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":213193098321930572152347625810107191161},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":213193098321930567368726337952138473781}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":22275850779219744158711878812548574397},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":89103403116878975865040433755984521547}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-179371970032483988490429922000788259715},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-358743940064967980955850346897572483703}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-37881038938130549205933598275458317021},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-2367564933633159390853219540674805967}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2591781473626181912373767427753490233},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1295890736813089553542948606752997375}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":76413488358517390775527087271526858343},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":152826976717034778029737211047822968305}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":895389192181572524019205197703703086753},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":111923649022696565088808235032412981201}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-32269324423005358744575770725643964573},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-64538648846010723227151901267924378765}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2505721656257137015619837811198927468115},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-313215207032142127763468833718027946289}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":340624369200962212247581272808889096873},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":681248738401924418163223283913742979669}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":483627489142552586818680655141654827451},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":483627489142552581200773660762354793315}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":22846301577879764634175447398509547975},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":5711575394469940817611707413938204361}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-178752170476978189839874773806055996649},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-178752170476978194163928180526864966049}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":90462929208290293622778658290683200221},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":180925858416580582017827485284111233029}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":17453256215876745838351263172989280707},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":279252099454027929116547247642591985497}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-52838272883346615740634185455725525},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-26419136441675064019511032133036813}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-136560288001600160817116416467262492785},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-273120576003200325210144378280262345891}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1294894903355688850868141691037166538611},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":647447451677844424200460471880471333497}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":31156878618747951},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-15379999393228389}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-166644001202023},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-18252908805888859}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":18162039999617867},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-9202572145776353}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":122945093073101},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5500756563133693}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-236629321175581},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2977019348070487}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-32435468230509527},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-20069971267092185}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":22022795012512903},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2373391809515965}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":111519556435941},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1160874028855573}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":139952992181847},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-41471453784961}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1804811396900345},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-289642466629749}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":34726805592900137},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":24378482220762473}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":9470299880482383},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":8345634890207211}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1105988732792335},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2766812225685005}},{"hi":{"denominator":664613997892457936451903530140172288,"numerator":10283113109003},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-403163633014573}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-279835429720355},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1380644999896335}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-757340582676183},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1185619806230835}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":21868491923793649},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":11894760647991151}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2661291443553519},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8107743254588701}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":965549668621781},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":563512619561717}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":220180700270243},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-57869145190663}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-3061648901934923},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5986343626792133}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-21224843898090599},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-4790991338428325}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":85070591730234615865843651857942052864,"numerator":637989549311991792397},{"denominator":340282366920938463463374607431768211456,"numerator":2207787755478878748155},{"denominator":170141183460469231731687303715884105728,"numerator":1021062328412441445037},{"denominator":340282366920938463463374607431768211456,"numerator":2204136649515662796697},{"denominator":85070591730234615865843651857942052864,"numerator":597952318433492727809},{"denominator":340282366920938463463374607431768211456,"numerator":1539590240780000622475},{"denominator":340282366920938463463374607431768211456,"numerator":1987485426746396483667},{"denominator":340282366920938463463374607431768211456,"numerator":2095435025274549857233},{"denominator":85070591730234615865843651857942052864,"numerator":350660928052805998993},{"denominator":340282366920938463463374607431768211456,"numerator":1760657000056983664519},{"denominator":170141183460469231731687303715884105728,"numerator":827156197176062099767},{"denominator":340282366920938463463374607431768211456,"numerator":2868994882425882846031},{"denominator":170141183460469231731687303715884105728,"numerator":1621976278235844786879},{"denominator":340282366920938463463374607431768211456,"numerator":3165966796793245194983},{"denominator":170141183460469231731687303715884105728,"numerator":1404476128231182490455},{"denominator":170141183460469231731687303715884105728,"numerator":1363727810793241837787},{"denominator":170141183460469231731687303715884105728,"numerator":1081010858247383291725},{"denominator":340282366920938463463374607431768211456,"numerator":2613862192422722066115},{"denominator":21267647932558653966460912964485513216,"numerator":134283487360578713249},{"denominator":340282366920938463463374607431768211456,"numerator":1756149025979909848265},{"denominator":340282366920938463463374607431768211456,"numerator":1787954310325506251555},{"denominator":10633823966279326983230456482242756608,"numerator":77100381116650600113},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":627},"tube":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":24937130153325768597975124088447972553},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":24204083487909113464793158015210610951}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-903072023519914366662749510959910145213},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-907046285789908854949713040756302979479}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-460068498325286071750178422359271230789},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-462145648939505593865408304351862357841}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":31065926176631334611513796934555339195},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":123066640266383201331538409196737742039}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":53345991282568823866156667787595926567},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":211836881213806260826506184650013698793}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":178404318415864074126945519463556041569},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":353423295409563163241483918070862450393}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-355711692963601257065133479213031553573},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-179551074482523050334456330029036131833}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-74314633440138990909429555032822552925},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-151859660751634943296211260308267097027}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1300228749789022623883990106865560375},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1277520403132226172322756785356126179}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":153154905745396311935808181019904323209},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":150000274915817901857250026615472583793}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":900998887293477159495835506153774644013},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":111836938456512009368090302714871234619}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-64209092753894563716375235299389191687},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-16154799397324348708122074934053744567}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2494827939879781613997261920345774159573},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2506983204878604512003355305218720136219}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":341217202420158782625894799116902675195},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":681078923024091151868911941898544879507}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":242057199067222138392324208427886439675},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":479462963080930950847520512922281521297}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":91643816769565065957290119660814730661},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":89264475863970916929615878140853653063}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-178456388341616020549004668339234125175},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-180847541114653645852943110438920493753}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":22876686660512740253031740255917426673},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":5644904001593186970888234693153244361}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":139672050250728234873428103029607594743},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":139395676623553292404277911944915770219}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-2796046772053230996132210890373643},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-10984398735146591016373597307639065}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-68164609727004943710156542181332043175},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-273211929374870747569117680962695324091}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2591159656142479826811398262699598677221},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":644525662143668482382392894882201206925}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":50799870389324289135812291390939326237},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":50799870389324283938888432933339684423}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-900435454594895229392433099811002273629},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-900435454594895233875675532885796507253}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-463361927172328827668775818968001552697},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-463361927172328831846030431601833431149}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":122289649673760749408705297931522744353},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":61144824836880372444650824068547756989}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":53596388240701084192491632290654446797},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":26798194120350541484457734446337915067}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":22439598054310419500062230998157691447},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":359033568868966708857175269711295094181}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-45176937128059724288115790726255234873},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-361415497024477798351852908830150226705}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-77057067125631680428061491133491938585},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-154114134251263365156467389339726405711}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2623634319908604942711399371623962743},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1311817159954301029928402196712743653}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":155356836710258385055280994563265482099},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":155356836710258381439081536040718646645}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":55651444119817217344288499443200195625},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":890423105917075474176114989615405135349}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-32403558038757071099647478021164343495},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-64807116077514148076860592228323923057}},{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":-19651078578173490143816908766293068345},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1257669029003103372514489265720342957295}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":680159338510112692641758916582411694231},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":170039834627528171545422231688754170405}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":487315618094725944689273701772879922761},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":487315618094725938937848958569878092889}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":93284404550074400062286590146401059085},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":93284404550074394463448259986384894147}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-176831044703168662546666526585351410121},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-176831044703168666971365108969560579845}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":179020128949565354703823644809951842131},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":179020128949565349357525775131656206555}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":279638835439311865802527552415067590557},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":279638835439311861390970201719797135941}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-5855943216704123753623757357877845},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-23423772866820108041258735444954735}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-136754830107210370460727174431545449605},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-68377415053605186148760719004871288437}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2600069022149048970875479011182884692007},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2600069022149048965829841785631963576861}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":22076583179993575},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-21398121270776443}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":353930162621109},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-16748006609444001}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":15260267601028759},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-1274767683496933}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":75292203665115},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5362489759905257}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-78681458577755},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1345126692310387}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-16961221051878975},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-39835696702653767}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":21379176656224571},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2274854563929175}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":179558484090275},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-307804930423341}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":129108794300117},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-180096484095611}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":984591831926451},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-232551222598611}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":146672428166495677},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":9768882920446225}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":4579144894771623},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":4171264755049261}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1665022327108323},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5662467683504045}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2642462481923085},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-47804494868423}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-198317785082675},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2740707393872395}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1629790912841919},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1169130197671167}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":10139992884137523},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":10767738761835857}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1108287054382487},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-3731934477118617}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":455879484848215},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":241809121341707}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":27350210965231},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-113224865687265}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2686129213136763},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5500013202136943}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-19957640780330371},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-9026453352441795}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":2598440191876574435897},{"denominator":340282366920938463463374607431768211456,"numerator":2241604114600625051701},{"denominator":340282366920938463463374607431768211456,"numerator":2088614577112381437113},{"denominator":340282366920938463463374607431768211456,"numerator":2259699068360129997443},{"denominator":42535295865117307932921825928971026432,"numerator":305893877626249276477},{"denominator":340282366920938463463374607431768211456,"numerator":1571887338653963209693},{"denominator":340282366920938463463374607431768211456,"numerator":2023453739349008026161},{"denominator":340282366920938463463374607431768211456,"numerator":2150171408368026327313},{"denominator":340282366920938463463374607431768211456,"numerator":1441427078332062889795},{"denominator":340282366920938463463374607431768211456,"numerator":1808098279566996294053},{"denominator":21267647932558653966460912964485513216,"numerator":104137293893103540121},{"denominator":340282366920938463463374607431768211456,"numerator":2938777831067963124047},{"denominator":170141183460469231731687303715884105728,"numerator":1655101720466290638515},{"denominator":21267647932558653966460912964485513216,"numerator":201877020534310509313},{"denominator":340282366920938463463374607431768211456,"numerator":2875711199565589061413},{"denominator":170141183460469231731687303715884105728,"numerator":1399708820857534580547},{"denominator":340282366920938463463374607431768211456,"numerator":2212344535068601365267},{"denominator":340282366920938463463374607431768211456,"numerator":2673146311191725081657},{"denominator":42535295865117307932921825928971026432,"numerator":275722250674723359073},{"denominator":10633823966279326983230456482242756608,"numerator":56453537994991563035},{"denominator":170141183460469231731687303715884105728,"numerator":918396428318101313589},{"denominator":5316911983139663491615228241121378304,"numerator":39418914667017903737},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":32,"numerator":315},"tube":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":25491413337912940064880652174605592583},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":6192699365356760718015996219312378321}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-899973191193937974076542794744123696513},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-451965221245370335843740231701230549013}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-115417460796221218753397781005055878249},"lo":{"denominator":1329227995784915872903807060280344576,"numerator":-1811054887197375156848622022088540843}},{"hi":{"denominator":664613997892457936451903530140172288,"numerator":240934638679500256055487435876937159},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":3816165450821168128377203568329613221}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":214575298010511443450413170429669348581},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":213039520578754914470761134099188014853}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":89856267501149920565472629177740818371},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":356079006074506594704414092369932703649}},{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":-2800057335923969696174557771090730691},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-180886674832633339907753942760110091357}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-18899854798279913772644654285624786029},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-154452012049068176606928820254324831197}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2632088076905444260895917627569606905},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1293651481075352600553502906025949169}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":77843629916807488109884376481281429137},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":152509167481859200453067039479627063247}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":28000541176492641475854879888527319097},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":222434015746461123786461642835046555787}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-64500181203679312051752909166599252309},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-64884857626993366425739229814462765121}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2504513921197682261651717873684910212135},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2516591271792229801332917246626059516381}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":681389099998522718848919626452375719343},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":42499092752033735956959301269088982433}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":243900474770581961106606360408131122921},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":60395471415060581802701720619559200441}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":93545066833359748537312925210346304189},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":91145221809092309142284473202304793113}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-176527519140564867737819655600591449327},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-178999353958801897100162461318564607413}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":90585224859209189480084977086879436507},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":5585141771876264431688861889026793839}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":279728575094777409902485042769053259571},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":139599578858083437847943746192102407769}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":7350604047460077428607716117135105},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-29762962937831186545490586544507051}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-17066714773884438943166183288470788985},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-273598832592644008526397933606432986301}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":325178213576165840809762861624611944373},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2588496928722716693504479553335881614371}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":25948335348597238406411562325714977261},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":12974167674298617880992048731024721521}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-224338148403505709484403187993926250497},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-897352593614022842491352684426548116021}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-116191158597263008644298142980999884195},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-232382317194526019424701874675513875971}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":121309426062091677477947386658965787703},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":30327356515522918211146467735520763331}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":215568872850494060648101790171390439583},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":107784436425247027820491375711526389187}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":361620278987449923302095176204004351185},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":45202534873431240011454778547619634505}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-364063938796225435688444527899060949319},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-91015984699056359952390858342447868089}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-78361183013244344097212361157713234163},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-156722366026488692606853234724191837011}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":165945562711587658323097995878130053},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":663782250846349892673344117381783877}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":39476382005118193923991358387824851091},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":78952764010236385991279422499995761713}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":885473868186094948548328432828513220799},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":885473868186094945190090011306390443509}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-8131963956599802331037165853788951897},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-65055711652798424667829489311013314615}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2524893396359771907541077499106276165409},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2524893396359771914296313660496265468851}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":339516215961743804894365712151431808871},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":679032431923487603197774194852580567269}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":245495668462787149146849393945764112879},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":122747834231393573101385653436366861931}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":95200259873307231548880013520445763119},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":47600129936653612901460683845734707117}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-174845813497254373208102598381228700457},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-87422906748627188867694526228533551911}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":177059312465134174538883528889351401385},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":22132414058141771133963366173807448347}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":280006400131346213273233893866984041703},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":140003200065673104372203990995366744967}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1727435652295038482330702184014367},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":6909742609176437458655160719483645}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-273880515761201389580632808779091469403},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-273880515761201393354407009822436276337}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2610246590731912678588235461345992507379},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2610246590731912673429854853877534199929}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":14268763678155575},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-13327702199286163}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":822600490969771},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-15359752646997391}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12756991220187261},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2759438840616509}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":102088690251149},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-325530586602825}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":19504405521791},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1215076192966115}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-17137896068965555},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-78059659126775259}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":20667400510008539},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":127125034723257}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":17784971151335},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-324010475965457}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":239036144717869},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-192961358625107}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2111113043018143},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-91442062799787}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":75856364601515719},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":12563723571152719}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":2199943274373351},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":8148917418882355}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":608725115102305},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5753297597362823}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":661065473361687},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":249463927209145}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-123725683822801},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2717666690728975}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1679577788652189},"lo":{"denominator":1329227995784915872903807060280344576,"numerator":-17880483369969}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":18685908026670825},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":9588075353898401}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-889774180978473},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-3425644259131251}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":860829276342651},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":202331164092441}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":216820877093031},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-56086776371621}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2308026759078373},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2509623241503325}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-4617317572591877},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-33786505550076745}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":85070591730234615865843651857942052864,"numerator":661101750694906792567},{"denominator":170141183460469231731687303715884105728,"numerator":1138426891936141794927},{"denominator":85070591730234615865843651857942052864,"numerator":534023422835055695233},{"denominator":170141183460469231731687303715884105728,"numerator":1158339051284701709507},{"denominator":340282366920938463463374607431768211456,"numerator":2503558265289164820907},{"denominator":340282366920938463463374607431768211456,"numerator":1605206581978029215497},{"denominator":42535295865117307932921825928971026432,"numerator":257568767004423505413},{"denominator":340282366920938463463374607431768211456,"numerator":2206213465903661542747},{"denominator":340282366920938463463374607431768211456,"numerator":1481237879733509801181},{"denominator":340282366920938463463374607431768211456,"numerator":1856701872950881232249},{"denominator":340282366920938463463374607431768211456,"numerator":1679068481843602178363},{"denominator":85070591730234615865843651857942052864,"numerator":752440338981490699373},{"denominator":85070591730234615865843651857942052864,"numerator":844403648830270217001},{"denominator":85070591730234615865843651857942052864,"numerator":823869023798802920765},{"denominator":340282366920938463463374607431768211456,"numerator":2944076975691052670131},{"denominator":42535295865117307932921825928971026432,"numerator":359122234250188893063},{"denominator":170141183460469231731687303715884105728,"numerator":1131819339060791407735},{"denominator":170141183460469231731687303715884105728,"numerator":1366792881939683877263},{"denominator":170141183460469231731687303715884105728,"numerator":1132206148720006512837},{"denominator":170141183460469231731687303715884105728,"numerator":929117584663396684387},{"denominator":10633823966279326983230456482242756608,"numerator":58965179528494076229},{"denominator":170141183460469231731687303715884105728,"numerator":1289591322558299649553},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":633},"tube":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":26037914719146658133474074392016283825},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":50658097161661058124659575372260113447}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-56055625590364418863315585845607914959},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-112603674118098911624218138298989745677}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-115794393505829386216151876341404636939},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-465021105513430372906290639190425341611}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":122418225172032342671590892341625508319},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":121132470189316410042734950439621124217}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":215757483687237233458293376310239825451},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":3347392440869455009198481557635017577}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":181004034847236053966589406157437149143},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":179351534388621943368809660144391854887}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-180540710316056084815487386046131400941},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-364422184555768416370490307071030317349}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-38446631061506253423645369786018912651},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-157062624298408485309996508174134660711}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1331676963243320842350140905500845553},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2619221030288819879318639991581102933}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":158238462225769786489468516593232949455},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":77518328048711890438963713423051681191}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":27845277518714356688389007312279158987},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":442395566890510024415062903587328383651}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-32385584075919791522019411541466337137},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-65130647408585174596600150477869545875}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2514138026309569341177234037989035892585},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2526138343275943313490536876754781192777}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":680304291145994884625354187860703893177},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":678854764787172964789401477276805159271}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":491474949957370265140282032389108421511},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":486853470109987680470911950123405472425}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":11932875454697629836888847322634720451},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":46521168992397939218853989949097106795}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-43633668244582038341173864875994299183},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-88543098558519917574941979577258436515}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":179271569145551639358192704741993470123},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":88378583592844396407251053810300222881}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":35011727167162540201177016633552073423},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":279588281895090921366698431325614612941}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":37989129875007903124540894964701697},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-30247428727023220393014494270833845}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-273458796234905050402513810216084594881},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-273967436030061955591919194487124382619}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2611590140091310716903222243820434427177},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1299394448966621052299733089461121004771}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":26487809698402338419575062766981729439},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":6621952424600583932286904465304155735}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-447143804203125307439280389905264936273},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-894287608406250619505727382516478751713}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-58259282452764474194881948674283338751},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-466074259622115797928245042669916171113}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":60146736607644197040416513783825168471},"lo":{"denominator":2658455991569831745807614120560689152,"numerator":939792759494440541645459219689409083}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":216742973258292297626027325425214601053},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":216742973258292292503934745467809942251}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":364172381101931792077115178520485234885},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":364172381101931788797917757286444772995}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-366687828677686138204339536701850924877},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-183343914338843071200984754712703272519}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-159348963102859420262890659362683877317},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-159348963102859424790067363909713189225}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":83945441264957564202796269793584229},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2686254120478639010281770250929777289}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":20059155751140857579555801062327856721},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":40118311502281714205864965741540781039}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":880544880618181778099659351070786610659},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":880544880618181774711562448126868081499}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-16321164927219652405734651772932921535},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-65284659708878615786871689825304632555}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2534388421733240101476444448070529463611},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2534388421733240108368885404007187145659}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":338934901528307304486608352131873863471},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":677869803056614602248542834553195762255}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":247326743738941644281474967975185595625},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":494653487477883282534774967417397752129}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":48566516141826084098324960526039921489},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":97133032283652162300324692771275659103}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-172797288182466388203113611247141795411},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-172797288182466392834999848121537883787}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":43761027428151718001632562996839801145},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":87522054856303433208046111762702312199}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":140177172606192492900917944932357966979},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":280354345212384981152885283533487894095}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":4769027352969714230103510555399621},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":38152218823753891142459010685478711}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-274232604329467393304743902092310497773},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-274232604329467397181278534528461524937}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2620323173948075960594267361578270956907},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2620323173948075955321538257817103794601}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":7727812250065135},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-15658683728788297}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":681002624166005},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-28192770070217759}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5323759351922515},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2969400434780535}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":51248350184393},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-630686937045403}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":235805800171405},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2194346117221951}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-33576967224779211},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-4729186734038977}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":4979596985386849},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1664158668628993}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":110662802058441},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1356144375882203}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":222749509549867},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-204461478935309}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1116780130526257},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-564695629943023}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":77304585655448539},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":58049701657903767}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":16839490481682641},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":1945427048219525}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":435706222070771},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2913015812608533}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2645873273999975},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":481396920630469}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-285130683321781},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-337276257854463}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1668389521623007},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4458244470018919}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":17135151093866995},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":523505546648909}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1350760317961725},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6280611338974865}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1626223561400905},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":163178412461363}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":107266989312447},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-112545817877881}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1932920044178119},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-569609142290189}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-16797588873325197},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-7866224013488073}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":170141183460469231731687303715884105728,"numerator":1345203961157955642817},{"denominator":340282366920938463463374607431768211456,"numerator":2313567842962690998693},{"denominator":340282366920938463463374607431768211456,"numerator":2184583464077603246967},{"denominator":340282366920938463463374607431768211456,"numerator":2375104549727604621153},{"denominator":170141183460469231731687303715884105728,"numerator":1280522537451371816361},{"denominator":340282366920938463463374607431768211456,"numerator":1639577665606760308733},{"denominator":170141183460469231731687303715884105728,"numerator":1049402929623570675439},{"denominator":170141183460469231731687303715884105728,"numerator":1131793781769262328205},{"denominator":340282366920938463463374607431768211456,"numerator":1522103641585738216431},{"denominator":340282366920938463463374607431768211456,"numerator":1906491873638284367037},{"denominator":85070591730234615865843651857942052864,"numerator":423500042934283191981},{"denominator":42535295865117307932921825928971026432,"numerator":385245251559455258867},{"denominator":340282366920938463463374607431768211456,"numerator":3446217129246294161719},{"denominator":170141183460469231731687303715884105728,"numerator":1681167264840231148801},{"denominator":340282366920938463463374607431768211456,"numerator":3014086420292138623489},{"denominator":85070591730234615865843651857942052864,"numerator":737040304803231973495},{"denominator":340282366920938463463374607431768211456,"numerator":2315938738906024301961},{"denominator":10633823966279326983230456482242756608,"numerator":87350517165795836985},{"denominator":340282366920938463463374607431768211456,"numerator":2324474653232245780841},{"denominator":85070591730234615865843651857942052864,"numerator":477837255249245151935},{"denominator":340282366920938463463374607431768211456,"numerator":1938266004241528441885},{"denominator":340282366920938463463374607431768211456,"numerator":2636357218226993267605},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":16,"numerator":159},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":53152715409152185451959251918524591573},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":12939277543410903605214519308984472603}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-893823990637387410029780586891722009863},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-56109041288214173714470460135922100041}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-29036994808725751803635959582400825253},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-466319091434012086048347537175253275815}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":121442484136104829076080807909095183729},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":120111903395973313094746597606824479027}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":108465218531683897806616540233417257511},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":53854396984488132244349845321240833699}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":364556281004221648717610150243581132607},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":361294056541141950244308014596329596915}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-45466558498325692478488068809538022785},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-367047176082804498433304322504848597111}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-78196225144809598348365429597840199761},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-159691607658314111673669488194117832009}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1347121786549016520456692411779137883},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":165673933755249740736252622727012665}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":20101088255692056093675830134282696977},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":78791476342177292837565655929257244605}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":886097165537212321690514152242229121635},"lo":{"denominator":664613997892457936451903530140172288,"numerator":1718484750050856621618470625593932361}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-16255564495593725133603250885316559227},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-32678397343305040836628117116348382015}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1261850488313300812932341136867810047857},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2535625173958304442628634525243157537111}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":679181752106821637923670878590615432089},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":338844275136740678287138168956060272089}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":495135241007997354849282435262779121253},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":245265451569319198289230205555159561135}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":97397887962774644553631065091815938003},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":47478039487238756304199033867991941599}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-86239332828080272562234826167915687331},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-21888603740505322669853067700470318321}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":177317511168088081036625120998646994189},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":87367762069274508029604601052357160853}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":17527461087621537099346656845810658787},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":279958291545724165983837034241704567021}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":69536915510652070355822301806466823},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-48832157654188418808099292765103}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-34228999413372430502592168051662941419},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-274317199849198899619691985872159656305}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1310826811433475686887874520392071296123},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2608979142716908373391422166199130683499}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":13509069772826179319648743842053969397},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":54036279091304711805370065709441961177}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-222810481621545089595727318914581320791},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-222810481621545090771623569859615387937}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-467291117410720716561962553167437887995},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-233645558705360360515098017553182933533}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":119241546513472449846220935616525950529},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":29810386628368111244049156464886143103}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":217907765450845751662207611291462282859},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":54476941362711436605738401821982021053}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":45836071220983934983660103160238211689},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":183344284883935738259589136731847249027}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-184642881720915593091648241744303330455},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-46160720430228898807477513280075411015}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-161994024829403945989538935602633602263},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-161994024829403950634181868432016913821}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1358499439528864610632052009187367155},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2716998879057726093158158592088156931}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":40765042703996024631803893455122767425},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":163060170815984094612226895774303926765}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":875639371802609987423644533751058437249},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":875639371802609984000811531505480552199}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-65494200213033827251018293862936706559},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-65494200213033833561837966764124546803}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2543823909453895054788532976031286816439},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2543823909453895061820628747813760550765}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":676673244661483132795606455268461654387},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":169168311165370781483578022664230447993}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":124575227655250740046048225823124661545},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":249150455310501477006318319241229489439}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":12385373236592836324408937810770651529},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":24770746473185671136319374675481592157}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-85343162230358801330188980847029894707},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-170686324460717607398953779116787935769}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":86487628500063188353196437362541903189},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":86487628500063185495118449272158151821}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":70170552569206579371895569621450951779},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":280682210276826312715577201254258252011}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":70292823174714229423231804294843111},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":70292823174710297643498805936267021}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-274565374772375610498987965024847401573},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-68641343693093903620231360407698841339}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1315149748094212996812059390164186785177},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":657574874047106497058837813777219432135}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1283452190280249},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-35218262889094059}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3830175375887179},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-25918106748990083}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":8887245703872801},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-1575177043657387}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":18035225323633},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2433129453321491}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":388226564496133},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1993448275930047}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-32037469710135557},"lo":{"denominator":2658455991569831745807614120560689152,"numerator":-567554660152309}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":9578732958396219},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1194163255794025}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":166337696577803},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-705468301656223}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":208983603055313},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-26809308638171}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2335439950069937},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-212680445960511}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":155375893995442939},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":62613676558088641}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":2006499040457035},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":1818383795367117}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":154212938089481},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5876342719775097}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2644822295577977},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":658061313188563}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-313553043785405},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1340325242337713}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-401179137601793},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1080874133656637}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":7822453640424777},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":3581012717351127}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-939228052318345},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-719406333944651}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1537875243558193},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":3908660632649}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":211794349725003},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-114028275807037}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1568046662209849},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4116519217881949}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-7502173006535231},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-29176355745943741}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":170141183460469231731687303715884105728,"numerator":1368296781122876065463},{"denominator":85070591730234615865843651857942052864,"numerator":587944406937251423915},{"denominator":170141183460469231731687303715884105728,"numerator":1117052998319218711793},{"denominator":340282366920938463463374607431768211456,"numerator":2435009649608136073035},{"denominator":340282366920938463463374607431768211456,"numerator":2619625811164346886233},{"denominator":340282366920938463463374607431768211456,"numerator":1675030971145710917731},{"denominator":340282366920938463463374607431768211456,"numerator":2138252829724667814397},{"denominator":170141183460469231731687303715884105728,"numerator":1161160338888770855327},{"denominator":85070591730234615865843651857942052864,"numerator":391013190246026802087},{"denominator":340282366920938463463374607431768211456,"numerator":1957492958622672575987},{"denominator":340282366920938463463374607431768211456,"numerator":1711370120014070265375},{"denominator":340282366920938463463374607431768211456,"numerator":3155405447222022826215},{"denominator":85070591730234615865843651857942052864,"numerator":879011159823500200163},{"denominator":340282366920938463463374607431768211456,"numerator":3430644866514130947511},{"denominator":170141183460469231731687303715884105728,"numerator":1542888552816410640671},{"denominator":340282366920938463463374607431768211456,"numerator":3024995642502127312113},{"denominator":340282366920938463463374607431768211456,"numerator":2369283667270440999527},{"denominator":10633823966279326983230456482242756608,"numerator":89314861877471066623},{"denominator":340282366920938463463374607431768211456,"numerator":2386001894755291243223},{"denominator":42535295865117307932921825928971026432,"numerator":245736212948483315253},{"denominator":340282366920938463463374607431768211456,"numerator":1990967464066696145841},{"denominator":340282366920938463463374607431768211456,"numerator":2694376676604881484267},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":639},"tube":[{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":3388312072148983625972763366589377485},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":52838133423740330729709793462208795943}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-222694149955926162912949945331536457187},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-894677720470977949267274894004184993771}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-116478285214174923096162451710596959425},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-58440541063857588016088453770269163153}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":120431042211210051501529522894708423907},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":29763838062998369323641142955787702453}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":218094069026293851563688057930704090397},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":216592851506292119275073266060930230729}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":183534202552336440251042104521889943071},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":363850600657182778608565929069071620917}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-366359045063868836451895978680341488605},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-369646881202041853976331556696412595767}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-39754182540584739405995203962797885745},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-162339059567543584013079248767091630791}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1362373079721164917197368004459455581},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1340988613630225570467942461186422565}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":81699084572364118116701250197935511119},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":160148254549615592444577347451859662641}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":440582792697602365262766267477542650527},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":437479268812487603133400349155560826329}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-32626836348106286656028002276840419571},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-65563542822872936420882027735166053565}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2533203519342148864736127516700207729253},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1272526271626530616069648414102200908637}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":42376454144842153954042688982122205713},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":676488633708875920350019831410902902303}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":62347582926060169377988843547513692669},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":494194912374483496702648769288316080487}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":99349984605387616735915485109864400285},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":48443352123951889237073968911326051955}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-85180178569769698349589650828271992101},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-173068058298347170183424353528650901025}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":175308972166071121416789398093605406887},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":172660347631428627314197939230166639371}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":140382396710453184137306664654066930999},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":280308739855882604806026611536413535933}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":101982893548117485698040484706241243},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":31059921632157936191838602569476701}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-274186496872043539190203214938785590803},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-274647571446282080335610084275011404949}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2631616891637823564274632289363891996719},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":327383539553374110957510420647335037413}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":27539136895597240246920590255463360583},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":27539136895597237463969655116216552479}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-444108465380493187851520242664355619477},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-888216930760986380486098695010146052069}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-468415560958613587834419692422976191049},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-117103890239653398100952045454880940435}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":14769178046175794502172008113580757585},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":14769178046175793878065122430236082225}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":27382894592431705501264593310198569829},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":219063156739453638651484011512732922115}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":369167594017794525777842575499288879497},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":369167594017794522354608373687699657487}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-371856372851116066561924624231166321087},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-185928186425558035459894827803442599415}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-164657637461593773967475057335283430795},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-164657637461593778732357458530334933553}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1373676550453647216504201133822781333},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2747353100907291218778903810473612659}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":10354154177989197126594066922303086219},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":165666466847827150006041522818228256757}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":870760400685875400899302208170691814007},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":108845050085734424679591961001738691209}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-32842293697276365653928179968034067501},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-16421146848638184442025982252682579011}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2553200659026750171693260465120020558963},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-638300164756687544716882576404368599859}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":168861139181994761437388356234123188997},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":675444556727979038748658661355671002339}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":501932446913999543221309908440743569823},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":501932446913999536902933221489816463721}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":12631298528958423576819755649895671637},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":6315649264479211400470960766860349201}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-168513820491688617822586970071817098657},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-168513820491688622670023683572757322011}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":170853525132778349393783762970852600965},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":170853525132778343549377657106277085893}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":140494761633424579455578295045818657473},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":280989523266849154013091896969280778175}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":103319973671234499251315921771358249},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":51659986835615227732525629919290217}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-17179891484937594052075860115848140447},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-274878263759001508923265776592069289905}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2640176341315154928259427489301238813137},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":660044085328788730688209750271956288681}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1622231931404833},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-38321827623380311}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":154243149557543},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-11953668706938621}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1874598157497599},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13220640880153539}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":226348410553457},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4671680789209893}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":266349309610543},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1813524203043045}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-7477834588113851},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-69124528556100827}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":9198334985684529},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":321115884421099}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":118911647896523},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-730202779498843}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":98627005593265},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-6971653202279}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2416249238272809},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-153642866357249}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":154164932356332947},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":64910715179886821}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":15219253716617387},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":417520059095763}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":108768359479753},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5899242981252903}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5281396858771815},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":196748337361971}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-667600986950673},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-333005565740657}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1506541608920219},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1041887126180251}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":14204828941684915},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":5976543404233937}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-274561669060549},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5271516438922195}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":728183784245309},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":176394250064675}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":52143164685873},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-58099311307811}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1219171872039409},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1848215848544183}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-3293055139004635},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-840442901336759}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":85070591730234615865843651857942052864,"numerator":695733146335350205091},{"denominator":21267647932558653966460912964485513216,"numerator":149469667705101096703},{"denominator":340282366920938463463374607431768211456,"numerator":2284683885181518713377},{"denominator":85070591730234615865843651857942052864,"numerator":624106273429694704941},{"denominator":21267647932558653966460912964485513216,"numerator":167457199648313542887},{"denominator":340282366920938463463374607431768211456,"numerator":1711597494310692788293},{"denominator":340282366920938463463374607431768211456,"numerator":2178923638468758175441},{"denominator":170141183460469231731687303715884105728,"numerator":1191220205469461152137},{"denominator":340282366920938463463374607431768211456,"numerator":1607114539055129145273},{"denominator":340282366920938463463374607431768211456,"numerator":2009730412201825067719},{"denominator":5316911983139663491615228241121378304,"numerator":27050603640153170611},{"denominator":340282366920938463463374607431768211456,"numerator":3230119515070945547931},{"denominator":170141183460469231731687303715884105728,"numerator":1793565876545258667139},{"denominator":170141183460469231731687303715884105728,"numerator":1750222567294328107429},{"denominator":340282366920938463463374607431768211456,"numerator":3159187345253694065759},{"denominator":340282366920938463463374607431768211456,"numerator":3103510005961251992547},{"denominator":340282366920938463463374607431768211456,"numerator":2423714242607701386187},{"denominator":340282366920938463463374607431768211456,"numerator":2922200691735737356987},{"denominator":340282366920938463463374607431768211456,"numerator":2449031706574519055413},{"denominator":170141183460469231731687303715884105728,"numerator":1010946484972662854675},{"denominator":340282366920938463463374607431768211456,"numerator":2045024768739336996897},{"denominator":85070591730234615865843651857942052864,"numerator":688321845782640862583},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":32,"numerator":321},"tube":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":6907029048151349681417528433499994779},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":53900728725315146733595603047488488665}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-887749256546534869773282235644178089877},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-111453750115489843904050841124159176155}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-467141555477258679030884017829572512819},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-468637174811879054341669369009203009023}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":59691825947411641864264668194133384073},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":29490649520328736226361332717470461883}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":219248286505094955066125952155905608765},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":108879409333520139397967228806908443211}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":184771598715736890538442772997544731647},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":183185694458180054673049843691268458983}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-368959749273213064238641109321685529963},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-186109945479697141842597424395936791939}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-161659464884961088357766635463450714959},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-20625633041173708084436204332032041555}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1377425724213111779891746042927280199},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2712793038016781930199787959555972595}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":41501753398867769434772595111584855041},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":81366371920242770465732143060982032885}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":438128689807605740757184911518061609105},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":435038650744598270303558466192249332079}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-32732825161741342175402741893170287843},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-65751149218994113352933582353278628863}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2542646426656602783309250770995768077573},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2554421254629525498102072819151932210677}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":676830625685425171238999826942856998917},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":675256815446004786805066112397926809173}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":502410057628679021426664106399389979127},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":497844338731261168744411364025130728233}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":12664945210923022073318252622157858613},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":98834477471115852096247662649219729091}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-168180649644568186979589464695557993155},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-85482366386811549278330462703963590005}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":21655835526120083989718725318101971157},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":85266206060308859902090263273259698017}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":281069591921711945390530148954229590529},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":280639167871839020196137984598814408225}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":67657622901099682405271007830803299},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":63068109549433734624938204964200895}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-137260875645776631861376726887467824381},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-274957986099776731485098564075029921315}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2641480740099697667478042813691844459985},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2629057135753840246097274415021989952207}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":56101287922264833922627660001272828875},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":28050643961132414131903121221522374167}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-885213961368186535929531443353708137611},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-885213961368186540795181234165090072361}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-234723990195559186793352978742680858749},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-234723990195559189129703330190989309877}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":14628613618880283105110205119155327971},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":117028908951042259722110722612870177229}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":110104525275487744521129117833291684825},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":110104525275487741780999641965165815149}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":371608255551343899079577992195498960489},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":371608255551343895580922428714125241499}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-93599579790392575018015463248492782415},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-93599579790392576128445639565887205257}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-83669936881594570110618284445154488577},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-167339873763189145109188172577910950957}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2777307222765939212648894486231788737},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2777307222765935910010046293360111663}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":168292282297116916594541843880324780049},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":168292282297116912468078866116109993629}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":216477715083805348204591733298431065603},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":865910860335221389310951218041041465731}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-32928044099475381990726819382461300143},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-32928044099475385296863075111743303635}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2562519493434978083160304424773588413055},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1281259746717489045239668993317274868261}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":674185545419686705581439396134820003659},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":337092772709843349218943334098679071505}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":505546937265866026829193450464888336255},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":252773468632933010180239541542665743333}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":103035509563408048819714415363385784667},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":25758877390852010613061258544048862681}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-166280715016667212513263432445680564981},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-83140357508333608735907993657470054587}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":84339859187105615382061986504987490467},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":84339859187105612394429004507734006155}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":70318950227614478938458797121173946639},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":140637900455228955363314298703347542671}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":68610684055592693537977355747270281},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":137221368111181228284798345155364413}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-275170696416970450188593189590718630699},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-275170696416970454389542393512169778769}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2649954549304017849299009419876043569239},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":331244318663002230459090379256801551919}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-4885775908950275},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-40693199863220645}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3011698981477875},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-11031107846285649}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":6312837049088937},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13739561606919929}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":178582125382663},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2228896206169467}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":671968700843337},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-412841889799979}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-27335590254800127},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-32634069873760823}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":4412268395422059},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":29085493008699}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":78189404636183},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1504849912197793}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":187535549304759},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-28853808567813}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1239166759332929},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-212929217684003}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":151338017551096275},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":16297082949149841}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":14362628365867317},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":1505826735342227}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":76998801122949},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2948565397087919}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2631310734920445},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":884630496894923}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-698418371557095},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-661654240059519}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-689807768259451},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-249720024468011}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":6415355560757675},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":1207466581836207}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-180522983277757},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2413243306053295}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1380887637424453},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":104380996657521}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":51287894286147},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-118993057220145}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-888645911167815},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3300614513498723}},{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":-88503132913047},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-24656397779945445}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":2829392805067136905085},{"denominator":170141183460469231731687303715884105728,"numerator":1216405426299431601925},{"denominator":170141183460469231731687303715884105728,"numerator":1168170162624490223347},{"denominator":340282366920938463463374607431768211456,"numerator":2559383051691854671139},{"denominator":21267647932558653966460912964485513216,"numerator":171258019637499740503},{"denominator":340282366920938463463374607431768211456,"numerator":1749308815465940498735},{"denominator":170141183460469231731687303715884105728,"numerator":1110425771320372252957},{"denominator":340282366920938463463374607431768211456,"numerator":2443975010324142569913},{"denominator":42535295865117307932921825928971026432,"numerator":206414901864178364363},{"denominator":170141183460469231731687303715884105728,"numerator":1031615071625369609139},{"denominator":85070591730234615865843651857942052864,"numerator":438416195683366037471},{"denominator":340282366920938463463374607431768211456,"numerator":3306132086068569754287},{"denominator":340282366920938463463374607431768211456,"numerator":3659513678367481327915},{"denominator":85070591730234615865843651857942052864,"numerator":892943543743311114335},{"denominator":340282366920938463463374607431768211456,"numerator":3234356209590484084303},{"denominator":170141183460469231731687303715884105728,"numerator":1591866691320583841167},{"denominator":340282366920938463463374607431768211456,"numerator":2479272277012232686835},{"denominator":340282366920938463463374607431768211456,"numerator":2987630659015439069895},{"denominator":85070591730234615865843651857942052864,"numerator":628400664321419991785},{"denominator":340282366920938463463374607431768211456,"numerator":2079395416110852405707},{"denominator":85070591730234615865843651857942052864,"numerator":525118348994106102145},{"denominator":85070591730234615865843651857942052864,"numerator":703284132228108009807},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":645},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":56282063164663473907313333569335745479},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":27472259708182293076226653697554002697}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-884743336607735236380839787590333217711},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-444301442833451587137785953595008364363}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-234138754692540048453659736249804554639},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-234829012560207503089160834767128335717}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":29575022156930820491397416831060657339},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":116833446044554022483453645367300198149}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":110196496270629299131313102607050776399},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":218915397205919754250245989746022712533}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":92994866468415604112917636766326425051},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":46106895476448372320755738716842605821}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-92883302734915636970476564789122028221},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-374764830054197734682089907704246939359}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-164320742433336724495619508752354387919},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-167689692715907219214174992382621561121}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":696137456002777847894349056335495003},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2743220131673533421801293297818987891}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":168635385212328130524810368317001632949},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":165336587029549263281733873074028631007}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":871375617538011936642032538400240080975},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":865223449016646579214729238303780666853}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-65658443352790690752134552099364217907},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-32959941885205548154676314133690066649}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-638007623759724791088595482564798322873},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2563732134917409237743167276668442710647}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":675605629485402855517896248347962487363},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":42124681369447797364654251027018026823}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":506022264553887925559788481132283961121},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":501478022731789715941060414618539713393}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":51653444984179798349007507308580783715},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":100799665816479358597482078431274561019}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-165940485769025447235608996263177818661},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-84399873285992265525812657870189925389}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":171131413990804457690285773723191143371},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":168352525410543374725265668398828974863}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":281353288265679014725180917474884725927},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":140474552466822918078096558334383322237}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":169521432815758613837579398029593065},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":47982127994252552267385055629608651}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-274837196664174783500203678578661261751},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-275247867612441996830304509128727860203}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1325623008794527986924577466165847581241},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2638946377284721472631026119594170347689}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":3569066573703376715698169613853158219},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":28552532589627010849626397384439256333}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-882234317480889771215814996704745919739},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-882234317480889776167238961215252433385}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-117597200285996466334481439504010860327},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-470388801143985870116143251672111805961}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":14483478358481194975783496765696298697},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":115867826867849554558430842139084497043}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":221345346509105882746031996971497993365},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":55336336627276469285467095498318054149}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":374009406930955275618877950721708136063},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":374009406930955272042446885452645697569}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-188455148312204510398569323433754798361},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-188455148312204512662648547607996614357}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-42510198157021501981008542227578464857},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-2656887384813843952155352044821087771}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1403426148004222480017556720169802487},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2806852296008441566638693739385808661}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":42734437172676853413617617600821099327},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":170937748690707409418430392501939129575}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":861093482019627140335928660408606606533},"lo":{"denominator":2658455991569831745807614120560689152,"numerator":6727292828278337006081495268020788259}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-16502245192250437835429678212668415759},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-66008980769001758108669026857249932785}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-80368164327281650277846054930761534721},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-642945314618253204089383070615824840595}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":672898022043040934674801557387037364115},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":672898022043040927385453985864902709315}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":31821451474573601577229363690304421801},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":254571611796588809306510419738341493795}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":105038622199130222009943328466260747627},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":105038622199130215478550603141614185663}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-163987985529054352121974058486290047327},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-163987985529054357193983150692197430277}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":166454673431807850192247243245742179379},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":20806834178975980510429028845154904017}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":281540549161602941789129864748991741999},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":35192568645200367078702518229385383227}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":42996003461677585795063106793002477},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":42996003461676516577729383397047417}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-275442086968558049424467522683987369631},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-275442086968558053739169238387188089817}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2659635012966651247647410028673740202385},"lo":{"denominator":1329227995784915872903807060280344576,"numerator":10389199269400981413669737074851088709}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-7362490921365751},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-5303498151311003}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":7063462952691975},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-10184138055810985}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2648314657854781},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-3539672467391489}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":520468496286689},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1055761434127363}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":402442707252889},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-23517710840519}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-24473480976724491},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-15293781614520195}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":4229755945710031},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-608475869309065}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":21887589931845},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1543997232139951}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":179710987617921},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-237070875331149}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":630482407121923},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-17453543050933}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":147199931771175157},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":31945128988093835}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":210853995718435},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":5326354220813123}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":226735442074755},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5870516073028931}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5231046110944643},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":955239906801173}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-720569632286911},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2625628771017773}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1231577206358555},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3811175834970711}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":11531455137255655},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3742077712244975}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":161521946842439},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4418784252664635}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1310742596583159},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":35016410424641}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":100783929035717},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-122185106302723}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":-9084819177023},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2930972523529583}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-594657188748725},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-22485810150325551}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":2875941426779241448281},{"denominator":170141183460469231731687303715884105728,"numerator":1237849133192860549925},{"denominator":340282366920938463463374607431768211456,"numerator":2389099019168441544567},{"denominator":340282366920938463463374607431768211456,"numerator":2623916194236126548195},{"denominator":340282366920938463463374607431768211456,"numerator":2802080652479658738887},{"denominator":170141183460469231731687303715884105728,"numerator":894098590905895270551},{"denominator":340282366920938463463374607431768211456,"numerator":2264070460424415741401},{"denominator":21267647932558653966460912964485513216,"numerator":156684586693306992321},{"denominator":340282366920938463463374607431768211456,"numerator":1696698001459545423621},{"denominator":21267647932558653966460912964485513216,"numerator":132376169260730386643},{"denominator":170141183460469231731687303715884105728,"numerator":889353489107037680473},{"denominator":340282366920938463463374607431768211456,"numerator":3383471072852535551515},{"denominator":170141183460469231731687303715884105728,"numerator":1866613106856853786905},{"denominator":21267647932558653966460912964485513216,"numerator":227791977991122828479},{"denominator":340282366920938463463374607431768211456,"numerator":3311323537254524515181},{"denominator":340282366920938463463374607431768211456,"numerator":3265695072863008974903},{"denominator":170141183460469231731687303715884105728,"numerator":1268000325707120593067},{"denominator":85070591730234615865843651857942052864,"numerator":763601304022287930021},{"denominator":21267647932558653966460912964485513216,"numerator":161234638849616328677},{"denominator":10633823966279326983230456482242756608,"numerator":66826078299072178845},{"denominator":340282366920938463463374607431768211456,"numerator":2157349683079552260037},{"denominator":42535295865117307932921825928971026432,"numerator":359246522888545696683},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":8,"numerator":81},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":57290174943647961664005556880717982623},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":27984594682166684498558714741705902509}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-440880086908950057116464349540502836963},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-221399428885110147047746767910247730701}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-117330347071410800947676761584027052221},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-470587309340394901750696155629620039471}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":58590075760524441631917287531368983269},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":28916931455245674758576309041701948599}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":110764043185827088494345958304626342613},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":220062491015344517625700102277226706911}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":187188034484936891392257206572273721459},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":371300720727062797002745541310853524057}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-187039046401286355288694409802993170207},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-94320089098137151381029787821702744329}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-167000637337747243271040498029130677221},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-170393001592166212773001204441890420995}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2813832290710733629980443886346794289},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1386624440941590303895556491568392599}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":5352606659514836055904015695782787747},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":2624373975463011060576146105376783807}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":433261601080119580938974479920587483799},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":215099945977515367820532173891422792823}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-65832317182378426384521855385985444727},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-33035013674050901176919843488166872379}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2561356544522841347008721412729651975257},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2572986033644208708524551530969993097683}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":674350083291224670246885457617950469571},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":168176176143961255898106211246417266501}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":509616126143342108303301743750342531601},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":505094805168368677255721009433772119945}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":105312242161803961215322529577618260875},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":51391269637348692405951544999184055045}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-163640846669932319313641739403662421161},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-83287016860929991966917674219153440341}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":5280123805903793918518535683824994265},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":166121527641819659107901455357174716577}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":281615387088456693122577020304130942331},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":17577379319556405653775756608081921219}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":204588223945602185570312995846949637},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":129736161907356677475296472964826549}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-68783064867300427700105703782987057249},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-275516628946889104682126557520628990471}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2660913625811152600435353638669134611045},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2648736874136558426254652966630662920769}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":29044703620924453191894343505276510397},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":29044703620924450269332061546150063589}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-439639629538311805169379826904094320337},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-439639629538311807689602671189968344985}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-58904810309668801966781842950109038181},"lo":{"denominator":2658455991569831745807614120560689152,"numerator":-3681550644354300161095641813887921171}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":57335014909501726821922136471816678071},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":114670029819003448263724187492376874923}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":111235970263373906642261621520612429917},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":55617985131686951888536186192949038771}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":188184974898856434098957236769845705931},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":376369949797712864541288026453836965099}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-379391030991917740018191109191774932993},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-379391030991917744635438460788067599531}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-5398763710074242160484299741717993083},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-21595054840296969284788682172955218915}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1417989992522791404278203818915498283},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2835979985045579321989748950820451697}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":173602980468678750852122368849460543457},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":173602980468678746503873087024391606997}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":856310839562312263411618821893691474451},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":428155419781156129899346062051996149559}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-66143552956454929700811548869436345455},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-66143552956454936625148406788797745553}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2580986822110439923041984130493119236807},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-322623352763804991332325206971097097279}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":335791901023965975041237947664412806775},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":671583802047931942644115602638450592319}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":128180037368877013301286010338850349701},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":512720149475508046424882271540391135491}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":107059999819867570459116269631174972341},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":53529999909933781880132251118065092511}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-161636646492950735826708092407550341299},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-80818323246475370507301162907546982035}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":82089629232628931706377420001782058279},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":164179258465257857167620173754000555019}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":140891631821046901774253589593871996899},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":140891631821046899126726149483739282523}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":207594258043968677160008400447691765},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":103797129021982139531248608318715007}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-34461479919987236502164607511038864371},"lo":{"denominator":2658455991569831745807614120560689152,"numerator":-2153842494999202316005475334491793701}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2669218674758334173717379023580510484383},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1334609337379167083922839916198941527919}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-9160188387676569},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-43673126129037623}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":4018915623705739},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-18812300287609781}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1106099647297729},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-3622304784945271}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":711453865404767},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1981996301792531}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":928572629637545},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1374880349706949}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-21429193411178673},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-56958387577021183}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":8106006324078891},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-308303052623073}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":7892284276991},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1577539954831183}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":173510244456689},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-3781448681877}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2548419813742589},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-82718817650943}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":142128833977614545},"lo":{"denominator":664613997892457936451903530140172288,"numerator":119773898542509}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12627372351023989},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":4600444977075253}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":92857238485183},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5819013073615769}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5185720123961221},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1002186986055451}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-183694903068657},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1300170692968243}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1066365992380409},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3618664258542519}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":1289261183304157},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2719138613769505}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":236465404811045},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4048085492650641}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1246325021854229},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-1888056226839}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":197803978443611},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-62948899961915}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-298472521735165},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-647133676025729}},{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":-60509434983129},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-20402451450890695}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":42535295865117307932921825928971026432,"numerator":365318128186281970785},{"denominator":170141183460469231731687303715884105728,"numerator":1260104709610053257009},{"denominator":340282366920938463463374607431768211456,"numerator":2442984247479526316219},{"denominator":170141183460469231731687303715884105728,"numerator":1345028852501196872847},{"denominator":340282366920938463463374607431768211456,"numerator":2865188097408224680127},{"denominator":170141183460469231731687303715884105728,"numerator":914147729472922151063},{"denominator":340282366920938463463374607431768211456,"numerator":2308614953185717008231},{"denominator":340282366920938463463374607431768211456,"numerator":2571405136162071293749},{"denominator":340282366920938463463374607431768211456,"numerator":1743283121582025224025},{"denominator":340282366920938463463374607431768211456,"numerator":2174123325343218771463},{"denominator":340282366920938463463374607431768211456,"numerator":1806422946595887662697},{"denominator":21267647932558653966460912964485513216,"numerator":216385275968499607855},{"denominator":85070591730234615865843651857942052864,"numerator":952076440068513369411},{"denominator":170141183460469231731687303715884105728,"numerator":1859589027289309278865},{"denominator":340282366920938463463374607431768211456,"numerator":3390129952126618300727},{"denominator":85070591730234615865843651857942052864,"numerator":837356151887097328151},{"denominator":340282366920938463463374607431768211456,"numerator":2593943319228345479509},{"denominator":340282366920938463463374607431768211456,"numerator":3122565072616630644403},{"denominator":85070591730234615865843651857942052864,"numerator":661881700460792993137},{"denominator":170141183460469231731687303715884105728,"numerator":1099524296870507973577},{"denominator":21267647932558653966460912964485513216,"numerator":138480677895764259719},{"denominator":85070591730234615865843651857942052864,"numerator":733960816742356797295},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":651},"tube":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":7285039430440931853561658102957128531},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":56974481816556973573781631185122760317}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-27462533178621181441408603996543419865},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-882615790343668883949701587384684239303}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-14696050418104610240350975429659872289},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-58928186378216363019772081777420992287}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":116023664047376822752811702146941160129},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":114465292252104193287374424132256710153}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":222653463522485863109273738061193302407},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":110600000087142939350522782204028089333}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":376731914126546314067193536008314741419},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":373706906131445156261919479591013219857}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-188296544755896220917383655663989054311},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-379765160637958231458480664524269734067}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-169699210302235534318926825936613269165},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-86557516780370135185000126737297958121}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2842690471810964753105817071111551165},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1401435138237413939626728784651293327}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":173951209257985155272811928793642648809},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":42650729934696914969763666500742371983}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":861702874212046758132296951229105573035},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":855608952287850580168614045223139163573}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-32993774298788392080558149975640844297},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-33100935155913227983570213373089088731}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1285312709018160264346167415870627653515},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2582183822403243330679724089973370091897}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":336532898970604794755031230893548518783},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":335694019479761520578726709992761779307}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":513190486086487238635130504208530944747},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":508693527760587660832786432039919519511}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":26833973064259450385580497759901624143},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":52391684985236908513510224343195116917}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-161282750289018501766666210716035166889},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-82144283611195837231842516578053466191}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":83372580223085903304007808533038378091},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":20480036287816530306291485132719280463}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":8807980710698865939926111536032955787},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":281505567652629517357618431888750313047}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":120250863966535812325107309565532045},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":20546366812972069978596646079549681}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-275406355203477205428344124769269088437},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-34470459106785705673697262714678580603}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2670484515654843460805363404231910925259},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2658429512667963217576573722798650323803}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":59054172369174882065753868235920508467},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":14763543092293719031845287318703884091}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-438175004333206862264632596964416117937},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-438175004333206864831022769915817975021}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-235998758054009607556712785715350177497},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-471997516108019220109485577602906216665}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":56717697600852929322834962455024619701},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":113435395201705853129982717453477821273}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":111794362454099054284857430242575530983},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":223588724908198102710778663904461794521}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":47336104140047103099081260684956774809},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":378688833120376821053341573404795539761}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-95459819758423268486272086092292236447},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-381839279033693078654145856304425896495}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-87749421073403482232349048264852939905},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-21937355268350871217427598852476652293}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2864682564516732783855775872820343563},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":716170641129182300409917953675169009}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":176288074593311044564482676932602201379},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":88144037296655520050668155053207588061}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":851565353921519408565195275773698511021},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":851565353921519404891377723892760077835}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-33130050433926808732095836746000746265},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-16565025216963406137169907427569470301}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2590137073884819479613392589672687490359},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2590137073884819487382977090040815974065}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":10472573500905526688572758363453453191},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":335122352028976850238991485926946226957}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":516276560808854492779758265081986530817},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":8066821262638351341220667025915941993}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":109099916805013526825085882301217039715},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":54549958402506759977589937134882606777}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-79613873805389445566171230332402593765},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-159227747610778896438640458305988419149}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":161854372118199103189612369191535697303},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":161854372118199096805304097759089250833}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":70500857521266639488624628993146589407},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":141001715042533276260286878697846377295}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":244037818345158237001850673450453215},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":244037818345153714447623186507554361}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-275919347883037835823761697637157562933},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-275919347883037840374833926219182689255}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":83709578864865117510982190065874060881},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1339353261837841877176909364248778949697}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-10526363590422977},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-44054746223503565}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":4389871567481535},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-17131639849323001}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3591336275218513},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-14645099482743047}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":460711822502053},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-916066091265365}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1030044667533571},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1246644589785745}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-18310071773471819},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-13121976071887885}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":15337470606317199},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1735675999500563}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-1041466240443},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-797826376334295}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":41663977726413},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-243733626501483}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1273639517191859},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-7951929525805}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":2117508078017999},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":28930195721126465}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":11696260883896533},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1950391297119179}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":135325020106737},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5701046433862827}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":79745324321773},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":524566295119021}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-186999738570777},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2563588400334241}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-225427596703179},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3397661357251789}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":4564715059203891},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1784140139993507}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":11433005025875},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-918445293306887}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1172906968999727},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-2609351506327}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":6006671266781},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-15992348364757}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-10929978144901},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2262008624850893}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-3039453346595475},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-9157578319378613}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":2969169595289235945757},{"denominator":2658455991569831745807614120560689152,"numerator":20049822009843044641},{"denominator":340282366920938463463374607431768211456,"numerator":2498020884868223950055},{"denominator":42535295865117307932921825928971026432,"numerator":344730163860535084535},{"denominator":21267647932558653966460912964485513216,"numerator":183091684996607248379},{"denominator":170141183460469231731687303715884105728,"numerator":934818583560586144747},{"denominator":42535295865117307932921825928971026432,"numerator":294315027424290695809},{"denominator":340282366920938463463374607431768211456,"numerator":2637360557650407258515},{"denominator":340282366920938463463374607431768211456,"numerator":1791107846834291130195},{"denominator":340282366920938463463374607431768211456,"numerator":2231571893869717269159},{"denominator":340282366920938463463374607431768211456,"numerator":1836869945877693767089},{"denominator":340282366920938463463374607431768211456,"numerator":3542240080369993365249},{"denominator":170141183460469231731687303715884105728,"numerator":1942394665999168628535},{"denominator":340282366920938463463374607431768211456,"numerator":3795334754419481097439},{"denominator":340282366920938463463374607431768211456,"numerator":3470816879916960096065},{"denominator":340282366920938463463374607431768211456,"numerator":3434951756040240693543},{"denominator":340282366920938463463374607431768211456,"numerator":2653145326175602408671},{"denominator":85070591730234615865843651857942052864,"numerator":798037983242368945365},{"denominator":340282366920938463463374607431768211456,"numerator":2716961751085338200423},{"denominator":170141183460469231731687303715884105728,"numerator":1130638476833668860951},{"denominator":85070591730234615865843651857942052864,"numerator":568883751286664106879},{"denominator":85070591730234615865843651857942052864,"numerator":749699889670058310315},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":32,"numerator":327},"tube":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":14812151048287118396686346338698732731},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":57960607580593392422210649263242565033}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-875874447711606586480614226105879772295},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-879657571450514396367937688876945598107}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-471134639860698315935182771136951646107},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-118043266506804828481475623394283745991}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":57415237346939502789851252204463217091},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":56613012972561743110560095977509454669}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":223769015912931670630425879453023547367},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":222327821039394044990113507340657194213}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":189522977935462604968122721805112375631},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":188036307894789079748701934373840091343}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-379077726289949130017513951089146632157},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-191105386654817615012142764958203192481}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-43104126961031622752105041021801174971},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-175855816626619072279194438365892232049}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1435558303193964536858488005216643469},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2832075916007540460686723477638663831}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":176638868148252514909372443494021217847},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":173265659615392772236595380505652399619}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":214229150576837658399454487651643571625},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":212714743714241732933956666419192355391}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-66124424278479823114938143214693784223},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-66315711058230888973672197563096140989}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2579837980761545727963255061539669747187},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2591326394250487678750545748875141387833}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":335877294267633338947168594154162516459},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":670046723661919399775724260712354094793}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":516744190457271953495481468499851658663},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":128068258452716903076481701241806567797}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":13672264356026691268619423986820513467},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":106802431483384678605965514251968276325}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-79433624813506306616381161220818535345},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-161944357255832755212584548656480647285}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":82237937188342266106551082609054989915},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":161509715262417844209628915271674602663}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":17629547483767987010155129274263878311},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":140875548704480566131780051060418907885}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":138623711933732847543837036567558923},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":199855017396908566170810654912880749}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-137829444505723765606312378385536760423},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-275988392495951139259545787744424206513}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2679959684098527754448114297791604064605},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2668025229276090436000964891554244804247}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":3749954618021949635010042393143472827},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":59999273888351188128568437949301235557}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-873447752981305458446486766938982102221},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-436723876490652731837490661543640985041}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-236333212476664127735864362540757656063},"lo":{"denominator":2658455991569831745807614120560689152,"numerator":-3692706444947877035782929611617518267}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":112163826678108619732161227423317194043},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":112163826678108614077554115854449411557}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":112347794229924288888972728337064435323},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":224695588459848571788075277042758147239}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":190482525744522131270712191953562474549},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":190482525744522129358439608666473296623}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-192126914034328642232100179516742137855},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-192126914034328644633930442588639252093}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-178256018119815487507159171430064704573},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-178256018119815492916862065414918916777}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1446476457675578442508952374419887837},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2892952915351153204604431710159247139}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":178993110188182997760487430583055614865},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":89496555094091496589849460311453850733}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":846859297959095656940161533416972022329},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":105857412244886956649984969622210801987}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-66358927447435627801965571745462114055},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-66358927447435635049424959619163345229}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2599232924321624739341907855796338140871},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1299616462160812373633671260317332628517}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":668882548928576516332676837547935248887},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":668882548928576508586304991584907087605}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":32488206653578368721014219644449297969},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":519811306457253892429372629151537708265}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":111158647568908309310478517798320597637},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":55579323784454151132931551672297562129}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-156762372140476663351157421055103852919},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-156762372140476668778469989433522137065}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":159480942572434983323176359578223743261},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":159480942572434976796755129892405028013}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":282200524779805962399139221298421201915},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":141100262389902978411467610927094728337}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":281299813843389832373091249428734611},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":281299813843385182053176144070218789}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-276123997790677601130624751086838690505},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-276123997790677605804469270098981892379}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1344049796123971318142242437986147031707},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2688099592247942630158690084149371487087}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-11573498463028333},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-5420201537376735}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":9405964403402667},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-7754140066415001}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":354858432333433},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-924419200754945}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1173564375701141},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3335071149176349}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1108435637626681},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-557347930792703}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-15298241614188423},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-47754628876461353}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":3618183297249465},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-268528492177985}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-23133884066593},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1602685203880663}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":39981208252265},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-242775276018393}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1258051387163139},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":15506355947877}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":63511800731334947},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":26972443584371369}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":1332532847431423},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3241969276081359}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":50071090125195},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5530670396481779}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":156728482695199},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1083139992375475}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-758502408049877},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-316221064820623}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-739350071500875},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1566357760002635}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":7965915460693865},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":962992760723801}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":944126947534937},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-415222959383573}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":550854128831407},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-64288334244201}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":185561956868359},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-4028606983569}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":87575280762607},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1950875802552565}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-1141608867281563},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-8080082666346929}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":3015780226113579172063},{"denominator":340282366920938463463374607431768211456,"numerator":2614234820951881817595},{"denominator":85070591730234615865843651857942052864,"numerator":638558579453857034933},{"denominator":340282366920938463463374607431768211456,"numerator":2827301301466671452497},{"denominator":340282366920938463463374607431768211456,"numerator":2994933978249935755659},{"denominator":85070591730234615865843651857942052864,"numerator":478064088773364510365},{"denominator":340282366920938463463374607431768211456,"numerator":2401821952591333903367},{"denominator":340282366920938463463374607431768211456,"numerator":2704850668783709232363},{"denominator":85070591730234615865843651857942052864,"numerator":460051633792321437635},{"denominator":170141183460469231731687303715884105728,"numerator":1145196502340932383749},{"denominator":170141183460469231731687303715884105728,"numerator":935052174431247919819},{"denominator":170141183460469231731687303715884105728,"numerator":1811862992395049465287},{"denominator":85070591730234615865843651857942052864,"numerator":990678629253218797999},{"denominator":170141183460469231731687303715884105728,"numerator":1936591978447893572597},{"denominator":340282366920938463463374607431768211456,"numerator":3553426556946770272065},{"denominator":340282366920938463463374607431768211456,"numerator":3522306510544138484491},{"denominator":21267647932558653966460912964485513216,"numerator":169603298920491197315},{"denominator":340282366920938463463374607431768211456,"numerator":3263208481887598055863},{"denominator":85070591730234615865843651857942052864,"numerator":697025346144913199253},{"denominator":340282366920938463463374607431768211456,"numerator":2325159800313989086627},{"denominator":340282366920938463463374607431768211456,"numerator":2336921196492889562047},{"denominator":42535295865117307932921825928971026432,"numerator":382861449880816188045},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":657},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":60190596401157764597370860123991300329},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":58927903032287888519604514491682311973}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-872975950622779312433479856280806059895},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-438362452002297665788165308013032038671}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-471904955536669731042318501863559691951},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-59103820156270571469173649416992883353}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":113600457575805429756146010128339571411},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":55974916917404859325692580072229753437}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":224874631967167054190604040881804189305},"lo":{"denominator":664613997892457936451903530140172288,"numerator":436417668644707893428208028637975369}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":381317194150135171235983042271551146255},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":378396793005959226588603632175264555089}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-381530137986272315274496589980695534993},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-192310774230239950990207065833203193693}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-175152561953928950365303419725418959093},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-178615363882709091359250185569264910705}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2899103545201113361623565110476979879},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2860858011107353183863683426389613881}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":179346466382524728180236406701159235209},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":175948253283398408092569632462663252273}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":213041524600154791057415070260386947459},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":846158653609621607585010230562078257243}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-66243239341312968564444313625542262433},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-33205927303359728780958955045555653925}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2588995119524424454925186921142240601655},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2600414663128374701807243604247686233137}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":41901142091364783588134855819850869363},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":334341289711504121997573058375354054763}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":520276088366627512817358429453183560697},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":515832168857990816173763162770444006585}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":111439184471650974171228568331834252213},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":108839998175387136153396685796310514197}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-156395431067268799716065160328977619257},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-39885612362236671240842761803609161883}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":162156998594727889322538691333546948377},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":39782683457360006998318868028114423299}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":282266993200948380535968418196225411841},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":35246768161801627009302349355023317757}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":19675637028303570685204058013543917},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":236174221222075557056996081981731709}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-137944628154038822130006088025272207055},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-276190172057679559897507389717652646787}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":672335042802678603276720619908622627365},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2677525007282902570047922755904673914325}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":30462339296026427466739907896142971351},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":15231169648013212202191798088278457867}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-870573644613986501562375481213846733503},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-217643411153496626722507894666847978791}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-473245761979872702245370210941822212017},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-236622880989936353734344281802814712061}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":55427627349758201984553556329122800293},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":110855254699516398172157504520683307157}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":225792416608103797526230469598828035829},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":14112026038006486962688475451349994997}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":191598821731711497290521079997597141941},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":47899705432927873833579520960975408475}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-386633495517606680870087985451816979765},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-48329186939700835721402168598181826473}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-181031966681263457518429982597744446783},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-181031966681263463066246003520331664399}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":730196129943501864023708214246622149},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":182549032485875229679067973613040913}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":90859074103669488581793020535128256507},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":45429537051834743115587918703219147101}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":210548700339792827630789434334782318409},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":421097400679585653355362729074489051343}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-33220170549839838828685685675778716283},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-66440341099679685070678462804278434839}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2608275304379525475511481308355335897373},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1304137652189762741797862928203504491613}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":667499158831616708117708494511580220269},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":667499158831616700212167103406047470233}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":523323238902711451895245850626536425397},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":523323238902711444619239995312311273981}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":28309116476671683805858330268689161483},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":113236465906686728000392822965362697413}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-154241635262418143815331413871242366461},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-154241635262418149366363866619145460765}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":39264981656023462989732644581746264299},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":9816245414005865330460596363328090085}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":282374015017758637796693006891610064319},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":282374015017758632074713755146247314275}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":319364796283531706640637583755744369},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":39920599535440865645460987485201791}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-276305165903501520494508635466020978585},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-276305165903501525294289472612311866619}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2697398953624738666064865014638506219729},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2697398953624738659808512656924238269885}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-12164000523401633},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-42268742662958881}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":2493242059750423},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-14019937204325423}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":135873545209225},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-14879391859122425}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1443989903803631},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2984523246848737}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":146806410249155},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-996923798664267}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-12400001091208137},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-2697168613758295}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":13660321092235639},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-631854451511887}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-8737872342245},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1602419491157991}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":154229329638263},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-240539205457561}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2477517506626367},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":50976773018037}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":118128371081281305},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":3095153102846001}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":9655849199934535},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2603450262085429}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":44661277297233},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5347545963593023}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4917186230681231},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":68710051368329}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-762496735935125},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-311478768447743}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-575518169263485},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-717336133269943}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":6895762802448943},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":114755643017503}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1127828683111995},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1501727990122403}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1034471110825553},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-170295346634901}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":89418246238387},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-64831275862723}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":366131120030059},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-417055267135103}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1584938950043647},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-7067411794808659}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":1329227995784915872903807060280344576,"numerator":11962270544330141707},{"denominator":42535295865117307932921825928971026432,"numerator":332977006534256365909},{"denominator":340282366920938463463374607431768211456,"numerator":2611650649647612371039},{"denominator":170141183460469231731687303715884105728,"numerator":1449236294906102910265},{"denominator":10633823966279326983230456482242756608,"numerator":95675198296908554037},{"denominator":340282366920938463463374607431768211456,"numerator":1956187618805331045749},{"denominator":340282366920938463463374607431768211456,"numerator":2450556587797369674415},{"denominator":42535295865117307932921825928971026432,"numerator":346738405525379674849},{"denominator":340282366920938463463374607431768211456,"numerator":1890614675255321369081},{"denominator":340282366920938463463374607431768211456,"numerator":2350615969858323158139},{"denominator":340282366920938463463374607431768211456,"numerator":1906181836634357712829},{"denominator":340282366920938463463374607431768211456,"numerator":3706650019526891576583},{"denominator":340282366920938463463374607431768211456,"numerator":4042119555591577449181},{"denominator":170141183460469231731687303715884105728,"numerator":1976384393320030990517},{"denominator":340282366920938463463374607431768211456,"numerator":3638002062990406752297},{"denominator":340282366920938463463374607431768211456,"numerator":3611519102141515066115},{"denominator":340282366920938463463374607431768211456,"numerator":2775512893248193340183},{"denominator":340282366920938463463374607431768211456,"numerator":3335778452614536129517},{"denominator":170141183460469231731687303715884105728,"numerator":1430494511744726322397},{"denominator":170141183460469231731687303715884105728,"numerator":1195369160296207481955},{"denominator":340282366920938463463374607431768211456,"numerator":2399889401397051158781},{"denominator":340282366920938463463374607431768211456,"numerator":3128170696384289209909},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":16,"numerator":165},"tube":[{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":3819556179977968452967855682952533055},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":29937768889103577002122149242597142841}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-870105743664329055927021894710176117399},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-436909543674929198934599518797870379943}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-472585079557470798885790331392519011791},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-236699266758022682372587133041729379791}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":56166756504368368955876137370957395453},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":55318324851227778057920901877481038915}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":225970196733469852648178013773988913535},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":224553965318335096136952750494952144811}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":191772336343058845936741427597173346561},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":47584803363948956879101518276890221997}},{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":-2999601561465603593440008464186948081},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-386997281878197504999113837392455312235}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-177907389775788137129820755079791562863},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-45348418304015410225801229095874931101}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1463322372769128111802176696748936743},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1444604689331848656802220083837296797}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":22759257796562216692595356015595688133},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":89325391083851788792012575328071569669}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":847454758792914922002578874136506047953},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":841500150454722271378405469140189047269}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-33172147958264691474438096457090178555},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-2077831600799744733742811844624208469}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2598097742211272435338214035150935334535},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2609449563314795475375152239405940142339}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":334529336726477453096376122466456145489},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":166824357052292751897999543320541281405}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":261892516306623399350617916694017770709},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":519369781328810236176943383992035365075}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":56759687476326364261159022627055274867},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":110896344526270032681812553999201937477}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-76934206374433127196656163812286138467},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-78541961591994468521743753828315130515}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":159789457766247345638645269802815853619},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":156704305828123722483956169755918005595}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":141218774647679674338831692702481778165},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":141087094361261123308427157274328208603}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":176587173745706724764598465961721679},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":68328438637289954750071175270985805}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-276096843394452401200899728454800810991},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-276368387356704400498149952576156350579}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2698627057247956579884649450171067329893},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1343464936957303873427902854951312460301}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":61830405059331088421558066615320614279},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":61830405059331082203895930428229196053}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-867728803613592071164820524962180771955},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-216932200903398019148720247568409610243}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-473736109150551190446597053168580388561},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-236868054575275597893398415279666338809}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":109509636986760768031245051994663024323},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":109509636986760762088459268406138733403}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":56719772880805234787202634183319565171},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":56719772880805233222451232874837473541}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":385385689984267822398739558348911342423},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":192692844992133909197888855125813761035}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-388977128480406348536835724649239029939},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-24311070530025397096148368438552212683}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-183826672417001275577096247591806674305},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-91913336208500640633111716093260572881}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":737042863833255368015317334878110969},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":737042863833254396830755612160699011}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":92231615567213944992700608674665193901},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":184463231134427885160857138262282783001}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":418786927831000724458854669046903413407},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":418786927831000722513663885485319279095}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-33252327176833847903553299046530760113},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-33252327176833851694596460964828513567}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-327158145614912056727373244397721438593},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-654316291229824115516268709514233884895}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":666096356364468324141792970289838452123},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":333048178182234158036763400585645993577}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":131702803723376002778131830717331011771},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":65851401861688000457919064033668282547}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":57666822175216531712161351561786918277},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":57666822175216528009540210641001887845}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-75833341247938429387366478400688949787},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-151666682495876864452287380764664477421}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":9662019298810876197689898209876277921},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":19324038597621751542902721555473386329}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":141261679769801912076333716628868391933},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":141261679769801909140664112836728966261}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":179108390702398949175232055491648279},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":179108390702396491120378857900467255}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-276462221210091075255755844504984086617},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-276462221210091080184718958648787937865}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2706605718762477582141177262540890770509},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":676651429690619393937947172347003650105}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-3100037101617177},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-40813157510969159}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10313129336674335},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-6290139419080167}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1566800021757479},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-1843356058817819}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":106792383300449},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1323391248523529}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":613587778502611},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-886848804585109}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-9672701101214621},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-19373890383822069}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12878298376368283},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1410611321749833}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-43183369005937},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-797100538195803}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":149268676756595},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-29635128218601}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2427656325300471},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":75953637303275}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":27253234599438623},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":11198862549003325}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":8682582485977639},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2002868850984385}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":2701107664621},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2561668887552871}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2386660210420907},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":275866890832891}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-756713891113083},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-304109077967215}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-418981829670677},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1305938133146033}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2958922751481663},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-25862749743061}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1271018850558073},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-677990694854359}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":969868881295659},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-206027005520201}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":86093740204777},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-64992471227585}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":132490078475377},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1412967830723341}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-950570604105053},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-6122854470033223}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":3108816861588993458887},{"denominator":340282366920938463463374607431768211456,"numerator":2715018785951641417173},{"denominator":21267647932558653966460912964485513216,"numerator":166880733241945624657},{"denominator":170141183460469231731687303715884105728,"numerator":1485695357031973609169},{"denominator":340282366920938463463374607431768211456,"numerator":3129501745604783388093},{"denominator":340282366920938463463374607431768211456,"numerator":2001466386508808695417},{"denominator":340282366920938463463374607431768211456,"numerator":2500761235423288252519},{"denominator":170141183460469231731687303715884105728,"numerator":1422281419190094022931},{"denominator":170141183460469231731687303715884105728,"numerator":971184465135291785607},{"denominator":170141183460469231731687303715884105728,"numerator":1206135431846089901901},{"denominator":340282366920938463463374607431768211456,"numerator":1945158674817483263715},{"denominator":170141183460469231731687303715884105728,"numerator":1895519911030740128413},{"denominator":170141183460469231731687303715884105728,"numerator":2061520918275485914305},{"denominator":340282366920938463463374607431768211456,"numerator":4034131249632844477359},{"denominator":340282366920938463463374607431768211456,"numerator":3724586567220622581035},{"denominator":42535295865117307932921825928971026432,"numerator":462827505559195839967},{"denominator":85070591730234615865843651857942052864,"numerator":709693511539223465693},{"denominator":340282366920938463463374607431768211456,"numerator":3409906307966301690297},{"denominator":340282366920938463463374607431768211456,"numerator":2935669015844196017741},{"denominator":340282366920938463463374607431768211456,"numerator":2458054702111379748661},{"denominator":340282366920938463463374607431768211456,"numerator":2464480585607829613199},{"denominator":170141183460469231731687303715884105728,"numerator":1597344557146286078437},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":663},"tube":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":31007768469758171472960239527508354365},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":30401736054500674730097302348727686133}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-867264942696356734436913829354864625801},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-870941278160389814940377995502008642377}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-29573472578312837990113912937303750533},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-473877568521678351877298644247458787863}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":13878696004782088267425544979135534105},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":109286434650853684436431890283720805853}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":113527796004554440845402480229380123779},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":112826031892884946241075061642123094245}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":24107967337175339212619751564417719077},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":382916550804380497698271738849813990801}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-386333125685554275779206628223399846969},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-194668412003039163344010099154273959687}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-90340496654316379547711649264631430705},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-92095363517469871662745068507527729793}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":738433566272135031411537257448441141},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2917123436961277402556080505474391773}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":184821696036867413957180853911341016691},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":90686654779806795037018660667688978433}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":842784730466844560844026658578602985373},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":836885439390112057635337448382889123557}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-33213950883125051388950115227578680003},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-33276147550272925786305818610067415025}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1303573388605537826359943820270318848521},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1309216024447786940317912158244298222399}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":333838805332899698405550653163492618013},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":665893092323972509877173190371958334013}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":527269880332716532746011765065946542915},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":65360590398533304353422058136918651963}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":28904739690706498495762580821462104299},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":112971744478226809557875322685417255709}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-151287342988981426141397532185910878675},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-38642472489866668542284476005682416237}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":157374205282449763510164709998572599195},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":154231418698890647997823395481720434757}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":141291942847179233089994834252283127263},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":282350696053691983840794208973209292519}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":196161833749491635387735708785362455},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":311258255037365108984600598024684757}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-276281028065969287478305157268855569207},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-69130601610322904410084984260371601857}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2707821459852184497287747941511013772467},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2696240897377244677866375402836927296759}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":62716521913212351328074534050862647825},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":3919782619575771563606659624520381681}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-216228579758037818260923106849404444703},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-432457159516075639289663963828568783875}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-474138076463547129070783847958127601245},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-474138076463547134529755815612515997079}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":108126958965856762130816346292694360825},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":108126958965856756038628355899095340495}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":227955492247788121116651855346214445461},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":113977746123894057359686551254629063567}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":387528312855160274233442452945712443527},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":387528312855160270137157595220661679501}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-391283603341309111689982706831924201393},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-391283603341309116794945043082264677411}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-186640104204337166032045634602364999553},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-11665006512771073241609295395783026019}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2975108388021383959867543168872710369},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":371888548502672496106600296460665653}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":187228382711675592308490539526268716037},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":187228382711675587357711208441716738091}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":208249579845191603321176373644107760333},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":832998319380766409310463407217067596245}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-33276091285530465269979985619857548429},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-66552182571060938293811301043498190033}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-656550869048672081111904291751758155853},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1313101738097344166429328128625620806695}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":166168990920663225090543524071800215247},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":664675963682652892127548269326906835717}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":530274096090867885871341114407834580783},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":530274096090867878244893617892759854823}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":117450453536573689890311072068075096779},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":117450453536573682299028748264523099761}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-149038688164542368079214821069319313411},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-149038688164542373886192382261582524105}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":152079100380214389871990095731001573795},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":152079100380214382900712153319671235853}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":282648008983274624017577124206067980263},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":35331001122909327249150308322128688693}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":99459820085900537953230957219980409},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":397839280343597097508305038275841321}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-276594525459462805912263360268837717867},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-276594525459462810973738640460987310287}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2715721033710865998177369192739536298107},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2715721033710865991652359546325309975691}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-3064284818107217},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-19533257457354875}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5257807788195835},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2810158599340451}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":63508763898085},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-3628895965903875}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1980933357472029},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2300698077947987}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":633915575309497},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-394035332267727}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-7149919420671209},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-34575330869442789}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":6072558360941159},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3037268886569319}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-12290485599907},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1578462107430701}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":145072063217169},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-232595390578687}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1182180677380079},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":45411658169707}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":49918982657239819},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":39809720404015451}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3880834915805811},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":360639961678339}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":47254934387479},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4882035709887135}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4607573994192751},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1095263745163619}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-371870353061699},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2362761909674163}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-33804520389287},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2365767357027843}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5033922826602919},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-970706622007653}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1382360633009697},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1223952729806809}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":908157642916293},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-236920469910833}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":10346338846915},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-130037103353595}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":668458890997201},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-37002718967663}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-762470917540535},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-10510336883916843}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":3155170585341447130023},{"denominator":340282366920938463463374607431768211456,"numerator":2767806872004773017731},{"denominator":170141183460469231731687303715884105728,"numerator":1364739108982575602743},{"denominator":85070591730234615865843651857942052864,"numerator":761522963595270450039},{"denominator":340282366920938463463374607431768211456,"numerator":3198638348467570581939},{"denominator":170141183460469231731687303715884105728,"numerator":1024064358078400498111},{"denominator":340282366920938463463374607431768211456,"numerator":2552473576932366012189},{"denominator":85070591730234615865843651857942052864,"numerator":729212701448992598163},{"denominator":85070591730234615865843651857942052864,"numerator":498876795391216698661},{"denominator":42535295865117307932921825928971026432,"numerator":309423566096657097325},{"denominator":340282366920938463463374607431768211456,"numerator":1987091029557226490449},{"denominator":170141183460469231731687303715884105728,"numerator":1938461252673449548727},{"denominator":170141183460469231731687303715884105728,"numerator":2102758528424657581971},{"denominator":85070591730234615865843651857942052864,"numerator":1029327789331255624517},{"denominator":340282366920938463463374607431768211456,"numerator":3813222938746935587597},{"denominator":340282366920938463463374607431768211456,"numerator":3795640114236179041735},{"denominator":85070591730234615865843651857942052864,"numerator":725871444570351825015},{"denominator":340282366920938463463374607431768211456,"numerator":3485637056072618857313},{"denominator":85070591730234615865843651857942052864,"numerator":753046689068865705449},{"denominator":340282366920938463463374607431768211456,"numerator":2527152161606039588039},{"denominator":340282366920938463463374607431768211456,"numerator":2530736713823125815001},{"denominator":340282366920938463463374607431768211456,"numerator":3262499949274129973053},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":32,"numerator":333},"tube":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":31449292844570737995443955764099674783},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":15427929580671370723557538626529704317}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-864454632779053749969740564407763834861},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-868092600372985223997674371169738203379}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-236838489534221489354692213362913111373},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-474268279889525096081510688954344625339}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":109688576925908511379668986952367265721},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":107899177534431077895429639574348107299}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":228130696469730573252985708506004785051},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":56685006076735520990140655674679747251}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":193932367438272259911400142798700022215},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":385110240551792629348330757191094657857}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":-6073146233102890050837932847224442539},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-195819527268399408042853962146044070685}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-91736679564067051109322071649846212189},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-93503246008402917901582592010905834047}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2980366754920027829348628527155093715},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":92018568744479680707922200556422261}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":187589388533699060395168093327829344221},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":23014485039035830433519490098555211531}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":104769752702271108177849844957273573349},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":208079090514123675092976136553348560641}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-66494368943266410197302997388423521069},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-8324652880909908286917375279472532135}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2616143172881579128775559332181778087505},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1313681546629376189604912779991344522171}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":83284613473646591051986334572523797839},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":332235696771064342837456807937847166187}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":530729493645003827345529233379332220211},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":65796981323472725128999942876598710111}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":29434551597205609346945519445245978037},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":57533235395306006822390118491112810511}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-37163349688508258340034009356923777097},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-152001491800526179018081974713108102375}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":154912222354689369539648698810797566693},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":75856543308767932886772713241024811339}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":35338181502137012430592031101268066371},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":282503127042104675929838445080601282077}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":108060356842862494376232470887076147},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":349991820741831093878071675048642773}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-276441180213100550887348568892311386197},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-138325795091502897285710661410007567421}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1358462265674405798369606068662453158869},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1352729592015331342265481930797567579495}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":63583146027833388108619782513195606121},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":63583146027833381705862358734835902803}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-431065625210733940308835308216525972531},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-862131250421467886262070783170924307081}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-474452301077099204047959951933207567789},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-118613075269274802406892888376271303579}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":106707234158277407240280256406133998199},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":53353617079138700497525187943191182121}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":229021494828575084464310476824484636403},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":229021494828575077926237805736227747693}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":97406168325127215011172180484868045361},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":194812336650254427926120144923576778443}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-196775912702628823335589540316126640915},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-393551825405257651882657530670626949391}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-94736107489233928418401317392860588085},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-189472214978467862818414737334796564607}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3001590564571469029988588441065387071},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3001590564571464929851067512166570121}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":190013607698509796778137761024014750399},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":190013607698509791698134353956499238233}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":414234961585900280881502775923127058409},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":414234961585900278849439552219287966737}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-66583242699138665360821088255116423577},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-8322905337392334161184621259069821935}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2635091227363658484470855850977569518567},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1317545613681829246525010808761074289383}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":663239801654332522902757424591283117541},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":331619900827166257249029207686017301153}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":533710749714031371530353369452080555433},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":533710749714031363722443018920199850479}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":59793580792663625625104413281657017251},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":119587161585327243468986086067915464905}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-146358853910334050815416463431268796435},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-73179426955167028377409873468746511989}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":149521338725344462369293708471946014739},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":74760669362672227621628455340364300335}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":282747406332844661963947722575643639215},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":70686851583211163945692294947085933103}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":438215331018027127502210962282384545},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":109553832754505482837992666047144811}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-276701433746328791344673931259442388977},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-138350716873164398271038625040798402271}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":681186519250113777445623512424807391973},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2724746077000455103119170583749744117057}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-2964341560959985},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-9278547016872063}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10639500654294049},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-10028436608722043}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":525480457136751},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-14247496693083285}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1128686941458223},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-243001455900743}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1299215893452267},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-700184403355419}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-4850137081077753},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-15352907186657249}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":2868020234845557},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3183566050861711}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-13058835710375},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1555579306461383}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":8857152565077},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-227943749535413}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2290477015003773},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":22321556703201}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":22703989246797547},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":17401035914606431}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1723781752475941},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":923619266094611}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":14262383500523},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2317920980862451}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4434088462028019},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":268801387287803}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-90637047067273},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2287451277494815}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-65105071793895},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-532614583883441}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2122038085871467},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-723694001241459}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1468628178739715},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2211748160526457}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":424694893576867},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-264129397741409}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":159119315993103},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-4073173967563}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":784807366310335},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-982267910405365}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":124368426954073},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-557953105056725}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":170141183460469231731687303715884105728,"numerator":1600683041739134013751},{"denominator":340282366920938463463374607431768211456,"numerator":2822189749400304672963},{"denominator":340282366920938463463374607431768211456,"numerator":2789798414297363713245},{"denominator":340282366920938463463374607431768211456,"numerator":3122612839567110755783},{"denominator":340282366920938463463374607431768211456,"numerator":3269035335843980040511},{"denominator":170141183460469231731687303715884105728,"numerator":1048105644103756596953},{"denominator":170141183460469231731687303715884105728,"numerator":1302865948597845855905},{"denominator":170141183460469231731687303715884105728,"numerator":1495402662860113652513},{"denominator":340282366920938463463374607431768211456,"numerator":2050068575635354120151},{"denominator":170141183460469231731687303715884105728,"numerator":1270000301469181830299},{"denominator":10633823966279326983230456482242756608,"numerator":63501100523789378219},{"denominator":170141183460469231731687303715884105728,"numerator":1982162477577424585687},{"denominator":85070591730234615865843651857942052864,"numerator":1072395127075443666389},{"denominator":340282366920938463463374607431768211456,"numerator":4202347825168167819213},{"denominator":340282366920938463463374607431768211456,"numerator":3903954394088489874161},{"denominator":340282366920938463463374607431768211456,"numerator":3890610370123603311811},{"denominator":340282366920938463463374607431768211456,"numerator":2969698796021025000845},{"denominator":85070591730234615865843651857942052864,"numerator":890754139676859768487},{"denominator":340282366920938463463374607431768211456,"numerator":3090588714634057505829},{"denominator":170141183460469231731687303715884105728,"numerator":1299037487709302712545},{"denominator":85070591730234615865843651857942052864,"numerator":649675193968359712483},{"denominator":42535295865117307932921825928971026432,"numerator":416457143122684414693},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":669},"tube":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":31881084118107551055141279896349159645},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":31300169494217130448154609885085527451}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-430837934831567766983418981611603497077},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-108159268342477461830922796049266554707}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-474089939592494295709771192975227057329},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-474571308303022629319897740605209240935}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":54155260795258973122609017112538580383},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":26618723835976526275300289275068104227}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":14324711612623521050662510602475741249},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":113908863148661378354618380736330341989}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":97488902745869980822301557404526728425},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":387258613063124753120263302265498513973}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-48874071546677002131219318157715058481},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-98475720513086740863009039691183636935}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-93142229064782830359980153981203548793},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-94920459438640356920406786081481430851}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":751634362909100053980099997253419457},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2971616269841933274734180169868479873}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":190377142022430171215762747638420793169},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":186878520566036189151261037175524814687}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":52098531672879195329028880405548331647},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":103474329114132500683362021195546738963}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-66540248031922134804231161776467967157},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-33313065771539910249692312208515626601}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-328135987129691623333412837571818187063},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2636243688609086364470447362700393510025}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":332429193586733651001525987134002158529},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":331517076132661642797136598329496505957}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":534162740300250206371729429005170596767},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":529842024512047619564134083080378299545}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":119877385713296724400908396129915423181},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":58590397202913338810521060239794017715}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-18245973022354541001908817872769561295},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-149379899718509712316294809092521334027}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":152404517129804745210287420923749220709},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":37287587408475297956828542798824001781}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":282801690280397193103028287118674816255},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":282630933283594331869888486272510780403}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":472910430023172370991370458280311805},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":389498041490310956010186413939427317}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-276576662414764716038081685072540221323},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-69188823215436403694974608709122982801}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1362968728073194551138104024453522690207},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2714585875662474534916376379127447902327}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":64430440697086416923561960516908168479},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":1006725635891975162950028409147318675}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-214845157319880735748784856108068894083},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-429690314639761474375756966562708738253}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-474679446514181915219876994354897954975},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-237339723257090960460985571238666018525}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":26312626131351997985334692020411204105},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":105250504525407985539352274706788142071}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":28759621556314138988995897803411498529},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":230076972450513105230537537856292043589}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":24479623162775753004070482044914756769},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":97918492651103010943400131729842855517}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-395780728567427549736534557348247720509},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-197890364283713777528849405939824269219}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-24040367689986313940460719642700023329},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-192322941519890517656610044973456933737}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1513806901996556298928098247377392081},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1513806901996554192834343974538743219}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":6025590364362885677947273250039089429},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":192818891659612336482031510753485698107}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":205997568757829062666724405136792695901},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":823990275031316246506749656502093700249}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-33299076035011228492208606104236129377},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-66598152070022465090970756630517653119}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1321964713009211211335386491697322403323},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1321964713009211215710656346109440827959}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":661789689035517316203306232201967513671},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":330894844517758653812370762376614202847}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":268560024591754391472063961587155856189},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":268560024591754387475238438834422696693}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":15218004186615601884296307555277115915},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":121744033492924807099244188189384355791}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-143628407254523359863430742862836295299},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-143628407254523365938366119746115402501}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":146920086241698103137460241728341118313},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":146920086241698095853273385508283663299}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":282820987368213057052493230510096255993},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":282820987368213050710647224153107935207}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":479327529418156139226268500402520083},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":479327529418150797488962390656709023}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-138391147544609834524404834554859625327},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-276782295089219674385644983343059375927}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1366841028565771396527644175945833378897},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":683420514282885696562712182078539769025}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-1407311638875925},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-2188551761864323}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10689208245177497},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8930169805373595}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":91175053892101},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-1746233636461305}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1276169426792439},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1582060117626305}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":330771740367949},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-313642016248473}},{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":-21805907765125},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-13572714678597601}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5431051037026045},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3263054634643217}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-52502706451139},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1525775566807489}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":34741977910715},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-223428945817013}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1103172004837023},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":38840201518851}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":82054445043379297},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":29870116389790283}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3042987282058097},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":448927341353889}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":142593579025189},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-548504267055105}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2127357974502765},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1041151335676767}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-697405017095671},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1103803181948331}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":144474682607},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1908910892474919}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1770908988658883},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-462126209207991}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":47893793230499},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-500104959674599}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":198326773495693},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-18005660719595}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":9555727702757},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-65182306694589}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":879751667527425},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-201221348145749}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1135673005725737},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-7492806368718713}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":3247368191998200475755},{"denominator":85070591730234615865843651857942052864,"numerator":719544361164386418635},{"denominator":170141183460469231731687303715884105728,"numerator":1425520021769572124883},{"denominator":170141183460469231731687303715884105728,"numerator":1600495589743971365791},{"denominator":170141183460469231731687303715884105728,"numerator":1670356923550001493975},{"denominator":85070591730234615865843651857942052864,"numerator":536437853940762678379},{"denominator":170141183460469231731687303715884105728,"numerator":1330287532343673030655},{"denominator":170141183460469231731687303715884105728,"numerator":1533230716765425710473},{"denominator":340282366920938463463374607431768211456,"numerator":2106093573074409918925},{"denominator":170141183460469231731687303715884105728,"numerator":1303069776146039631819},{"denominator":170141183460469231731687303715884105728,"numerator":1040023944929105873585},{"denominator":340282366920938463463374607431768211456,"numerator":4053273953687411316029},{"denominator":85070591730234615865843651857942052864,"numerator":1093816897274565172905},{"denominator":170141183460469231731687303715884105728,"numerator":2144640373471031444803},{"denominator":42535295865117307932921825928971026432,"numerator":499603095956507469875},{"denominator":42535295865117307932921825928971026432,"numerator":498445272699841588375},{"denominator":340282366920938463463374607431768211456,"numerator":3037464993280232478735},{"denominator":85070591730234615865843651857942052864,"numerator":910522915399854422581},{"denominator":170141183460469231731687303715884105728,"numerator":1585461231239830706123},{"denominator":85070591730234615865843651857942052864,"numerator":667717127856686147221},{"denominator":340282366920938463463374607431768211456,"numerator":2668416814798140007425},{"denominator":340282366920938463463374607431768211456,"numerator":3402215497549066618621},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":2,"numerator":21},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":64606453852601595719276152902213409103},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":63469445158414691259927492471902484819}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-858929681229690360353854563554023593723},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-862486980331665389140761474483804748071}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-474415076672211147670738624813855722413},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-59348415090136463930368986726043865077}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":53447706002095204486952600142094048377},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":105013633545060391637655763702670366761}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":57562383209521839577975221888588022079},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":3576328846263304550261245082654343981}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":195999654734196178414902685228620589579},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":389360824837410689076955280646141237127}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-393265667817233325369780247599593539107},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-6189488182773070912246383995736995481}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-189114245291620916021195666611564320887},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-48173485540022581044316336538527404541}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":758060542196723699020729739282345409},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2998184830769750500269750440612562669}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":193184939455277800584503743505013687637},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":189661237503313346266315532651217271015}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":829041931920197342390865708725850190647},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":823321844436229536112264142128912707915}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-66555734955282571446730458561032573947},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-33320231762405121331092138393435381821}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2633981936459486272958184279254430888615},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2645074845501208388084899994286793932577}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":663423869982745487956030316127400191803},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":661583186698615837423301402965252704739}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":67196061790347918063479147020446462769},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":533282111424170032524066334537711505231}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":61018380704388986120077963695629277237},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":29828745956791512845825136974690912195}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-71615864566386976303984902665100456409},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-73353156109475923052234870346875143473}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":74926061912483955255349895500926106745},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":146544272828733429096638967901813481533}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":282872035348928097391913401277962955287},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":70683389666097735012104955400179197591}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":514313037921716885567213616431848453},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":429760030250944714216943425158965381}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-276686830524400130095786790627428231289},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-276832862743686742584658194748546552617}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1367430724119019839065472211428414544627},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2723622146862945705895640156937954313973}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":65258613775953609354438136099629155763},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":16314653443988400692034535538176187343}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-856663460445742789802836154315254397319},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-856663460445742795674412451260789896511}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-474820201941519409102558124864875220409},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-59352525242689926866118980304048261265}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":103756840766969834875068233833849049351},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":103756840766969828312533944229453578787}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":115560897785794814008963599707545043483},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":231121795571589621190537861193341744795}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":98418860208465731582228789444027670603},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":393675440833862921935318226178728609515}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-397969275017688028300769148760410512479},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-99492318754422008433716942370641575861}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-24399025532847558259686391954463380597},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-195192204262780472365202626985749051109}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1526587244214381411821725266182811617},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3053174488428758496395097936038599453}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":195644200782128142636050977580638957241},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":97822100391064068644185769450790503501}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":204890216373549317924385644244034194101},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":204890216373549316858780704860672304455}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-33298613623453081224566486393502774763},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-66597227246906170736730621648677986709}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1326359548866425352681475969087121830055},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1326359548866425357144091917042831141993}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":660327441664780623452926761970781269853},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":330163720832390307348312260545577455875}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":67562609345316785089807669472822571029},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":8445326168164598008354732129804844351}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":123921330537210542464387431638760755561},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":30980332634302633572832785756731107691}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-140848600204976643878744022798240355099},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-140848600204976650092424051551216877457}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":144276429649122142709602511859952337133},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":36069107412280533815944678089446673307}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":282868181115534686111721858688555285543},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":141434090557767339802623704923192390089}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":32572378795591974460580200652067261},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":260579030364733050105242149010028787}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-276836453001644658816859065360944902315},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-138418226500822332148360286071468963569}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2742530210164272155873622634434174338035},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":342816276270534018615644152806195605129}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-10518300139197345},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-32815743404100823}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10664538220466069},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-496620957956769}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-140357805112787},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13667520583472897}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2842027969656007},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1218613449103051}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1339146118673769},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-281828298102829}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-968382962496195},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-23897151122375855}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10313865303060183},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1645879259830739}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-100199622265299},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-744455952405045}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":136614072309243},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-218780082772249}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1056241790762185},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":58552712860443}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":36813590367835427},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":1569418411598797}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2667269872890379},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":20713931523355}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":44307723542681},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2070526954872897}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4070682871182761},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":498445838591683}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-331943929693147},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2123512680576141}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":59568336612611},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-212666187831795}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1460189026105287},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2180437400668223}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":789160631835737},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-905630064118945}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":369784405366525},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-154846783180047}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":73389761530313},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-129946917427703}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":477722446515491},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-649612604552103}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1901883818922663},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-3100026904719721}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":3293138848251829751455},{"denominator":340282366920938463463374607431768211456,"numerator":2935778843235993862409},{"denominator":340282366920938463463374607431768211456,"numerator":2913190165381268811193},{"denominator":42535295865117307932921825928971026432,"numerator":410158139310186044469},{"denominator":340282366920938463463374607431768211456,"numerator":3413693717709516731371},{"denominator":170141183460469231731687303715884105728,"numerator":1098393500707305548309},{"denominator":340282366920938463463374607431768211456,"numerator":2717042507549166534651},{"denominator":170141183460469231731687303715884105728,"numerator":1571927525659439865385},{"denominator":42535295865117307932921825928971026432,"numerator":270452999825135746393},{"denominator":340282366920938463463374607431768211456,"numerator":2673838692374094643155},{"denominator":10633823966279326983230456482242756608,"numerator":66599550641364022945},{"denominator":340282366920938463463374607431768211456,"numerator":4143796167517929089889},{"denominator":170141183460469231731687303715884105728,"numerator":2231306894406653676839},{"denominator":340282366920938463463374607431768211456,"numerator":4378149583544216179353},{"denominator":42535295865117307932921825928971026432,"numerator":511484814990640583745},{"denominator":170141183460469231731687303715884105728,"numerator":2043263617036415111303},{"denominator":85070591730234615865843651857942052864,"numerator":776709365992190455445},{"denominator":170141183460469231731687303715884105728,"numerator":1861455102480193433635},{"denominator":170141183460469231731687303715884105728,"numerator":1626618349894948353055},{"denominator":21267647932558653966460912964485513216,"numerator":171598703818311641571},{"denominator":85070591730234615865843651857942052864,"numerator":684982487715561930217},{"denominator":42535295865117307932921825928971026432,"numerator":434278831877936320931},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":675},"tube":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":32715828056644471380601512318632678433},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":32159597269865286751489730834333074421}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-428108534439409634821130136339437620091},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-53733258499419515401894993477599463753}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-474653050608392845229514334221884254821},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-474917009666283545133140933352998000807}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":26360821635628744979085328611728943645},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":103515466371445100166315852993229448533}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":231293007691282939334994932861627172729},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":114970928711880450720576691305681667089}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":393995070718321053032329625006669354697},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":391416070591755487189297293554224623381}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-197749787821443319716323797652314199147},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-99577776222073935617879303385449591223}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-191962659461213786920902322250700868485},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-195565480047981032948736668960670794397}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":764369321900484923324772230776222317},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3024295639147682684820865374294079951}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":24501593049721959282727111696099384925},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":96232009566574871697694345098168813673}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":51534744986081564316001861123388863349},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":102362434039677155645588525737841846167}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-16638849043530482653403516741252559355},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-66638953195789249278148432610657800175}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1321413148210790848701857529270604995121},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-331732199048748618759286788109566862341}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":661975175367656555567442991040728361559},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":660120312046264161926075404852143138235}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":270472818326609617785388695611520990509},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":536694983909096501548221264807376521921}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":62108297172523312951878528640531286431},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":121469304509355716120964980268195303277}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-70223243915897321299182890502970684429},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-143981953857048779642810602072692879079}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":36814025470258822143099508928350883281},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":17986993185957929277877512257725330071}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":141457957693056736891722561653874307317},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":35351304976333569907264265500337603915}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":139107801111507133038943138155112255},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":117690113603763317853718032081205157}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-276771034248876964302884407473480967651},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-17305227665769000735133563852302533883}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2743697748804408828362608640555515082729},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2732569202501224337127319848931894713635}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":66067915804911638671207507365367516619},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":66067915804911631993907772277434163181}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-853980723444696582716068917722959707233},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-853980723444696588706091858120143879895}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-474875281517686568726499977553414050611},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-474875281517686574678982941739953667811}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":102226342573430388288621966217611776983},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":25556585643357595390417678090594509287}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":232155832057476418179001679536578876525},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":232155832057476411203009121774529479447}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":395628355648684629226978896585602679129},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":98907088912171156182060741929044735981}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-100029113745274408607673871887346552321},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-100029113745274409995264958031535262977}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-198079907124281551922799148296449448739},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-99039953562140779184427629812323360947}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":192391847087269803994642248307116211},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3078269553396312418501163984041294469}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":198489481721713125250041844730555635915},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":6202796303803534992617855832328377947}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":101897884101605142248119085990485515317},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":203795768203210283403474273285807349039}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-33290391458916230707111168450389371359},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-66580782917832469886063573709402614261}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1330730642812901128245647509090852857653},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2661461285625802265594608478683932624683}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":82356858959546572522416365273609104937},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":41178429479773285702583729970926885265}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":543852114196480901041583165309513618727},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":543852114196480892663260279521263313835}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":63059654848567814308352129817444169279},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":63059654848567810120813748207527717349}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-34505176977040772391939158863425439519},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-138020707908163095923502529819144548763}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":35397869787718146654877971888629856561},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":70795739575436289504233257485835589113}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":141444205149176549706092130392321031089},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":70722102574588273184255144157823626407}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":563688730219531614835518676858557129},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":563688730219525970325404680306754813}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-276863246056489817093364727856549776433},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-34607905757061227839992392297572339801}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":171955737338082247283275730795513756785},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2751291797409315949436885865465095895903}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-1209301694942443},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-1910053776372699}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":661122059011875},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-7080188746251637}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-291558373350361},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-6675487911644535}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":781110848862315},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-429594052318103}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":673901848308845},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-253655382910243}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":636366462621651},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-20965096182784907}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":9834184040803065},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1630298862540057}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-89653807821779},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-723390826008089}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":135199510927457},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-107078871493711}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2015124651150893},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":7637111537049}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":65600960163387389},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":641752642549937}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4640780615762395},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-45533202288287}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":54743841629245},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3897340625604813}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":970844106882969},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":469965503319719}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-155819477091881},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2035481221954659}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":226294150520871},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1508069932389715}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":37095347562329},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1227834084950145}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":804793516637263},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-205456205738617}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":172206599766817},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-41166687988359}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":17633377255569},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-129613809764435}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":127062391930969},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-514712441385159}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2562950088626741},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5042237207844067}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":170141183460469231731687303715884105728,"numerator":1669319712160267732449},{"denominator":42535295865117307932921825928971026432,"numerator":374375330140968358189},{"denominator":340282366920938463463374607431768211456,"numerator":2976235098163731514425},{"denominator":21267647932558653966460912964485513216,"numerator":210217102194491676699},{"denominator":170141183460469231731687303715884105728,"numerator":1743997675661896739725},{"denominator":170141183460469231731687303715884105728,"numerator":1124678581851694582161},{"denominator":340282366920938463463374607431768211456,"numerator":2775175624897494479721},{"denominator":340282366920938463463374607431768211456,"numerator":3223027377100176539377},{"denominator":340282366920938463463374607431768211456,"numerator":2222706381315809325013},{"denominator":21267647932558653966460912964485513216,"numerator":171445889797495079341},{"denominator":340282366920938463463374607431768211456,"numerator":2185505264952526468487},{"denominator":340282366920938463463374607431768211456,"numerator":4235918115881194901425},{"denominator":340282366920938463463374607431768211456,"numerator":4551654672093117393791},{"denominator":21267647932558653966460912964485513216,"numerator":279312134350269430713},{"denominator":170141183460469231731687303715884105728,"numerator":2094580368396234179439},{"denominator":85070591730234615865843651857942052864,"numerator":1046884378606968749159},{"denominator":170141183460469231731687303715884105728,"numerator":1588935266148757225335},{"denominator":340282366920938463463374607431768211456,"numerator":3805521059673084532277},{"denominator":85070591730234615865843651857942052864,"numerator":834395333249180572801},{"denominator":42535295865117307932921825928971026432,"numerator":352781865207232749583},{"denominator":340282366920938463463374607431768211456,"numerator":2813286439656226054531},{"denominator":340282366920938463463374607431768211456,"numerator":3547759111037913870923},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":32,"numerator":339},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":66238214338524251024715488587920540235},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":32574884634500654258703662818894649885}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-853538947760387599422724782993391689785},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-857010628521893373035711081312614503431}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-237393681740851521225817526425005746251},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-474963001908502058507122761702110544757}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":103954212288736665787554056124969878663},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":101980497071068356662695835412784841097}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":232325769550139944346226544082598448269},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":57747005171271007432198668490327659559}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":395942170575225593230488066950213543489},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":196711790986855757006816344035447183117}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-49711656821108906046041257727172568243},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-100113364764259761923180232262164238935}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-48707405789812745464851917000742457803},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-49613858548636456010060585532829677825}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3082239747125350795716599722228228673},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3049945015240248240914930826570501145}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":198860500878118823332100332823842925697},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":97643417052397919419534169666274660487}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":410059992553516023642853922014350490007},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":407264394489342145702027587851041099735}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-66539545323045202404379862870796282543},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-66621916281561281206569608352711956629}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-662905500059217232993226356908852280691},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2662592975196686665873370530824731240669}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":41282132478624619271525589378668817559},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":658647339725861059429582751378526225591}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":544293055788495499499615430618884549933},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":270039760657602623658189618347621809953}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":63208570505256147481690508307746093845},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":61822009131199613774996133969707159133}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-137613337494886283827079990472296216557},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-141208073839431135233017836359877312619}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":72308767566667574634927323944281413629},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":141206480291205083667333289801481181561}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":282934845346953323512336607589495896333},"lo":{"denominator":1329227995784915872903807060280344576,"numerator":1104852223312851067465744245049454333}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":37452906562386216311924643199268855},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":512481566921831282346005165554335389}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-276818633872135516467909339510142106553},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-276908079849146983914466230413780686987}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1376223811958715947141812463515254117643},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1370714137651404977498217071959228717749}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":66858638126992368792821857796417634625},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":66858638126992362025140742736047963629}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-425666686888987511733672979113009127743},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-851333373777975029579077428694047682535}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-237422711902702521129854170283633793843},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-237422711902702524170299778260183241567}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":50329569416320875125182070314549923795},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":25164784708160435838761780949166283095}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":233178947314748486549202161439993411513},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":233178947314748479421920857868602429051}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":198766010599785001732063486105984151789},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":198766010599784999428550895104577531213}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-201110643247508414632680696610857631809},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-100555321623754208733851472116345577433}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-50246484338653964925936414519051778497},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-200985937354615866311785653631080106365}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3102896477488708259380505000127468875},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":775724119372175923150317118615459585}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":201354661477054934674351676834197609701},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":201354661477054929046217990127224594869}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":202714542024080896453099841694347273259},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":810858168096323581326229254032217052091}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-66549130837299765801140961931634422819},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-8318641354662471807559753110377277391}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2670157049939050175868933446483357493281},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-667539262484762546288447628543726380941}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":657373786730694943221943840409728633153},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":657373786730694934098228043401389845849}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":547172663350082975639904401999759553095},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":547172663350082967062466669786139104187}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":128338223086565539777062508843749791599},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":128338223086565531195810206639408673443}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-135146027344434674835387941435872808041},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-4223313354513583791769753786650653831}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":17358295954695901489853714634321247593},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":138866367637567204138878265064590270269}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":8840034118418760653540219952646328815},"lo":{"denominator":2658455991569831745807614120560689152,"numerator":2210008529604690109884929340132231673}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":606900993821185695705026184311963187},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":606900993821179893815779244585132541}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-138431004221937680112510598687384053315},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-276862008443875366002090174195651949717}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1379984051609068266001830760366983684763},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":689992025804534131189484480554861380345}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-543729772496033},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-28317791494684049}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5226396742271559},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1580198016789931}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-413863522883439},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13039314269017363}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1701315883444117},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-524209124333469}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":676210177898665},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-458463859268647}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":253146569749739},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-18349322921413839}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":9436857782539883},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1595371343062815}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-71355607416269},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-700762247651437}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":67601683643501},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-209773524840555}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1913358153004941},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-4159486795635}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":1814266273729339},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":8062902526789627}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":500898960300333},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-718031843561045}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":134454644057023},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3662346539225017}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3698858726722687},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":218035527003825}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-574908741802045},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-243431868758763}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":326671166752889},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-665701558109317}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1900494655103299},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1340903348289981}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":815064188112913},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-749121690688175}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":10031760978549},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-348344937935439}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":136076019719563},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-129306023030499}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":133000358233981},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-399329881025969}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3137971495657431},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2008225373469677}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":3383830748472617461737},{"denominator":340282366920938463463374607431768211456,"numerator":3055857348441238862103},{"denominator":340282366920938463463374607431768211456,"numerator":3040439502182937822481},{"denominator":5316911983139663491615228241121378304,"numerator":53869633515558933543},{"denominator":170141183460469231731687303715884105728,"numerator":1781819873171793979121},{"denominator":340282366920938463463374607431768211456,"numerator":2303502403753666914699},{"denominator":85070591730234615865843651857942052864,"numerator":708753983455399797575},{"denominator":340282366920938463463374607431768211456,"numerator":3304019332692992552885},{"denominator":166153499473114484112975882535043072,"numerator":1114936252819524781},{"denominator":340282366920938463463374607431768211456,"numerator":2814065882514923209309},{"denominator":340282366920938463463374607431768211456,"numerator":2243064091014733140675},{"denominator":340282366920938463463374607431768211456,"numerator":4329666168863928916299},{"denominator":340282366920938463463374607431768211456,"numerator":4642426568217860345709},{"denominator":170141183460469231731687303715884105728,"numerator":2280928242572930019979},{"denominator":42535295865117307932921825928971026432,"numerator":536089772479213261303},{"denominator":85070591730234615865843651857942052864,"numerator":1072656330516257268329},{"denominator":85070591730234615865843651857942052864,"numerator":812654949679449553911},{"denominator":340282366920938463463374607431768211456,"numerator":3889974161819111054149},{"denominator":42535295865117307932921825928971026432,"numerator":428000943285632269085},{"denominator":340282366920938463463374607431768211456,"numerator":2900944490778842040291},{"denominator":170141183460469231731687303715884105728,"numerator":1444266878372034236317},{"denominator":340282366920938463463374607431768211456,"numerator":3622858222046139625679},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":681},"tube":[{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":4189148799285547216813362669910397329},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":4122588730976024753264332762894111243}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-850896285033345422397782572403861463829},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-213580859705933901796198222527683349741}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-474757844579313802224627199195447166245},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-59366600484444083911232866284057138719}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":25607071322971347324685272522346596787},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":50204429053667689598774926785331770527}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":233347661350809476615037502929542447831},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":232023406580439403935005968068525454565}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":99459979811233409679344055933298417437},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":197691313180106256031391858401642917441}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-199922845687635460510112862401002978039},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-402553327433538055124923350076785232583}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-197715042407327994529227000115040157883},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-201363689576863568464948479730109810887}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3106527033812132581791665509394954403},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3075129833350110178135552459110526081}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":25216016658118069126828586817717146381},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":198129631550242960513676129956035612937}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":815735517106837159886078354020780497859},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":405105537083438470437410847625420000093}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-66508493149677449445609236490030928731},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-16647416381881909533808127557603456403}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2660370088818719536051544693246838582283},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-41738782138899167819516374068695104015}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":329521257786887221801210569148270618667},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":657166076599755809371518979418880514513}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":273804824209825102993075582887223031515},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":67929326299238315564534050378321719719}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":128638652947995966563224914110813888819},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":125839382669262248428116671982301911401}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-134733577043534694395074222890062928141},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-138385944670899584982216786388933979449}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":70968765499393084144555123283041278899},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":138477012519650351593126658649474497817}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":70731873843477528790817865404341253569},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":70708720990107587918520171310272337495}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":642740167801866942389165517989689527},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":554905237154821417873875454006067005}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-276817452277884859809020871587658306531},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-34613348442599161722934720657960471833}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":345139045292977797316770448491059298277},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2750200623527704123981632784947051257473}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":16907777751575234926434639675777352741},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":4226944437893808303022883294925407525}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-848722344164158609520695719203275892281},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-848722344164158615757417162172765010597}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-474731391243513640171284908325352416749},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-474731391243513646383950134965498287689}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":24763846947792811437142056272559364847},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":24763846947792809670213634047331090243}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":234191004421592845190618798449212419553},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":234191004421592837909317958857843278623}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":99846444278664471173562929011156653859},"lo":{"denominator":2658455991569831745807614120560689152,"numerator":3120201383708264687310214073415780617}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-404282815222908734693079602200542008307},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-202141407611454370243150581875251594999}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-101955082703938893602827882394776127685},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-101955082703938896989698820977483369061}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3127053271597379040375263738996258077},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3127053271597374348934930749711884017}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":51059911823112569922518019649574990391},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":51059911823112568479182437929190952443}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":201646830098083700285340280188577478513},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":403293660196167398266738360645175585311}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-8312822351968606186925655516486979783},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-33251289407874429172771447351370156065}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1339403733814260680369797039854623177263},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1339403733814260685104766842259175578425}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":655885989261166395364769846306361189137},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":655885989261166386051197372928986057085}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":275230713421129324559727144631618096613},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":275230713421129320169125158027493311353}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":65289158701366302812917545348310412195},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":8161144837670787302136680341666985475}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-66112938032487717240870018133174462485},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-132225876064975441132028700246524257009}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":68051124952526309576223907179748563297},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":34025562476263152799950944759756064493}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":141422818531515769010027026108345569415},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":70711409265757882748729377457529754907}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":325387994174336747803857630333708275},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":650775988348667532210928519692326623}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-276832070522705927737594636407571946321},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-276832070522705933669037243478378421559}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2768560432871457655753358344583208729155},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1384280216435728824177089549011793635821}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-7654171687243309},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-13054645485569311}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":2571030746199935},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1412985747381603}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1011360988221987},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-6364957072020957}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3674992910087955},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-112084482184191}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1352887509919623},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-209604750799051}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3230355805485321},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-16063448761057815}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":2283352999149599},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1538785293778753}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-46289972050469},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1351491969276147}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":136539498967331},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-102707823594723}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1805814327305289},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-13675636066389}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":25509348914948031},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":11916422969296053}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1716917954523005},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-516837986395119}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":321454472765387},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-859301174411051}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1759149375347807},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":793943600201763}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-258986667584781},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1861100194185519}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":418014435031929},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1172361010988991}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":745114177561727},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2865830430167257}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1643279979814081},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1367914709487297}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":597082210119131},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-366934625624839}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":131555096227745},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-128809270220611}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1100884544823365},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-300133093853271}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1813621337053363},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1557984570576693}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":3428676985432509497625},{"denominator":340282366920938463463374607431768211456,"numerator":3118352753451757396081},{"denominator":170141183460469231731687303715884105728,"numerator":1553163377021747512753},{"denominator":340282366920938463463374607431768211456,"numerator":3533854894869519321039},{"denominator":170141183460469231731687303715884105728,"numerator":1820324766873589405801},{"denominator":340282366920938463463374607431768211456,"numerator":2359262510421420076661},{"denominator":170141183460469231731687303715884105728,"numerator":1448302337641844256447},{"denominator":42535295865117307932921825928971026432,"numerator":423358785747713578567},{"denominator":10633823966279326983230456482242756608,"numerator":73303749859908409645},{"denominator":340282366920938463463374607431768211456,"numerator":2886670233182332290473},{"denominator":340282366920938463463374607431768211456,"numerator":2303922648594549071709},{"denominator":42535295865117307932921825928971026432,"numerator":553133323941185164851},{"denominator":340282366920938463463374607431768211456,"numerator":4734967923074967196365},{"denominator":85070591730234615865843651857942052864,"numerator":1164196218627778079775},{"denominator":340282366920938463463374607431768211456,"numerator":4390601315040695277281},{"denominator":170141183460469231731687303715884105728,"numerator":2197911653713625758967},{"denominator":340282366920938463463374607431768211456,"numerator":3325142153960695020663},{"denominator":340282366920938463463374607431768211456,"numerator":3976320512062891783621},{"denominator":340282366920938463463374607431768211456,"numerator":3512567789184868187615},{"denominator":340282366920938463463374607431768211456,"numerator":2981698263188304320785},{"denominator":85070591730234615865843651857942052864,"numerator":741430150756645974825},{"denominator":85070591730234615865843651857942052864,"numerator":924896562918475774675},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":16,"numerator":171},"tube":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":33898172567188292302622929098377734809},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":66754448459505226182906840773855656791}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-424145029491004896974681770180640642117},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-851671519866415611315712305419802088519}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-237319308664139179017691001725896821447},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-474868402302863569485623729327877160445}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":6304101923692247286711782876289607263},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":24700177828683473304286168576079571395}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":234358473083275852226510100438888150411},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":116523944448011607888483248669339604697}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":199843884267335505369426912374976529403},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":49661561714736513581002278821424643193}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-25122242758301088493134538350663453293},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-202304953877405774821120203761296053215}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-200618756944790207159611298729278819929},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-51072640260761683150238722499884626241}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3130722867749103357879290502754449877},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":774951164087164821337038667856685499}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":51153967723268245139884030236993845177},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":200992304875275145544738197569471923603}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":405701895783975812030876470541248257637},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":805947556851671241568217200230445548449}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":-1038448739382246017237160431998795733},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-16639738584792611097266721760591181109}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2669071564246439043643957441278411144563},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1339963210586275182946858745564425688093}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":657562339485454199820136877840189819149},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":655676811937861633838206505734601214747}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":550895076209607355913929680941543751807},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":546759061921246923856748557191202670501}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":32720344051308189703774195503967099825},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":64027825258912364063500293454399726643}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-131808525842572164276159836285571133385},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-33879215211160406919171149378935037447}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":139217219678216117931683990593503027695},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":33927174817931764450785314400798953435}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":141446001020117808580596803558475565473},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":141399734763802767566009056443324500759}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":686893104323899260130033247624067715},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":598012981543099964225306333244889127}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-69196893802135977235508689377293828845},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-138438394954051301133773060649298032993}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1384846636723420789497507977071567752595},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2758887528748280407620484807316921828117}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":68385701756022888697361263249865324009},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":68385701756022881751067607881376715915}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-846148545726912344811197517706507623815},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-846148545726912351176206899731120143489}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-474533969674477574444999267559036991363},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-237266984837238790396430437788223254549}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":97415277171004185923122668208722838303},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":97415277171004178678897774813485161755}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":29398983031869076189327702012675287177},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":235191864254952602076525762480645034687}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":100297248893552849084567176891521888259},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":401188995574211391504892935593859705051}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-406300114304415627822010461851879005661},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-406300114304415633741991849702928635903}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-206852444833333219398016737610570269079},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-206852444833333226341265097350629110803}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3150738467724673643635740473892197027},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1575369233862334412069431120167017043}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":103572163293985744128169400004035981457},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":103572163293985741167181401945707871885}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":50148225106024419530044177721515829309},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":802371601696390707744391606091024873321}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-66441429756765606045517689796796930483},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-66441429756765615089812955311771310723}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2687413631967635064132872246608743518723},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2687413631967635073791513243718407593329}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":654393275736567680067541320829241142577},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":81799159467070958819984311330543725503}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":34607332417394592972443858492591984603},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":553717318678313478569373503095394243397}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":8302489586848930801598174997405308215},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":33209958347395720954810079311455817877}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-32315397742183495273534512090418956493},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-129261590968733987897133761303738754753}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":133300301885045518751846421821714750945},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":66650150942522755311309575131818293697}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":282781452648262685836810662715418470369},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":141390726324131339315089059457758681763}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":173823640321515285354828860210227031},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":695294561286055012283358101266588389}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-17298297460384667867707971683590962351},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-276772759366154691973122716941290309479}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2777070110564275629702925635659468324239},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2777070110564275622146914564915142799243}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-1663907406606459},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-23897912406917025}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10015328629734739},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2503452736525209}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1167056818972093},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12372951009887459}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":981891838298701},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":46724165293673}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":671101581293907},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-189842233339607}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4217615462405997},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-14048356309921029}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":8855197781896323},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1462110543269907}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-12823320737749},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-161809857066765}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":34759441449163},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-100622569168171}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1693090075376205},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-28891948013209}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":22224009842448167},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":2028622434819981}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1452284374576091},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-647254374990961}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":362517513874085},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-200592606614343}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3329692645762703},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":714997788087415}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-457451831409019},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1770211616048231}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":123229787933945},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-512465736633057}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":565390422902837},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3006446947629017}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":206089976826727},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-310984044522759}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":68998354303031},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-193027073696601}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":31956885055417},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-128481703890623}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1128618612257091},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-53607726913339}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2007799088501263},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-579599770675581}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":85070591730234615865843651857942052864,"numerator":868284551635713514613},{"denominator":170141183460469231731687303715884105728,"numerator":1591248589947627433629},{"denominator":5316911983139663491615228241121378304,"numerator":49592581266587645331},{"denominator":85070591730234615865843651857942052864,"numerator":905527626569006221927},{"denominator":170141183460469231731687303715884105728,"numerator":1859523532933281998925},{"denominator":340282366920938463463374607431768211456,"numerator":2416678753000227760479},{"denominator":340282366920938463463374607431768211456,"numerator":2959984804216090597051},{"denominator":85070591730234615865843651857942052864,"numerator":867905884760565380669},{"denominator":340282366920938463463374607431768211456,"numerator":2409748268975327014973},{"denominator":340282366920938463463374607431768211456,"numerator":2960987093729394395051},{"denominator":170141183460469231731687303715884105728,"numerator":1184069725980820694803},{"denominator":340282366920938463463374607431768211456,"numerator":4522145533218737623067},{"denominator":85070591730234615865843651857942052864,"numerator":1207329678138805546379},{"denominator":21267647932558653966460912964485513216,"numerator":297114506734063551977},{"denominator":340282366920938463463374607431768211456,"numerator":4494863460013146435519},{"denominator":170141183460469231731687303715884105728,"numerator":2251582241215509164509},{"denominator":85070591730234615865843651857942052864,"numerator":850373946964283686761},{"denominator":340282366920938463463374607431768211456,"numerator":4064612189451042729349},{"denominator":42535295865117307932921825928971026432,"numerator":450414475359932455587},{"denominator":340282366920938463463374607431768211456,"numerator":3064567850515165103721},{"denominator":340282366920938463463374607431768211456,"numerator":3044896913477157500707},{"denominator":42535295865117307932921825928971026432,"numerator":472250296046691613759},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":687},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":68548479470906522609074698037474754523},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":33764590588450155881921479275087066329}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-211431470736864887300967318282241708823},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-849055284299347400930033594533078502915}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-118607778726102036802400551968483052377},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-237382377640596017590549952443337440163}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":24816600830603870928967854926683409835},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":48578124004986552021419737870397547687}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":235358065359995795659700023745297021775},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":234061330983992509270386618070456945433}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":401485081061712276242490851831588045761},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":399152521120540724834953684437954209827}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-404022886090827880124550015287215311213},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-406622177411636425809845882221459026595}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-203540672332918079282394821755422010701},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-51808900770628789628751062474425300459}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":394332164273252589665023077025511611},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1561993077877095709557173371216193985}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":103761779182988671737086288429152383821},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":203874768284280599521458326456701119391}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":807125989682272004031144859646857608735},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":400869648391449987566653736460201958729}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-66398294778371885059737506899957171759},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-8314270741376620811051270032312072293}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2677727548285180118095400230048575672499},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2688526741718592544537338724456259237217}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":328037626934065928489967243053319595305},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":654182607798477240828288090302882431437}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":138536905216745335997207608491591819571},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":275025924864200281077426262465804205179}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":133145550800328986202995102093671388055},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":16286633655930513640817690977416986561}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-128839522480738421589296717342653825435},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-132602137574335109970110031924623555579}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":136457753372737523819389133512399531845},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":66451359347944238574987972091199367445}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":141429134824677435422043918111192427055},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":141365971893060771301874999182235478433}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":731685939258001491425039021525707377},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":641785993803185981187138219597144811}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-276725384154287156939442004837862306475},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-138421962281820676652829468452496953593}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2778191685184607651394003460036639506335},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2767490293725552092460865279777801106059}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":69122812883202013728450016768965975757},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":34561406441601003347043307447857648137}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-210903217282836607124035651646499921027},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-843612869131346434992753976889152362347}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-237126983961847441528949147274451303117},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-474253967923694889544435517598492378623}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":95739024242508706145807548382814627719},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":95739024242508698720871205549322501329}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":118090692806550651402834977830315009045},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":236181385613101295207957649237209394745}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":50367635059021252728030174143562599259},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":201470540236085008436319794661618325905}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-204136142120421432468903614815379570983},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-408272284240842870988215809925711711351}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-52453153046749710043172900406570022435},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-209812612186998847289334843982904092925}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3173951107447945670789132048966852737},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1586975553723970359869608299635033055}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":26258570864587794659204402433519507941},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":105034283458351175599760877577992725441}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":399105995937375821811269552107296324127},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":798211991874751638750958662487133182513}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-33182990370822164101713356620808876939},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-66365980741644337445288584146448764099}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2695976652161587731193731632955971426377},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-336997081520198467630596670175920436155}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":652897435938009508330438519890296097863},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":81612179492251187328041561420917387207}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":34808703929956011995771567134031328575},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":278469631439648091364612958495662491985}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":135123005316187945755708324055229831421},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":16890375664523492066292808847641316407}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-126254527117594236529242837958565145011},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-63127263558797121744363581141524361857}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":130461719887421231223445433889825982213},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":130461719887421222913637934973995061671}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":70671985145594447924316902246361757461},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":282687940582377784304653381568045593647}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":370218650045299444667870805492604131},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":740437300090592590123029625193787105}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-17292712456332735325987674209894648949},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-276683399301323771468031868484422614529}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":696374619371367344833570203029623650791},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":696374619371367342904485417349635090975}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-1425625276852393},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-5435880738963015}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":9692529381721375},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2209962351694789}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1307073412534195},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11993184532920277}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1040333355125061},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":305590511114505}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1323711993479781},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-342394459224587}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4998414561103073},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-6153240583525753}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":4309569902979015},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-684126638328543}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":7008808562347},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-153956447488045}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":70817224328137},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-197052455582709}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":788104687956581},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-91468310777743}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":9599597738190015},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":4717666232399815}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1212148847608797},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-188501931451857}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":396715103398671},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1493027649010827}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1568326618437251},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":79468547408979}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-49436498313781},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-104650326711061}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":138232185705081},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-445100394103335}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":821218900437749},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1553444736628185}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1647888698860103},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1128320356981419}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":507451538046461},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-101272094559249}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":62296932664009},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-127984869026107}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1147012999806133},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-70739118796239}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1078301458978029},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1624204838169639}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":3517173680425701118497},{"denominator":170141183460469231731687303715884105728,"numerator":1624149314462266891821},{"denominator":10633823966279326983230456482242756608,"numerator":101351977139663584161},{"denominator":340282366920938463463374607431768211456,"numerator":3712466243545291370325},{"denominator":340282366920938463463374607431768211456,"numerator":3798855320158483959487},{"denominator":21267647932558653966460912964485513216,"numerator":154737015591547999615},{"denominator":340282366920938463463374607431768211456,"numerator":3025198612324296648591},{"denominator":170141183460469231731687303715884105728,"numerator":1779160495667452462359},{"denominator":340282366920938463463374607431768211456,"numerator":2475524788381396273821},{"denominator":170141183460469231731687303715884105728,"numerator":1518527926291543285999},{"denominator":340282366920938463463374607431768211456,"numerator":2435773380501369552747},{"denominator":340282366920938463463374607431768211456,"numerator":4620928969295842088885},{"denominator":85070591730234615865843651857942052864,"numerator":1231379793210123830317},{"denominator":340282366920938463463374607431768211456,"numerator":4853051763809049698767},{"denominator":170141183460469231731687303715884105728,"numerator":2300779469559983851625},{"denominator":340282366920938463463374607431768211456,"numerator":4612682205072284136585},{"denominator":340282366920938463463374607431768211456,"numerator":3479740198108054942291},{"denominator":340282366920938463463374607431768211456,"numerator":4154902361353387539509},{"denominator":340282366920938463463374607431768211456,"numerator":3696306657438742576369},{"denominator":340282366920938463463374607431768211456,"numerator":3149606229703528533515},{"denominator":170141183460469231731687303715884105728,"numerator":1563056948158717708183},{"denominator":170141183460469231731687303715884105728,"numerator":1929083301327320039377},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":32,"numerator":345},"tube":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":17320797713559085581749212564300943715},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":68285980745110275020408802928615569859}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-210800611397396740846441382460309594569},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-846475890186615172041811496629887368019}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-474141152103844209790329539646184955355},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-474577616071214622015364357590811487909}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":97630786961172058313593494454003041295},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":47737844529746667204442617100112133467}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":118173148366454802818796892842631420225},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":117531796989812023062647990940120236159}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":50403896791681303880494355535188052371},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":200481043411592415778054139414337187555}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-406045772084865526890501287432848483537},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-51073649285045817025699128678016306153}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-206480659529665656112908759546619523985},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-52549628141585322240997134496775929843}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1589062773333570112282045673093064239},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3147695458953283112980503206458995203}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":52612697559834163210968930088416438133},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":12923558858613737295137168863621308539}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":802903194973006739382583861629384495837},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":199396815551711617590953420744273870615}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-16580402690977311312471404721817152617},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-33227371489097050313791329801637097351}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-671584785469989859882155596080324250005},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2697084042756715685571121004996738931497}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":654583026885748434894241299291304110553},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":652685515393940886627241516869697686345}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":278683038115917340299591089564543388999},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":17290996911636458698244975172311918057}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":33857852550582433552321025180888012345},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":132551880410388789331457674392850823349}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-31456980897304863898127307570881396701},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-129643109566457824819869820550320579587}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":66830152756518732275746374303997822841},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":16257533654139750819378685368026244233}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":35349718216981206788170631064073700497},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":282634814859979969619821192739901523461}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":194274760003346672677532349747264647},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":686205174760795936902605490517063305}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-276632331633982020859739349400406725421},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-138394181223753605492860434567306645829}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":348326117775367708872015306534245853091},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1388005120191100808360723510815468772897}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":69842880256844148694186038877116781111},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":69842880256844141572686670833206710231}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-841116185668861460343082939108866125347},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-841116185668861466974626171628917582621}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-473892217427256870829495442517567628009},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-473892217427256877458244916138096401911}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":47013437927377122993935837796478521349},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":94026875854754238377935555598224421723}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":29644928166586861900813736555003589725},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":237159425332694887446312289738345765483}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":202320733331312800525748808025931899169},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":101160366665656398994548097592785196717}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-51274806601844394999280835797219636975},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-410198452814755166178835220506227212715}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-212790486963229034129905378283668422845},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-53197621740807260355979422519626810387}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3196690730095789583278276754862828361},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1598345365047892248537393733210467641}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":213012215948469843958334933000905186227},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":213012215948469837728500278062911193425}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":794109383489283782485381891866513159459},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":794109383489283777471582476434025719357}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-33138261080391996377938446153218419417},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-16569130540196000549691508578524969597}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1352248826485745782396593155746228743287},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2704497652971491574840409156132672466929}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":325700126124856495684889319590800184027},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":651400252249712981460779770875456093289}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":280063097054136548988909785728386203163},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":560126194108273088556332097588141183669}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":137428060470318377156700153943154699649},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":137428060470318367707878370326793249491}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-30801514147000714377203446764477927183},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-61603028294001432314344964566065556237}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":63793859926523076532629950287867489355},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":63793859926523072285383329203873489435}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":35320562358133338458567301274344145857},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":282564498865066700085344011290788614191}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":393092280478363164946867223923128269},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":786184560956719856157976182967027755}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-276563312443320242117524506211406865327},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-276563312443320248536373826605533862457}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1396923444994920394749883565926297400883},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":698461722497460195404870448163603540413}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-4711162275237181},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-19710235981234703}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":9362620827172019},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3924255681442321}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1397768141467393},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11631120644685519}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1095142854591075},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":536554828531785}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":162933306210813},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-313126686469829}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5593237014067987},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-1352295872616921}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":8435231280014389},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-315985638135819}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":37183113002803},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-291217255862573}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":72292261937781},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-193404171659165}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":728522392809247},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-254883733668421}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":32914006949578623},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1595802573762341}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2003175043476931},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1697790604862379}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":435681156604489},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-86893102388581}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2953266666151173},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":275136638858691}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-329622509304483},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-791011235670013}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":38001895952345},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-193205470747951}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":559941914137763},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3176805110183831}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":822451053993461},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1024124271034269}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":29046982661617},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-424070111654899}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":15226652679121},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-127256734776727}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1156834481934159},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-80395780525673}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4550113190802321},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-258873711201083}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":170141183460469231731687303715884105728,"numerator":1780371092242551018339},{"denominator":170141183460469231731687303715884105728,"numerator":1657882486410885710733},{"denominator":340282366920938463463374607431768211456,"numerator":3314369620134012777887},{"denominator":340282366920938463463374607431768211456,"numerator":3804966137989071394229},{"denominator":340282366920938463463374607431768211456,"numerator":3880097993054273397991},{"denominator":340282366920938463463374607431768211456,"numerator":2536644407038364004057},{"denominator":170141183460469231731687303715884105728,"numerator":1546144392753021253993},{"denominator":340282366920938463463374607431768211456,"numerator":3647005536279794681401},{"denominator":340282366920938463463374607431768211456,"numerator":2543101575649873179175},{"denominator":340282366920938463463374607431768211456,"numerator":3114916471504737352943},{"denominator":340282366920938463463374607431768211456,"numerator":2506884048614055811909},{"denominator":340282366920938463463374607431768211456,"numerator":4721442720521007350121},{"denominator":85070591730234615865843651857942052864,"numerator":1255902453547472742659},{"denominator":170141183460469231731687303715884105728,"numerator":2477249116328188960243},{"denominator":85070591730234615865843651857942052864,"numerator":1177685777683583648389},{"denominator":21267647932558653966460912964485513216,"numerator":295275637586379475651},{"denominator":340282366920938463463374607431768211456,"numerator":3559936202663597541073},{"denominator":85070591730234615865843651857942052864,"numerator":1061811321642701122331},{"denominator":170141183460469231731687303715884105728,"numerator":1895798377520532577973},{"denominator":340282366920938463463374607431768211456,"numerator":3236867754597461509543},{"denominator":42535295865117307932921825928971026432,"numerator":401178005197741533581},{"denominator":170141183460469231731687303715884105728,"numerator":1970069938397536258365},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":693},"tube":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":35000459736285967157947492739363176191},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":69025245484383125847219017919933706089}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-840716875617618710784445773367570977069},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-843934646188427293238121555302552877995}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-236884781487416463641171113809869854667},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-237153895347895331564556275031344851803}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":95958995280069233802209752481342594823},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":11719910613057994654773464211885772417}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":118661511904846074047204268092114763983},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":236054536924591200442796439332093462659}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":202462743438614863924087622263452310357},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":50340073858950978345530842312589425581}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-204011819614349761693048938909006726617},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-102627522337533234725797848436611771249}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-6544954913465815194176123330943387265},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-106589553395916812902096247376041054763}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1600563599811301785118860941737972963},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":792732885412688989643178941950040545}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":106698705813121979532995886802475087073},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":209698695282308839214358419528431231013}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":798736398229929176508858082924496713791},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":793492334678153847645668298024479313979}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-8278869510826431384036799456844695363},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-33190491740546217965588413778264074091}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1347453726126695268552072764005500533207},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1352799725667681239000003287630840705243}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":653087449212104617817746506537944815039},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":162796829117788380736166660565120224709}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":560549377857733555692213456931368060195},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":556538138992803141288893967864762058217}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":137739180826980319719322783897265572059},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":134832319148322116176011324635001831661}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-122775102696394668508345083966823881215},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-63320564915530431465495918947927033971}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":32706517500112660188868252245677513377},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":63591284435078272717598630126446298055}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":282707968713556760060229080373336074047},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":141253843700883538215307184346734443785}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":823112545653665062499049681135721055},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":731251161694695648747916041308766049}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-276508472028143876252924180984605213167},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-138351417832505213245966361447702454871}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2794946404020526425002357541266456003201},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2784448707870463032353006572279991597805}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":17636592826300471155881345631752108811},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":70546371305201877415907202399867125159}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-838659348290754342051763728759175960451},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-52416209268172146801349009270092621431}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-473449571905218556779522663252538098777},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-473449571905218563554078922388793569087}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":92279108424467349880732929257463278235},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":92279108424467342081418142265261574231}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":238125838399404486345916849683012611549},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":59531459599851119605079053330010183723}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":406289619288621303667159790876965680243},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":6348275301384707788571718274078724581}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-412077775041993544254338610703186868125},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-412077775041993550576946112948577439083}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-215785871545988790900935699984021972179},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-6743308485812149949261858880983176847}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3218957360694312456817048495219482949},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3218957360694307231751755266069184813}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":107987550739721888044352126202614164237},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":53993775369860942424870612758088320029}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":395032293257088408618230439211830135217},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":197516146628544203018341952613628953535}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-66173336891237356538885808388163304465},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-66173336891237366186314232500831097855}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2712977774347331912473429683088102445809},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-678244443586832980680173901382480166217}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":649903498962832247588679093603797964011},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":649903498962832237472223305332371658235}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":563277058293289326307633688085449024233},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":70409632286661164582835957458762491667}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":139755218667207347970171877034752646031},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":4367350583350229321668917949829990133}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-120117567357256041446015688962019124285},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-120117567357256048730311166902458590487}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":124679536616084368302357598207187647933},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":62339768308042179809481184234409163603}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":282410521913047807756372598321291260599},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":282410521913047799977884007130256576319}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":832516496989599402399042584949784697},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":832516496989592749582405321570648085}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-276411819223979258094221349375032706159},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-276411819223979264683984838314658081909}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2802116717860224398453319393505714191013},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2802116717860224390405346070748111296125}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-233073449653245},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-2225089539510283}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":9032107783922365},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3512617851445121}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-361314872715169},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11277446160302621}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":285885121847611},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":369794093569423}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":640339159770391},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-290370099361845}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":375462014024027},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-9576681412945871}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":2072852792479457},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1148757344978573}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":1969345557403},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-546890622297483}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":18510258599669},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-47634151376085}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":334215354912429},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-331330357980821}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":27996645386288953},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-298660014514851}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":818773185144127},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1858165694950129}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":14884513796395},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2592014089716457}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1388127031203613},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":57479463108081}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-260717706349631},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-372429767787087}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":81846631728907},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-335726369612365}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":342460420182391},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1608892057194801}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":410178664366133},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-928649549912843}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":423025003374349},"lo":{"denominator":1329227995784915872903807060280344576,"numerator":-1730404113817}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":119595971881307},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-126286706145091}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":579630760865505},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-30298282035705}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1180720317339427},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-272393645041513}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":170141183460469231731687303715884105728,"numerator":1801901027146504919935},{"denominator":340282366920938463463374607431768211456,"numerator":3384903937418335307479},{"denominator":170141183460469231731687303715884105728,"numerator":1693636606737396507091},{"denominator":42535295865117307932921825928971026432,"numerator":487456934526152455067},{"denominator":170141183460469231731687303715884105728,"numerator":1981399766328638243507},{"denominator":340282366920938463463374607431768211456,"numerator":2599277118631144988377},{"denominator":340282366920938463463374607431768211456,"numerator":3161298456659765347991},{"denominator":170141183460469231731687303715884105728,"numerator":1868860641097019854541},{"denominator":340282366920938463463374607431768211456,"numerator":2612532477305237998221},{"denominator":170141183460469231731687303715884105728,"numerator":1597305033295274354455},{"denominator":21267647932558653966460912964485513216,"numerator":161345746146365628373},{"denominator":340282366920938463463374607431768211456,"numerator":4823712464200301277503},{"denominator":85070591730234615865843651857942052864,"numerator":1280907856765410877245},{"denominator":170141183460469231731687303715884105728,"numerator":2529113367963267190799},{"denominator":340282366920938463463374607431768211456,"numerator":4822472399706992146089},{"denominator":170141183460469231731687303715884105728,"numerator":2419191294103599976447},{"denominator":2658455991569831745807614120560689152,"numerator":28454265303499628493},{"denominator":340282366920938463463374607431768211456,"numerator":4341696330187080971675},{"denominator":85070591730234615865843651857942052864,"numerator":972310965647822271597},{"denominator":170141183460469231731687303715884105728,"numerator":1663204097845175277553},{"denominator":340282366920938463463374607431768211456,"numerator":3294881149689910804517},{"denominator":85070591730234615865843651857942052864,"numerator":1005996006886130431769},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":8,"numerator":87},"tube":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":35351068423580641590428997919346119487},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":69747407302364459171778745588261289753}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-838270032139944025028942302545712102825},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-420716212474926146928739967552360387719}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-118329300950071632713057368273280749681},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-473956107830253582636691076720762697327}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":23562817861193455773411559332360229023},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":92007315544578052035900622163625437711}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":119144050681737283798678846801617692841},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":118517008442415239270320288976733278533}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":101641871858024249410362359958803299139},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":404427464354906551348941606853019046285}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-102488902980587830973108958481208880427},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-412384020846389684910544356255028007073}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-26551773384626991720154041110082294437},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-54044296484786734361990705177933943357}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1611831193396294384182678122536001371},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3193693879351695133598057357790454947}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":216363247767949982598917978875600304471},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":13289992442477419407542255552461724821}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":397313251173915830542923843373467630071},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":789455313762352875081189740141737508865}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-33063305989539228249452642485076360143},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-66293178847640173943195006707763257683}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-675858400557923173664484341658529474119},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2714074109629681396010426813018490541899}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":651590304210902198471135529963377908555},"lo":{"denominator":2658455991569831745807614120560689152,"numerator":5075701442179766620762239252692388743}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":140924118160866493613103967749553544811},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":559729496493251656790100566964908266877}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":70034540773848432016311051306108904015},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":34283653420985744806837822179352539759}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-59841224558504161059867058345066956031},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-123597568529224480463018352981133385359}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":127956260458707476095115520189373578987},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":124270854402094245796559326252010831773}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":282588337026296297710034258450943332407},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":282349955414000397295075778088064932455}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":108713299404349731670111440526064273},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":388452178574022261567714894802139323}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-8636035175144106668656788540274343011},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-138293333268255059553706724164754605765}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":700801360825991980776893224017455387245},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":698201762683178885919090139674313800333}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":17808445811855973461333982750473640899},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":8904222905927985819087562135627472991}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-418121596295449729393596598849663282635},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-836243192590899465698651185589226845569}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-472926907077831259906592362798714918965},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-472926907077831266830608407162766463663}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":90496027885089684474189011037814407153},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":90496027885089676481023471463541810815}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":59770119512822592388925024309801686755},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":59770119512822590365432060457030984795}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":50985629148761278462461215470207490869},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":101971258297522555593052357533442611257}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-103477358288513959771797701110823052393},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-103477358288513961387935845016013600321}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-54699637794860172158908798686499518095},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-109399275589720348148331806523152030907}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":810187874434689872752631549362354817},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3240751497738754123263718031305070403}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":218957031466921793849534165370924179571},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":27369628933365223412146828315129030179}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":786078332935985453923800155360680323947},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":393039166467992724302108110564366848459}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-8257087439949788406150716715055165249},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-33028349759799158552368232188159790537}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2721418171068763426247222706900057928001},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2721418171068763436698475773348850414885}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":324204470795790876499435027130084160159},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":648408941591581742670281161246335458481}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":566390813246790961900164332088351865479},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":566390813246790952026554491071615705259}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":17763086471683450135121016727984776565},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":142104691773467591171699096707109401317}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-58495231111325730898361238750980202421},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-58495231111325734624795913400990888439}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":121738423174750757514099414610453892327},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":121738423174750748637472990366515322653}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":141112700507560206499711262341928963977},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":70556350253780101255201846716591304671}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":219853271435040170256044277245173225},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":439706542870076922227180934648993631}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-138114119457727225748498352118034487585},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-276228238915454458262078582519208082491}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":702577335664286818984491499674852793145},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1405154671328573633859218717419434206937}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-691383159220409},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-8006015496038217}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":8709608837516029},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1598045046655735}},{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":-11372603048815},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2734383280716587}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4738862313273955},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":915831272184617}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1256784413850541},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-273831520494701}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":6263170612578145},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-4276179746868915}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":8190126518739237},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2057169473334329}},{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":1492988782277},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-509813720198127}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":151825294479239},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-188047472243935}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":303971288927417},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-410706181651659}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":23584790051460915},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3639227056426741}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1319761928876451},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-497029314987267}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":64629316752779},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1209536849837083}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2604590151129621},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":364840009524533}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-188822939989227},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1396799800353893}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":692129289090281},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-584260009427473}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":80680142348439},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3234334350952685}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1637044491807483},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-841442994319421}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":383343351647845},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-57779580862463}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":117908478632773},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-62652789782751}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1155709180666649},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":10689929598445}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2417988151897805},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-136111119611513}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":170141183460469231731687303715884105728,"numerator":1823155546854629896217},{"denominator":340282366920938463463374607431768211456,"numerator":3455723041095484726399},{"denominator":170141183460469231731687303715884105728,"numerator":1731001640631029731667},{"denominator":340282366920938463463374607431768211456,"numerator":3996580858271615753499},{"denominator":170141183460469231731687303715884105728,"numerator":2023492581198787115649},{"denominator":340282366920938463463374607431768211456,"numerator":2663732739048891582973},{"denominator":1329227995784915872903807060280344576,"numerator":12626059235009316637},{"denominator":340282366920938463463374607431768211456,"numerator":3830513603785150730861},{"denominator":340282366920938463463374607431768211456,"numerator":2683873234146688812845},{"denominator":340282366920938463463374607431768211456,"numerator":3276178956129277288405},{"denominator":170141183460469231731687303715884105728,"numerator":1329889177553709684843},{"denominator":340282366920938463463374607431768211456,"numerator":4927763711388344716781},{"denominator":170141183460469231731687303715884105728,"numerator":2612812532585139697621},{"denominator":170141183460469231731687303715884105728,"numerator":2582146663315922814187},{"denominator":21267647932558653966460912964485513216,"numerator":308550269782496118611},{"denominator":340282366920938463463374607431768211456,"numerator":4954633880363735146723},{"denominator":85070591730234615865843651857942052864,"numerator":931608244200673215309},{"denominator":42535295865117307932921825928971026432,"numerator":554788996609778277673},{"denominator":85070591730234615865843651857942052864,"numerator":997326786529686770215},{"denominator":340282366920938463463374607431768211456,"numerator":3418284786012812253681},{"denominator":170141183460469231731687303715884105728,"numerator":1691270183315972009779},{"denominator":340282366920938463463374607431768211456,"numerator":4109761795886559675791},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":699},"tube":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":8923418008526715000682272958433514775},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":70452929887089450461512648681353319759}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-835862757365748313476967050085381471259},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-209742520153938754853857623203568367035}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-472784952819456288721933082610931883797},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-473523418470303260757650682608447451403}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":46253944097918975238417960571302614163},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":45110045241065972257903002245104491487}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":239241382435204803933949370559535643075},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":119000944531046665570511820024547136127}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":204078337183311054786248552138436808071},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":25380135545274936632731962423156158751}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-411840841800333640647251038307949602013},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-207105087108466338359063380030649503789}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-215407353601739470908957679235224323705},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-54798133261058167707184471131044388223}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":811432922249025820015637669086114061},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1607991217663720502080833321406896463}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":109674052035837175853643111320169902019},"lo":{"denominator":1329227995784915872903807060280344576,"numerator":842188763334532701947716269741393117}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":790574327057899664384230453124783009775},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":785476921620671192906534708312578871923}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-33004425662334366220671702519169944065},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-16547903266325136928383303393583176277}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2711918729876602590465510217371581262817},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2722509174583895810544704872337769837183}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":325046683619015576908799367002554113389},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":324097342243021045764201166095514427331}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":566806319452178555296378311025202184129},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":281442459082261922851694349082042994093}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":142421323221697630094120850451806144139},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":69729492413909764046662938405264857937}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-58275683436992694217509285144842765863},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-60256905927698616603782950051884646039}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":62526054747640709016944417034673202667},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":3791449396978466272455514926461940215}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":70609561369490645616827867246359636263},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":141080504914407417678961382271494478037}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":458430177746968740582001441799493381},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":102893119644472083536945112959503313}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-276165611540091222259255825031089547405},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-276439175633300158286732506701612725249}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1405693722115098680880095777579187591361},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2801086637152449615810363238902634946997}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":35952820682055834206968478179286671859},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":71905641364111661037471265814906424321}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-833868537737840941004331019981093673473},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-208467134434460237015200377472716774967}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-236162560211289573527924149253756816707},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-236162560211289577066518095780551308811}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":88677969597572211278596630656753957215},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":44338984798786101543506132535570291837}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":240023195874138191141832171377979730423},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":240023195874138182876468849262707199551}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":409427232387234561214244930904169387227},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":409427232387234555754122701564914684143}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-415692636608449910154093597099384379227},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-207846318304224958382302612620638620191}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-55457073489355661711567538365192710257},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-221828293957422654697129761450321809789}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":407759262605389190599892174043149711},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3262074100843108010435689816849620223}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":13872362130535090459091653237747494549},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":221957794088561440626131442072260957633}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":97768910153737014017556096845763868963},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":782151281229896106657052416819383986865}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-65926875609295916666119901647942717049},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-65926875609295926733366649168452669687}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2729820012392816767852737416675166757785},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1364910006196408389256002159970392954487}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":646918336200956972038339049146411496119},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":646918336200956961492827073278910743205}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":569466429281294265845126693071657793541},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":569466429281294255737530530580974107941}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":36119170811516451695998343032292382975},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":72238341623032898318797061183399777975}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-56913078875865614353752427838428738933},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-113826157751731236333232376242992132817}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":59382824984766484354099544392407252585},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":118765649969532959633897039383571590425}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":70502131196895196239257155772900461117},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":282008524787580776773333376853037170993}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":926854156056913914443797348872760027},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":463427078028453444665509146381683221}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-138005945074440582709800087365331498541},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-69002972537220293091129429557168166779}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2818426156153392897401976348883910607821},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1409213078076696444503448987345472019299}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-925532889544289},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-7172525384401963}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":4190823476807221},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2945170066916193}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":-22437817746293},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-10592468791365521}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1218194724104409},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":532363806991671}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1229812055554357},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-262755112567929}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":6380865784974185},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-3864814500184147}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":4069562796686279},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-451564864508003}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":130551279614681},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-235917434531605}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":77818595285139},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-185827176666737}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1098631136839809},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-246374446811099}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":2455212291306501},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5747592623063509}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1044246667726487},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1044945516302397}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":555502961285881},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2259792729818749}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2437545582712879},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":269086486645165}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-115637192000313},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-325839402950979}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":720500939868607},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-509802446666115}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5760048378165},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1616024426542879}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":408926260177273},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-190354930773925}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":21639242093171},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-482482625344987}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":58513678580257},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-31104182437741}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1147750897459739},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":43494816366567}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4897361346349947},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":100483831851481}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":42535295865117307932921825928971026432,"numerator":461028324784917325253},{"denominator":340282366920938463463374607431768211456,"numerator":3528229581546376447879},{"denominator":340282366920938463463374607431768211456,"numerator":3538589368302566690719},{"denominator":340282366920938463463374607431768211456,"numerator":4095790278767165469623},{"denominator":85070591730234615865843651857942052864,"numerator":1033170228693513051073},{"denominator":170141183460469231731687303715884105728,"numerator":1365027029711117340151},{"denominator":85070591730234615865843651857942052864,"numerator":826312710344605182073},{"denominator":340282366920938463463374607431768211456,"numerator":3925429201608626806489},{"denominator":21267647932558653966460912964485513216,"numerator":172323847065972760639},{"denominator":340282366920938463463374607431768211456,"numerator":3359666709175834246571},{"denominator":85070591730234615865843651857942052864,"numerator":685421371081971681165},{"denominator":170141183460469231731687303715884105728,"numerator":2516810903345702405339},{"denominator":340282366920938463463374607431768211456,"numerator":5329632043984964023279},{"denominator":340282366920938463463374607431768211456,"numerator":5272754903704202342599},{"denominator":170141183460469231731687303715884105728,"numerator":2526898743692565970499},{"denominator":340282366920938463463374607431768211456,"numerator":5073199009729491720613},{"denominator":340282366920938463463374607431768211456,"numerator":3812862138498592406431},{"denominator":10633823966279326983230456482242756608,"numerator":141785932066819986093},{"denominator":340282366920938463463374607431768211456,"numerator":4091847208764032918875},{"denominator":340282366920938463463374607431768211456,"numerator":3512556268806011241053},{"denominator":170141183460469231731687303715884105728,"numerator":1736229109810482144215},{"denominator":170141183460469231731687303715884105728,"numerator":2098768419449820980559},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":32,"numerator":351},"tube":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":36028535035143916759833661188324265177},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":17785576733443084222426045729847945927}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-833495877492648729891893844622864618179},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-418274224912019218171923222970468171837}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-472173709990139429154234948036687636211},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-118252648910782589976440253494166673777}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":90729147802539072989345048130884117667},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":5524871789252824239861542462450641755}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":240182718427875223092262616987880226003},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":59739501724584121986806105530398219729}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":409692575171703208830632862369928121301},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":407684195192133223876829048529861452603}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-413678507710550571464259014994826252617},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-415987762145603247693576907280462566615}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-109208922100209661181760741307170150529},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-222224913990632985084658601731894758719}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3267336141783047020329856679275062817},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3237797648400499356923035714972487295}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":27793970771597329604308666573442857385},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":109289919360913290896515385023542016649}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":786580613543294402485216699886903971241},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":781557807470204916871051256823690753855}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-65877937929406342658127682475216116659},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-66076561918508536487692995943000327737}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-680090997031309779647947635643596630531},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2730905817560482195146112183632077325341}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":648598404956251899402828136031698774733},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":323351885654775217681623660257708743069}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":284938944863362250024120296161893822567},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":141500840076144028339369564338704059775}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":144796108231187669117250129265253570143},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":141805645500387582511082315067424131941}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-28345818412783235182054310736918534041},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-29347815238205048660213917424199080227}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":122114867971300867959604393970032205473},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":118350420005799763504554602573272329565}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":141128542843785040114745039703028405873},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":281940238963073407928814534383091229385}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":241138511961031092124840600098179487},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":869952978839712675116028232618211013}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-34493156054692842668204608029943454273},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-276259682301889093475016551461284049587}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1409746900466764980255530413341233908145},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2809288847293104746297034835500799229655}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":72562497310717416959918996049065460013},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":36281248655358704750448246076184840389}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-415768093678318890925486540220262127029},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-831536187356637789055845040021267147753}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-117911282742560406848786676759900577333},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-117911282742560408657319566472447601081}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":86825298224695130823716586207402526319},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":21706324556173780607261594144977554583}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":120476920944019880363988012774570271511},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":240953841888039752288147243216181011009}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":205457884817597540566446540517027593385},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":102728942408798768884077760656154453759}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-417426622124328051868761145710014924367},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-417426622124328058629334394651074911671}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-112437425415670482041652153364559663945},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-224874850831340972128337813482895037805}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3282926578317514759649430670930081715},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1641463289158754547307361169795428511}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":56244289456316514496209283348595599429},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":224977157825266051094599166907004651163}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":778284020706436480855177147474851078511},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":97285502588304559400065063993858590377}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-8223015126407880896138003239236870003},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-32892060505631528725865430127456624939}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2738184481707636207565094328041008488661},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2738184481707636218436484907757029470413}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":322716714372677957665582099940219078325},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":161358357186338976140955912115092308367}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":286251444910552194272737541703450257679},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":143125722455276094549612636818211214357}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":73435693843101215561086980060882740175},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":146871387686202420733946082118568568773}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-13828260407734658452786523197635279847},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-110626083261877275425294724969681841663}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":28940626041990393468452432633186689997},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":115762504167961564597270116548630121685}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":281759279629922851605923730082318174837},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":140879639814961421606035329218463843543}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":974819414212688812797994183064739143},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":487409707106340797115929564814197925}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-137881045714150192240692827232441565837},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-275762091428300391610772031428635509671}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":706617139712681147968154204261287806517},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1413234279425362291648932441954945828939}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-500397312567269},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12797247317890479}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":4026942906492435},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2749836996418987}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-692790429968663},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-10242284962711929}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2487607811944211},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1185516996611815}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":599979246934827},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-32103267584631}},{"hi":{"denominator":1329227995784915872903807060280344576,"numerator":24932151566459},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-7078035724045419}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":2030661978349091},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-774693079730149}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":334709410775139},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-217334102305923}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":79838504450907},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-184342066496875}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":980789675435393},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-72980147441395}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":16142827129555341},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-7532278277127075}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":806773323623465},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-541535866535595}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":147896544241991},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2114280964593355}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":35559923719259},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":172200680874217}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-20643811463329},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1209925473259711}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":46283763220075},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-223399162127171}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-56636201539011},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3215159263952161}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1638242131194675},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-685372908170137}},{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":2427172366203},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-503987994402757}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":117127192626697},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-61863804902649}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":284161125631591},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":4342201182849}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1228443790092367},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":237945969061801}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":170141183460469231731687303715884105728,"numerator":1864752676861000755823},{"denominator":170141183460469231731687303715884105728,"numerator":1801215288964483372459},{"denominator":170141183460469231731687303715884105728,"numerator":1808530675536521330097},{"denominator":340282366920938463463374607431768211456,"numerator":4197333209964432515689},{"denominator":340282366920938463463374607431768211456,"numerator":4219913662774162492655},{"denominator":340282366920938463463374607431768211456,"numerator":2798284288871456156405},{"denominator":42535295865117307932921825928971026432,"numerator":422535223556686695665},{"denominator":340282366920938463463374607431768211456,"numerator":4022516151353977855541},{"denominator":340282366920938463463374607431768211456,"numerator":2832517182156131913001},{"denominator":340282366920938463463374607431768211456,"numerator":3445118200928261389999},{"denominator":170141183460469231731687303715884105728,"numerator":1413658240104643918269},{"denominator":85070591730234615865843651857942052864,"numerator":1285327982678028565501},{"denominator":340282366920938463463374607431768211456,"numerator":5435693936924439710215},{"denominator":340282366920938463463374607431768211456,"numerator":5383669223892815882411},{"denominator":170141183460469231731687303715884105728,"numerator":2586755841874051331219},{"denominator":340282366920938463463374607431768211456,"numerator":5194113345332330568017},{"denominator":340282366920938463463374607431768211456,"numerator":3901499718750869364373},{"denominator":42535295865117307932921825928971026432,"numerator":579783580648067329593},{"denominator":5316911983139663491615228241121378304,"numerator":65576970757651040711},{"denominator":664613997892457936451903530140172288,"numerator":7049380756053353429},{"denominator":2658455991569831745807614120560689152,"numerator":27849161366384643661},{"denominator":340282366920938463463374607431768211456,"numerator":4287373747626018661161},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":705},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":72711869951006305457197587474385115893},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":71816060410012256101946118719517319085}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-831170203545096978161765294490182215193},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-208542088162036458401284716850486445529}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-235742198394844666988658531513070314331},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-472418534159566911928116094975989867013}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":88915381978232409033885872591233993649},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":21635314542907607870248363861364221217}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":60277989797976932265628059393761810703},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":59975555543040947213949340357027819365}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":205587373012074754337652220924598743563},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":102308266051338779135164515877803502743}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-415467815721505820787099092143031984093},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-417716024590946714457044139507532679875}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-110722714558588345948980634221366689705},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-112637038759818120690525058212042370019}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3288477223019223359045642766046924289},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1629570210300658708072847400190334577}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":225374000020500900955602240326229568745},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":110789107825839639183650676566519819557}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":782646028931680661869893907784900117457},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":97212318989229395571930322474503964435}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-32867062918533781871514968546868722511},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-32974146125327316866146475377211805967}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-341096318054623452541869350960709552755},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-684816305998819773878195223845389130983}},{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":5055524802043424389412178180787648333},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":645218790055544823780561229395767337131}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":71613771012627988984755807472352141433},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":569083791634657627277473204870211188043}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":147193630039434572769483526233802277971},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":18021850033628102688978579100488472583}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-110179599775004410149983945286074064893},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-57115665430128219621241101074603917713}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":14893225534880047965501301336860411945},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":57672130591983116782948596896609323609}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":282044246544670768579217969413637490729},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":140843514486885466178662254196152141839}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1012766974632927474868218636360275531},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":917308287326237935382440232472237037}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-275691354838876294918175268678132983871},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-138023752591663079373722328655978719047}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2827525916034604196356678350306433311223},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2817415071722147188190255710489331535467}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":18301231869285088850757940803991268229},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":9150615934642543482687165530159420617}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-829246930360796167455115739159897605259},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-414623465180398087406518606969575263977}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-470887879138570974383384533792205489943},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-470887879138570981778292139794386332745}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":21234601892711107885367969777515611419},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":42469203785422211469473358128943570277}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":120936132312282258656702150896200721609},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":120936132312282254347990261965444324919}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":412350226045471896112481663419471040871},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":103087556511367972593883686706488730241}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-419110653740443174884011865018880775965},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-209555326870221590899419290657853728021}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-227937955635950475999780292442153239689},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-227937955635950484243429449026380779007}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1651655387360251373341242574440695541},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":825827693680124231699539997757947585}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":228014871566875928829123607575161516451},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":228014871566875921763962729440510291209}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":387238537862024528722393063392027126317},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":774477075724049051611292915325397234279}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-32814340608431095844938603513683157811},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-65628681216862202191611113675990330825}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2746512776191413632667386968662600475783},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-686628194047853410938776813965344832353}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":643955954417421685351586180697508119381},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":160988988604355418589347415360434176443}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":575499192009907058931489793173460354937},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":35968699500619190521217058155135817619}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":149288990407894041252502903287977577989},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":149288990407894030617671432076700060963}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-26847919956892418398945265488273636935},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-107391679827569681580610839066161451775}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":112730288955070759967182427341568151579},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":56365144477535375241860199666975241083}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":281477050180730855448092697091428460543},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":35184631272591355854859612648948495121}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":511644234633892821128339776490285541},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1023288469267778225202968156218969903}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-68869540410002878184183149064252469387},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-137739080820005760027669890325487708449}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2834437958575952254545211437446074982755},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2834437958575952245786526221666749174299}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-98921093696949},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-5694609433161917}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":7752722045686219},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1313372966068201}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1296611811258489},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2475339164417185}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1261955545479909},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":638276261194033}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":292309669081299},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-64255800918385}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3143827388060453},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6572116037698717}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":1015629299008767},"lo":{"denominator":2658455991569831745807614120560689152,"numerator":-10141642797745}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":206068729283949},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-799486176621753}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":163928149294901},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-183518634564105}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":865187564840369},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-678863280756285}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":13082678441463985},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-9022722098576713}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":38003923463249},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1111986643311497}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":314514823555961},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1987792857530991}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1061856363875887},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":9124673816679}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":34105014490361},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1118196949629335}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":754888294121221},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-395571463016127}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-216465683928689},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1593432636954671}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1647525043839593},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-153186266122971}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":68955581187865},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-527503480292323}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":29542494637221},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-122889939038503}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1122772190814193},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":89871367017947}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4893614239210851},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":693045354916767}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":3770761623799005389021},{"denominator":85070591730234615865843651857942052864,"numerator":919738886913909387509},{"denominator":340282366920938463463374607431768211456,"numerator":3697449500628667216275},{"denominator":340282366920938463463374607431768211456,"numerator":4301260695791257886775},{"denominator":340282366920938463463374607431768211456,"numerator":4308711175799816397321},{"denominator":340282366920938463463374607431768211456,"numerator":2868467028411351150141},{"denominator":170141183460469231731687303715884105728,"numerator":1728704323283039124645},{"denominator":21267647932558653966460912964485513216,"numerator":257613998280018510927},{"denominator":340282366920938463463374607431768211456,"numerator":2909941988855532870867},{"denominator":340282366920938463463374607431768211456,"numerator":3532579667041902814293},{"denominator":340282366920938463463374607431768211456,"numerator":2916735553029058488827},{"denominator":10633823966279326983230456482242756608,"numerator":164089548040821280941},{"denominator":340282366920938463463374607431768211456,"numerator":5543858835188137105357},{"denominator":340282366920938463463374607431768211456,"numerator":5497097234270217097633},{"denominator":85070591730234615865843651857942052864,"numerator":1324001963798665394167},{"denominator":170141183460469231731687303715884105728,"numerator":2658707580187880094919},{"denominator":170141183460469231731687303715884105728,"numerator":1996206701678369230845},{"denominator":340282366920938463463374607431768211456,"numerator":4741729883868754668967},{"denominator":340282366920938463463374607431768211456,"numerator":4304607496287017727895},{"denominator":340282366920938463463374607431768211456,"numerator":3708526735168422006895},{"denominator":340282366920938463463374607431768211456,"numerator":3659303075746570871551},{"denominator":340282366920938463463374607431768211456,"numerator":4379340507605220757185},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":16,"numerator":177},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":73352323336383469405535225519002777615},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":72474738863421180622603299311741197179}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-103610816520495684633972094828816838311},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-831830593489156934831852627086795558511}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-470717956053464365482900821045546310431},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-471748150405439108978875760005708998707}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":21766737939746927526483896653404246515},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":42325208208030958641872792375247822101}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":121014476550525177992146299020630560535},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":240834385086594129655242203546836192607}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":103150692854113317463969788256972195541},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":205364162496416526972623959501070339591}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-417207999155160889040713874877671644549},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-419394228846832517321186581002081187177}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-224489861450572291377255314853421847557},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-228339755258259018437745231411373395335}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3309156840451144327370823177088797861},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":51250189136673518435375691006591175}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":228414551986396445770321788590964446073},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":224595225140696007241741097586673201111}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":194692792664691767049158904146353240611},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":773899671135461194782050927678817378673}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-65577658686329665859561883493829729479},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-8225882658698623731357593350754528123}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1368569790223259355125323843006957979057},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2747588593057693683395114104085818008031}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":322810711810263583169422485753382083557},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":643741474868814656262037257442527318029}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":575902153007259429624134498546567079013},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":286062596955765797353353942887936568873}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":149614072761522621844970192136042063035},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":9160415306253483232600629353129308119}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-106941787224253712472181050239608690729},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-111035449488279893531196244628470331273}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":14518275453257758450270587474137487179},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":112309209045057130318615009388591778549}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":140899557332532800637210975562077134733},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":140700382156819052294719871452408289367}},{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":8292801129892288364110542879078739},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":482595310972255723984024422707701353}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-275403249733132560897981151512404566105},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-275801962727763483912193240552552642907}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":708871299812089516289505283112120143729},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":353183338739706774553064273672936288171}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":73833531396335043943773907915410821737},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":36916765698167518159189031537462535833}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-827001541734604310935297124672027818297},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-413500770867302159226168869982239384543}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-470054326602526796367532365606177980571},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-235027163301263401963554985846475815847}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":83017720389301639582902675192223631261},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":83017720389301630767647956324741359701}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":242778311193932468248344118351193848023},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":242778311193932459450138195425246134477}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":413730210769228444703551923356368226063},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":206865105384614219411123542500887746761}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-210372011446116758935206857564161464233},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-52593002861529190617971968402329360731}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-231017325132440785815936033700806155049},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-3609645705194387410355385512297291959}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":103850904950943067720692904227903349},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":415403619803771523502717792410079355}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":231070664739762097993682617602856759689},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":115535332369881045374741786757300001931}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":192682727441011265184595402759341121161},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":385365454882022527359172290110667618843}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-16365197687970128250408111192153587189},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-65460790751880523726290487268483176119}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2754806106475726121198591476989174002213},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2754806106475726132506970957738247890021}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":642487637006432016340823370059147315751},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":321243818503216002557304955154808499977}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":289227173657040965154367617106886493213},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":289227173657040959733018882690993924499}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":151729667021007803973988500340173303329},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":37932416755251948271922629570832712575}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-104124399313679805749441267886168283203},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-104124399313679813920788738075034695205}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":109670322828760125613942019255564273595},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":54835161414380057959370441878720932367}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":281161219773656077367773879782812093503},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":281161219773656068537860172338671983839}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1072240857633964242131208023523263521},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1072240857633956621428542981386480327}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-275159420557500383804663544125428388849},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-275159420557500391317365308165428219213}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1421167884576739062966131258181406205983},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2842335769153478116985235938782695455863}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":553766870921977},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-10180216021814657}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1869748436388797},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2566698623921295}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-582445552059959},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-9560117099554939}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5090085106483909},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1336297501178931}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":570346452008563},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-264252059914309}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":6113402188974079},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-3089361688012957}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":8134101773501165},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1055221582358199}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":491701524852349},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-727585967898121}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":42026264933565},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-182948048632805}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":187868441921635},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-386497097362861}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10494260818149793},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-5124467834752805}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":455442578921741},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-566079122484619}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":166421165908633},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1880907415667209}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":247556931307075},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-27520626338815}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":110463273256381},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1028329506102959}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":763622626618551},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-359636417331871}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-150097468583915},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1575026879907223}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":830530752953641},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-542005867741211}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":241602114290677},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-551133851910997}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":119445498912835},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-121930592174245}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1107176878070139},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":106842947100819}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4843642852012435},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":848233935938875}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":170141183460469231731687303715884105728,"numerator":1906346277714398253359},{"denominator":2658455991569831745807614120560689152,"numerator":29363400662500318259},{"denominator":170141183460469231731687303715884105728,"numerator":1889892302715194554025},{"denominator":170141183460469231731687303715884105728,"numerator":2203812741269969241645},{"denominator":340282366920938463463374607431768211456,"numerator":4399102258990491891055},{"denominator":340282366920938463463374607431768211456,"numerator":2940646273114513866273},{"denominator":21267647932558653966460912964485513216,"numerator":221042276336467378063},{"denominator":42535295865117307932921825928971026432,"numerator":527925463737420486241},{"denominator":340282366920938463463374607431768211456,"numerator":2989520039771451952631},{"denominator":170141183460469231731687303715884105728,"numerator":1811049379905073585891},{"denominator":1329227995784915872903807060280344576,"numerator":11757844311756917171},{"denominator":85070591730234615865843651857942052864,"numerator":1340581915342599995893},{"denominator":42535295865117307932921825928971026432,"numerator":706773558384812161629},{"denominator":170141183460469231731687303715884105728,"numerator":2806552862943363380095},{"denominator":340282366920938463463374607431768211456,"numerator":5421348165019502889043},{"denominator":340282366920938463463374607431768211456,"numerator":5443148429398899251303},{"denominator":85070591730234615865843651857942052864,"numerator":1021418077541255470673},{"denominator":340282366920938463463374607431768211456,"numerator":4847599466215374380183},{"denominator":170141183460469231731687303715884105728,"numerator":2207478228677043476997},{"denominator":42535295865117307932921825928971026432,"numerator":476293901479127856007},{"denominator":340282366920938463463374607431768211456,"numerator":3756350381853034430521},{"denominator":340282366920938463463374607431768211456,"numerator":4473511291085600441271},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":711},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":73979032795511893816408718502416538157},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":73118915775099064977618280190145983961}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-826645646347709978357605148335628415735},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-414767980958902876098487055180827784409}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-234937675924850464929582306759922000529},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-235500191085333827106875377034613476775}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":85184247347425472615618368566366641105},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":2585182799425470683567296131323373199}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":242933547118204309196713352093880973315},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":60438586086873354937863663472666174153}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":413976263847841146747485147995946859175},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":412169555178541973000873590896064343879}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-418898318642513224812547001431365967629},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-421021669621812725527195635107490795431}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-227550877177226440594945614763757605089},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-115710830882233397321646194674345347765}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1664688659647290661586789914162155615},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3300414491990043104978668653663370735}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":231473148994575072829179273488797020423},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":227630618519353793867827557635253626235}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":774956570698143014616869944586934794827},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":96270202619650430362003971094644078557}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-32704384554397390877291693333707509361},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-16413278973884090004486882008097542919}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2745472291622102445332083413191486361453},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1377938568657607159342559482851802124597}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":644142888417972612601741032078849304383},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":642273548412463340100192520464460709921}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":9044575894980564412282581027919678079},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":575126562535590484556516012981760907381}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":152057610749526247572224220583379947139},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":18622670740686306369506806916452741763}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-12958911083108475409367333194427876165},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-107805056623425445836796636367246084887}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":7069835457821280983822840996383316297},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":109246583624443138001335172135507224575}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":140760537423359470690535301465291723147},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":281080828186838082051291546738056844341}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":555334048840648192763891587553938841},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1013579621666276207389099576450951755}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-275080253060289534548134224365731058753},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-275522373704425074000584842704782929531}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2843373066068155746431078040513532774363},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1416722584427298150635232454108607539615}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":74448930204234772295964264217693721971},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":74448930204234764585345681885169762127}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-824800783266156007924466449233934839567},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-824800783266156015606811064839942685075}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-58643182025042938164038302397734024767},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-234572728100171756520255387577262215077}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":40531844079606395361314454035753095873},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":81063688159212781689660864560661297483}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":243671827341665371437627168320460876371},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":243671827341665362455391981158212556745}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":103763840184334865572918368853135800635},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":415055360737339456261928885430130883229}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-105581512126160684638064408154067663907},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-211163024252321372894263812589722925337}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-234112659068194749656405092695836428219},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-117056329534097379155511173668980513743}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3342683809275426064969697910607465653},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3342683809275419922333975332503787591}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":58536061863841606293609893766974146625},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":234144247455366417746988843030185206387}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":767045929365447362793113601173933224881},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":47940370585340459786168243427187934241}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-32640336305174416746833938629684059685},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-16320168152587211111293121864118257087}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2763065696312522263511560391616860101033},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2763065696312522275045067762850702854447}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":641030188265561575371844626838235646789},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":320515094132780781954156100664821494781}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":290683691060807650235381399131458826471},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":290683691060807644685784807735392898095}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":154193583028454805943178835012504090201},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":38548395757113698700114134599123535563}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-25206425858310391864819718917097651367},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-50412851716620787910987817356982538653}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":26645984724835180621373236243390361373},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":106583938899340712573598029682554925501}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":280811170893353945583834089642031279225},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":280811170893353936527753800937792313845}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1121656066806781415058040830600224615},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1121656066806773585414445965930452185}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-274805189342065718590775862118053143225},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-274805189342065726302570853928877639941}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2850163409151431287065771028537151347135},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2850163409151431277925838777187309970629}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":19305728606841},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-4540729561985717}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3609324459450399},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-635369516628731}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-505560939908305},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-4606271864614589}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2550724007677455},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":683681207168285}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1110996542718701},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-4321995199551}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5877253864139287},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-736013839243467}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":8147159728515069},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-51917939146037}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":286250907289567},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-653929630361597}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":21555151627619},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-183169662356529}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":162224364707645},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-866780638479305}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":2061909830774203},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2805618716589153}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":41322994850307},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-71455712681435}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":698131571007989},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-892896820363419}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1843534773735289},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-62847029986633}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":46469331553197},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-940017866191587}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":383181589397475},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-166173238010117}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-92781487738581},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3107821271800253}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":839051431863557},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-471592839078605}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":207906817285753},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-287366241962965}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":120939758940851},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-121556926600735}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1092102267904941},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":1891633368815}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2383531916893847},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":963642492687897}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":85070591730234615865843651857942052864,"numerator":963826033163346143823},{"denominator":85070591730234615865843651857942052864,"numerator":960291856934877803723},{"denominator":85070591730234615865843651857942052864,"numerator":966024519318850352431},{"denominator":340282366920938463463374607431768211456,"numerator":4516482154712621937961},{"denominator":170141183460469231731687303715884105728,"numerator":2245558449889503207415},{"denominator":340282366920938463463374607431768211456,"numerator":3014866412308917116143},{"denominator":85070591730234615865843651857942052864,"numerator":904532626839552542923},{"denominator":340282366920938463463374607431768211456,"numerator":4327308014105339829267},{"denominator":170141183460469231731687303715884105728,"numerator":1535658841741807075145},{"denominator":340282366920938463463374607431768211456,"numerator":3713724608179807035113},{"denominator":42535295865117307932921825928971026432,"numerator":388400139764046051475},{"denominator":85070591730234615865843651857942052864,"numerator":1368937749128792537575},{"denominator":340282366920938463463374607431768211456,"numerator":5766752443654315509293},{"denominator":340282366920938463463374607431768211456,"numerator":5731765228139879474335},{"denominator":85070591730234615865843651857942052864,"numerator":1387399007112117431547},{"denominator":340282366920938463463374607431768211456,"numerator":5571360598953177566381},{"denominator":170141183460469231731687303715884105728,"numerator":2090673505587563406477},{"denominator":340282366920938463463374607431768211456,"numerator":4955946382797651857135},{"denominator":21267647932558653966460912964485513216,"numerator":283002484564529304803},{"denominator":340282366920938463463374607431768211456,"numerator":3914821676183992115421},{"denominator":340282366920938463463374607431768211456,"numerator":3855897010386546097967},{"denominator":340282366920938463463374607431768211456,"numerator":4569964223964250138353},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":32,"numerator":357},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":74592622306847721179810866366603905367},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":18437296990458406722332493393989543215}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-824448316145468685180852254581355213459},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-413642616733365249963473619292358651831}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-468957569390128607438799195439920041331},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-470176188515015492425811169298735503463}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":83267687923795503879658011869608138205},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":80768012578856860912104647294786324317}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":243825586850666507483919119783787734339},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":121330973616036560389859046237202797493}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":415294863571430935162717393828308740851},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":206778180228936302947764080777245718823}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-420538062198726132118489822398395488453},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-6603088580215624838089511679666353641}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-57657048798205977595660005439366184833},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-234519494588992664715600138991855640947}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1674570694943931874315939162673148421},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3320349799379317570176171429826310667}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":117274749336385926721866880718000584747},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":115342063818047169669505665083943089643}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":771202699653804625059122586867158697947},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":766484800756208981851712830768239820469}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-65227678166645503183467066093558858039},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-4092918259389998153329429227710389991}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-86055308966513144771841332522465853363},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-172758255150092219855975687576409437377}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":642673294314231627134119603567458777741},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":320408360618117759600578635341683706699}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":290880654374212184891414216942033106957},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":578086907154710536097505468637421002279}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":9657775511987585425972877909540631729},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":18927392528031618945296376862244932497}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-25092391627434522763161150605663469077},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-3266925092455069611650148543495542817}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":27515153022293072868296692145387909761},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":26539429871262658220184819380175310027}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":281209510525769912563851194012131963777},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":280726603004631560603078053917956516589}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1160314928576773544595341735400877655},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":132806856218927675967917859436675973}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-274721686210819383240903416720663283787},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-275208057707131614436972185236960240433}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2851190936523156184254115294571351642509},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2841351861667958331733138232339619962285}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":37525882576407486150874310893881498637},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":37525882576407482252266775375641253173}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-822645404231311592142255610861246013749},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-205661351057827899999051270548629954763}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-468162271875021522856988505554198316687},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-117040567968755382689460132559240104369}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":39538395417247481576065629116715522919},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":79076790834494953896353062048459883921}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":122276328747129909920093941329685028909},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":61138164373564952667653463894566015173}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":416325340451827526464490378861067283491},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":416325340451827520282134654964704182049}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-423856077097116693297866327413195712933},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-423856077097116700701508488947365743245}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-237223640252533074788162550985466805291},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-237223640252533083655346225197578227715}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3361678406265343448337921607712956923},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3361678406265337137530286738772592687}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":237235310678679750957918158839397835915},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":59308827669669935835725218356808775573}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":190855621979531438689552123399572334985},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":763422487918125748341424651525231736473}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-8136067215861834245042529333033123735},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-65088537726894685142720942991931495543}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1385646391122018388757568300067484414303},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-346411597780504598659797790278161223883}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":639585307287336704318290827416940269711},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":319792653643668346305996860390792889467}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":584237338336522393681092939112375610225},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":584237338336522382319459518666611591651}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":78340446718604811237604420702173322973},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":78340446718604805535503854345114034813}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-48748531414112484351045887160432622003},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-97497062828224977261113509105690209217}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":103472484192624557620459631643517335617},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":12934060524078068435846921894907425961}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":280426285631241438365717560868220871973},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":280426285631241429077865254726655243631}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1171513558236776908224538863410899979},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1171513558236768864213882103088230053}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-274414791039243018626292789400700725025},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-137207395519621513271153846499563368605}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2857922300698493942470956247175362060381},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":44655035948413967705209296992989889259}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1851151951441875},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-4041360872429661}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":6960306892528337},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-39811959013189}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-104847250746397},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8858857942483803}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5082542136819953},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":171520265196925}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1078427713028999},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-146536727702431}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5604332592847913},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5666895912800585}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":4076287391837655},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-629958674272401}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":163418298521187},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-290146535245275}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":11040151407099},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-183855135608609}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":8561448802741},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-957641665160447}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":6312900845067157},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2993254662230341}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":14346146616111},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-573106841211765}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":362816794491811},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-850505633924219}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":107049272325015},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-220508243918987}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":16230789011241},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-853493602460417}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":763474392724037},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-312294471952483}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-431363012324035},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1530306021015233}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1698091435083493},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-50152625193273}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":87416466327969},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-299108864997765}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":122613108475335},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-60499117498891}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1075951323700495},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":132958373013105}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4667975776652983},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1045282372730147}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":3898602568581392094865},{"denominator":170141183460469231731687303715884105728,"numerator":1963484990765251108217},{"denominator":10633823966279326983230456482242756608,"numerator":123450687571919149815},{"denominator":340282366920938463463374607431768211456,"numerator":4627887242902477958681},{"denominator":5316911983139663491615228241121378304,"numerator":71637286371718262213},{"denominator":340282366920938463463374607431768211456,"numerator":3091172226333928726471},{"denominator":85070591730234615865843651857942052864,"numerator":925454172375089010325},{"denominator":170141183460469231731687303715884105728,"numerator":2216795610061461711781},{"denominator":340282366920938463463374607431768211456,"numerator":3155403637185691121021},{"denominator":340282366920938463463374607431768211456,"numerator":3807507889918887098875},{"denominator":21267647932558653966460912964485513216,"numerator":200523923629798862967},{"denominator":340282366920938463463374607431768211456,"numerator":5591189093180977900413},{"denominator":170141183460469231731687303715884105728,"numerator":2940810823861366032599},{"denominator":170141183460469231731687303715884105728,"numerator":2926573793334688342887},{"denominator":170141183460469231731687303715884105728,"numerator":2840408076814884344575},{"denominator":340282366920938463463374607431768211456,"numerator":5702100028472626949899},{"denominator":340282366920938463463374607431768211456,"numerator":4279509552767897629389},{"denominator":340282366920938463463374607431768211456,"numerator":5066841078585910649125},{"denominator":85070591730234615865843651857942052864,"numerator":1160981441636362872109},{"denominator":85070591730234615865843651857942052864,"numerator":1005501301643622399601},{"denominator":340282366920938463463374607431768211456,"numerator":3958006980302737662397},{"denominator":85070591730234615865843651857942052864,"numerator":1167194702116325653121},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":717},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":75193735777860513415970536456779425311},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":74366174029387459159720697799543882267}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-822295299302416445354735322196954873059},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-825079170373238190079263925377943914805}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-116991403743989299096054952834907195191},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-234638274834859885223382663466924376463}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":81317721426452330906179093303146959539},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":78777388754056929070677243185762537167}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":244704916594339674469619195612751486313},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":15222314977932735764474309817849658511}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":416558238392110514303042138383525086469},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":207444187165626891573124817428820027237}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-422126545314438076984945174457368180571},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-106030394304121173164517438461842418897}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-116860758684938129007270927459543509223},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-118816467176530587216587115243778930311}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3368452175447933738552768292287987631},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":834955164369618485688527300936850909}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":237643289523236479496091618476967778863},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":116877732501690427665210933868103390525}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":191877492678191648024639813250382943199},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":762869557239574299044102736924569549201}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-65034594828645025805601043703740879453},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-32654007293046856591451324058889592199}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2762033588493118512515453568181682691267},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2772354666687156022476521800334433533371}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":641214354611406209335726795146019577695},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":19980396598529995928028284820850110131}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":584626550842677637212303399163303180015},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":290502626131859736472410708519196195907}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":19626827340756838928644561967991481203},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":153880134617610359619489876224665146371}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-24259523000277957850422581398453171529},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-101246549147922658535340669304984593611}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":53488634665171819856931068024096184339},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":103043965020314467430170227500906392371}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":17553987764532428974305262071407513917},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":17521091927554355221148947521040877735}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":151299788746165030658791741350749079},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1111795817566490623208235947719474851}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-137163436260546462671154572012330174407},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-274858335655507148631488821940348811795}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2858940234006012467511012448333237129175},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2849188206389811145749708369037871035729}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":9455337022209458801922528024018162249},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":37821348088837831265090964492457092435}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-820536142028800405246635812418613475743},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-25641754438400012914956490791444038279}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-467105798651125608493116901327418424283},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-233552899325562808285351580200534029203}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":38528768283506635203735345184361491493},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":77057536567013260923668340719313248637}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":30677580599186690616058044370987454955},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":61355161198373378892044219096696149861}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":208769920911584729545139540200238571857},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":6524060028487022699235164952101969811}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-425333482897087095265744394371771192555},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-212666741448543551420657621267703553689}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-240349934647707351256864395694362099341},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-120174967323853680170742241676394229433}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1690108107725990278867432799604096987},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3380216215451974074036350538526479257}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":120171763207799773061835476721067238511},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":60085881603899884579166920439713683283}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":379930444656715274941883809106302673819},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":379930444656715271628252216348095081975}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-64884584486306437779386355366675262843},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-32442292243153224598390781452656401641}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1389744306637471820988748412844113808759},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2779488613274943653975235701600944455965}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":638154679886590732792926012080205760781},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":638154679886590720838272123584461711169}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":587063273968724872175423466443780564295},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":293531636984362430272636595653560521503}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":159191742382788187416947845063397621931},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":79595871191394087873057366133802621841}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-94139956171924247205327674799697548561},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-47069978085962127982898580792604945837}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":100337318955995542953225799169205880247},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":50168659477997766296256401922944314517}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":140002973070458989824357799184441595421},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":140002973070458985061672847528902479737}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":305448197328238480512585451281631691},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1221792789312945658108656293899677291}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-136993775535549991773461981774794593467},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-273987551071099991672416749411670134383}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2865613868368533500861834220369273666055},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2865613868368533491321758848716158961805}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2404223246943021},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1795070107736711}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":6706273845586299},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1291556253817389}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-20140213822369},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8500448339304247}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2517491558481573},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1346616243221499}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":260808592353197},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-313690687565483}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":332040024968019},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5493977683145543}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":4072092529804799},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-461822344040035}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":734523786016197},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-506411394534407}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":180694701960761},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-184758147633009}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":448973386022613},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-522672304706345}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2328582674756783},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-6261622655567481}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":74814930634163},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2284166382757551}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":187170159663069},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1625982179957029}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1588544137958651},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-311733765634237}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":331697100903665},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-769220909916573}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":755719764520601},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-298770634250307}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-482245049072387},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1504960443326563}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1720569628319033},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-331682248186233}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":71419354461145},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-621194243809131}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":31106424085439},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-30053164217595}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":33091506665761},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":142623763621009}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":142214979127443},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1098150420410165}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":85070591730234615865843651857942052864,"numerator":985648588837944152907},{"denominator":340282366920938463463374607431768211456,"numerator":4015981301760621264053},{"denominator":340282366920938463463374607431768211456,"numerator":4038789201556076322841},{"denominator":170141183460469231731687303715884105728,"numerator":2370949665320633998175},{"denominator":170141183460469231731687303715884105728,"numerator":2340071530414014515481},{"denominator":340282366920938463463374607431768211456,"numerator":3169608858423934220981},{"denominator":170141183460469231731687303715884105728,"numerator":1893890560539058066297},{"denominator":85070591730234615865843651857942052864,"numerator":1135577355840405726115},{"denominator":340282366920938463463374607431768211456,"numerator":3241849074803916060473},{"denominator":85070591730234615865843651857942052864,"numerator":975875222170660538573},{"denominator":340282366920938463463374607431768211456,"numerator":3313623002552877267579},{"denominator":10633823966279326983230456482242756608,"numerator":178396762089724898665},{"denominator":170141183460469231731687303715884105728,"numerator":2999434125312474557285},{"denominator":340282366920938463463374607431768211456,"numerator":5977325994108920228361},{"denominator":340282366920938463463374607431768211456,"numerator":5815074587109324350525},{"denominator":170141183460469231731687303715884105728,"numerator":2917708014576348401835},{"denominator":170141183460469231731687303715884105728,"numerator":2190116739777418690593},{"denominator":85070591730234615865843651857942052864,"numerator":1295088867883930093243},{"denominator":340282366920938463463374607431768211456,"numerator":4762684569639062749973},{"denominator":85070591730234615865843651857942052864,"numerator":1032992680109109204667},{"denominator":85070591730234615865843651857942052864,"numerator":1015686483694703908013},{"denominator":170141183460469231731687303715884105728,"numerator":2385017979731050759059},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":4,"numerator":45},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":75783035619371354098529712944692782397},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":37485256439376571719266988464950501417}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-205046835464411042948949848237588730869},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-822918522272830203129583492354874058067}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-466900515979155344801980408288685808479},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-468302466974562218086269432919993513537}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":39667412151988244188456799012771077121},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":76754489609161236129090202303454325759}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":245571379366529749962701871351146989495},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":15277466635944919144051643626614377513}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":208883041754799505647760751710481942051},"lo":{"denominator":1329227995784915872903807060280344576,"numerator":1625645538632237930349750453136742483}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-211831555529854597748373627779641049665},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-212796385716892086753968985949697489901}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-118415264315780991319635127503226490781},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-120380822420636452064096606298783981649}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1693656589982066766796499290794688401},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3358830098076581982412207400790366057}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":240754191112376124305846788759604333047},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":236844323963824589902573549257080381591}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":763878743456062907914619804449706912049},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":189829047019172844087626674533638611629}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-8103714435395301374377093147832642279},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-65117295753976048936910298548408563639}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2770264631276371834264829198344040266951},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1390273070476510633383951607027151313971}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":19992742813371352648092188129995029989},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":637943142622417480532358094929857315831}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":587447643170773213501015846605413447607},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":291940318899691700538532185436759956297}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":159528385065816644989052546579028773779},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":156364505478475496191224948680469851881}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-46839172157276355477130376142932167293},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-48960682442649836758715241165003389619}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":103868684462904845119792055093168214773},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":99906681760101970126467822795682678771}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":140241669023625399832639661772118852199},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":139956406943578593334830849491546317851}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":157612189306338143321071950203717075},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":580791003773165749753902401679406021}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-273895137764704188023119602893324100723},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-34309066286496195519443851795791201763}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":716655596042001362008522606757994370681},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2856955624757437098144428849586947598609}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":76222400521107285763185260292351691461},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":76222400521107277783782168138639600837}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-204618430691654662767855923185085051417},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-818473722766618659287952960810435540669}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-465977082647042603804251829698489536359},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-116494270661760653015681532929932826191}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":18751615351604372405704207606780083393},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":75006461406417479905654814713039045375}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":246275631119044312936814399100577590717},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":246275631119044303382371030133391341919}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":209349292023920437285330171449853909611},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":418698584047840868070206354149285770247}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-53344708494769439935638713527131763671},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-426757667958155527237258781845356732305}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-121745595737176718256090326326203093697},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-30436398934294180727402876819038490801}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3398301077958444254119498948125968707},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1699150538979218796331845186336142629}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":121734273959030125947677640714624403233},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":121734273959030121945919324988659790551}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":756361391452246913756746526447351384469},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":756361391452246906910743611978586542301}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-64668998268963604028286864195387201131},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-64668998268963615684981500305637335031}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1393827225273042485641238404054567377837},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2787654450546084983519622535010331087011}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":636739977990211408118834523075372205583},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":636739977990211395910082611922061219045}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":18432633241230227826360074621096978207},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":589844263719367278538643776200208118091}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":80863131383392188741904514935202169059},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":161726262766784365541072268638460768905}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-90755869291667160313321328915272139809},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-45377934645833584640255739214142990669}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":12147476995872568019174577185963161737},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":97179815966980533560268667119754494237}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":279549535093076250998652559361350974623},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":69887383773269060307468965572334459573}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":159059154304360957425730715257743455},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1272473234434879169827524360106208961}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-136761398862226162693171318073985365603},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-273522797724452333726705904337677416807}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":89788735566568155208754410631422701429},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":44894367783284077452070060257820903877}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":723318030875737},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-3184799964036141}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":6458930674469325},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1318148115969185}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-27228480877399},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8140221514868957}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1240462303503335},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1297400422664169}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1005400226307415},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-42285987643491}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5017107923207017},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-334641109690653}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":8109220550499675},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-10220857306839}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":203563166079593},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-6760542306677}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":23085071736859},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-185927924242335}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":353090971043789},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-567515663197547}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3254447033092777},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-6445143460606617}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":88560856187233},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2263855882688567}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":383804576563313},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1560274631109431}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":735624260178405},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-398867149766603}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":401261624954919},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-343872077460035}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":371891470783039},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-290980972738079}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-525076633764311},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2957102782828699}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":872623289709049},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-262939929551121}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":13995795367773},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-160851784974569}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":3960423505173},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-119235398875659}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1041314070022239},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":37382938531657}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4419632412559249},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":281628371080075}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":10633823966279326983230456482242756608,"numerator":124678028582525945553},{"denominator":85070591730234615865843651857942052864,"numerator":1027065021605398615913},{"denominator":340282366920938463463374607431768211456,"numerator":4129233298727710468915},{"denominator":42535295865117307932921825928971026432,"numerator":607322396954080621189},{"denominator":340282366920938463463374607431768211456,"numerator":4777221012639529396727},{"denominator":170141183460469231731687303715884105728,"numerator":1625110904346185947877},{"denominator":170141183460469231731687303715884105728,"numerator":1938035159335079576103},{"denominator":21267647932558653966460912964485513216,"numerator":290845034842891556041},{"denominator":5316911983139663491615228241121378304,"numerator":52042620609116840205},{"denominator":42535295865117307932921825928971026432,"numerator":500219696458101986655},{"denominator":170141183460469231731687303715884105728,"numerator":1711496692433702634039},{"denominator":340282366920938463463374607431768211456,"numerator":5828346141846755629049},{"denominator":340282366920938463463374607431768211456,"numerator":6118571699508706047639},{"denominator":170141183460469231731687303715884105728,"numerator":3052187510259410215781},{"denominator":340282366920938463463374607431768211456,"numerator":5952438761334557654771},{"denominator":340282366920938463463374607431768211456,"numerator":5971367863234014632527},{"denominator":340282366920938463463374607431768211456,"numerator":4483593858743432388569},{"denominator":340282366920938463463374607431768211456,"numerator":5296562971090720915219},{"denominator":340282366920938463463374607431768211456,"numerator":4884387970849255147935},{"denominator":340282366920938463463374607431768211456,"numerator":4244789037696502348741},{"denominator":170141183460469231731687303715884105728,"numerator":2085090594101847697497},{"denominator":340282366920938463463374607431768211456,"numerator":4873826995293030179325},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":723},"tube":[{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":2386287542984128666119689695478168801},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":18890715566701791888499700483189366431}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-409062589347389826256459561239612553913},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-820804026843691608919239770331321155223}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-465763320859206321444667317900002533013},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-467254962850227760473596032034411256289}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":19329875310316894487830429181482118389},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":18674963624681125628202863838224205853}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":15401551057938667176505078688777883867},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":122654535055995360047649305702687588723}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":26182382587565218764392124676915885903},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":417386699647850114142247952479509249893}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-106286782549231847975771019712294547429},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-427010657198524425529687231876084962549}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-119977448520456575084066488623223528719},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-243905273108855161055447159526574220913}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":851432069065410213701206488862409635},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3377381542028677765062075247865766497}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":121940927139019378573984609325791743253},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":29993797359416064250259827732471397073}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":760309327527252990719798153206768413745},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":377912472694514291179746402732080504117}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-64613223486881971331759026922680627763},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-8114341963558090564389675060131536953}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-347308032842847055185677061983235752315},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-174294235504028027900388736993142422059}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":638335228080442119922494451395476837737},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":318264873070964124313405030220894661865}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":295111831054781330482989504363376826325},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":293356059865426996915930716785857417881}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":162065838639912054348447953423246824665},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":79436199177109427950705520391876797589}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-90291809683133942055798061354060228217},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-23641882001003017155615932130473942891}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":100736216208979633142909425736741172567},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":48373621839569365623036581130205752463}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":140033747027870477020378433576889908863},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":69863003726877802530086045375959201111}},{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":10248373716259000583995006050381153},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1211792895272033834037244440613858863}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-273425810639761957464096665329843595597},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-17128122917161374717083825215179729193}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":179639925867421552215621487689161084239},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2864655541089621119751960520215109890519}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":38395785705609824799572228604461426709},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":9598946426402455189858861417388433237}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-816458861799821833817344693924301451869},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-204114715449955460556271120017076171489}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-58097148890386808886984723144424818409},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-58097148890386809942432876067094759819}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":9115516122383136146618914974523977075},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":2278879030595783725530249450543894309}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":30889682137396249004183699493498318591},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":123558728549584991140678346951708833777}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":209900656760201041927755460715559185815},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":419801313520402077189387010804117732253}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-214064031139564365779115439791250863135},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-107032015569782184872925371042275991051}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-123323521665284101503278622490536448365},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-123323521665284106270563725998172118821}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1707968599100665625426165516202215861},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1707968599100662203310041416099207099}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":61652502476445945051367051114982930079},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":246610009905783772000799387959600823249}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":752924209611028087345869421811408832223},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":752924209611028080272719033655142360969}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-32220975515387741408396397220307207433},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-2013810969711734209914358419188943505}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2795791567009136203737593901810187629475},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-698947891752284054054808699898161391667}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":635342859032950836693205659491101770491},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":158835714758237706056115631065137287599}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":592579399561596353865911433021598739765},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":592579399561596341679955263569394576687}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":164284575907037736503197682067227235961},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":164284575907037724283145370599173784857}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-87346294310651242432578081241714781857},"lo":{"denominator":2658455991569831745807614120560689152,"numerator":-682392924301962903218086230598472161}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":94001359843920967514593358498375200759},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":94001359843920956683514396866509956785}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":139528218064856369096951926064264585201},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":8720513629053522755490124176622715679}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1323534405152617187755574109864873747},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":330883601288152116672358403049806035}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-273019862635023652238430707005032521831},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-17063741414688978799949695330718365657}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":45012511505602130974454115413171655837},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1440400368179268186202275586159183383335}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3328359483817063},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-705720276949863}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":6221320423965571},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-85022601905755}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-97956531612073},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-7782115615526083}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2433089867249889},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":153286561223325}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":965200005590713},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-183611197145823}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2372381867912391},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2619054488416683}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":8049472575350831},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-224534289946617}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":892260897793529},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-180049732321965}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":188580116039019},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-46834802066979}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":261120392812737},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1219857935713165}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2080483858894699},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-3284937756785747}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":22310990329477},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2235854420151749}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":785110809013035},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-751848520296351}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":680700283446275},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-241512785232295}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":117097859581265},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-609556635339077}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":182155151063279},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-288387168582401}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-280759320641019},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1453501256810813}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1772887317362043},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-196264034675419}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":20685706507341},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-664789994128293}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":64544400915713},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-118142195413535}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1024557478569199},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":9691711286989}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4283014255100155},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":566796513634727}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":4040132295874057985777},{"denominator":340282366920938463463374607431768211456,"numerator":4203865422050159142177},{"denominator":170141183460469231731687303715884105728,"numerator":2110894409294701807335},{"denominator":170141183460469231731687303715884105728,"numerator":2488994924372885621383},{"denominator":340282366920938463463374607431768211456,"numerator":4876055784811084499407},{"denominator":340282366920938463463374607431768211456,"numerator":3333056963877143990613},{"denominator":170141183460469231731687303715884105728,"numerator":1983365582644934235121},{"denominator":170141183460469231731687303715884105728,"numerator":2383642238663727225863},{"denominator":340282366920938463463374607431768211456,"numerator":3422115936140440855293},{"denominator":170141183460469231731687303715884105728,"numerator":2051166833880500592791},{"denominator":340282366920938463463374607431768211456,"numerator":3536567583960690216783},{"denominator":340282366920938463463374607431768211456,"numerator":5950232197248515483295},{"denominator":340282366920938463463374607431768211456,"numerator":6240819304487304165727},{"denominator":340282366920938463463374607431768211456,"numerator":6234370645402207631477},{"denominator":340282366920938463463374607431768211456,"numerator":6092977545752065249469},{"denominator":21267647932558653966460912964485513216,"numerator":381876602951883769237},{"denominator":85070591730234615865843651857942052864,"numerator":1147416826348877164395},{"denominator":340282366920938463463374607431768211456,"numerator":5415538496240256603255},{"denominator":340282366920938463463374607431768211456,"numerator":5009109565471891055507},{"denominator":170141183460469231731687303715884105728,"numerator":2180266473316667101161},{"denominator":85070591730234615865843651857942052864,"numerator":1070095443599545418913},{"denominator":170141183460469231731687303715884105728,"numerator":2490127266175847844049},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":32,"numerator":363},"tube":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":9616116051212265627814297337777249005},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":9517987177796870177990379173404927233}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-816109534045507640519789295923146178545},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-409368205201148830686652239687790693539}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-464555099215766834761376159509112655123},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-466135080806073253985098351098580405341}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":18818071215498402934143893347937943645},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":72614050306232390598988145944460620053}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":61816267446792323776387255143980144415},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":123082846744626318817675626586609421443}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":420014101737445444509282140698689536655},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":209276207707831290899598966588619161681}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-426578001298895419061267110491698362093},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-428374667891496423299693085546232579287}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-243094273904566550826205465704298687293},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-247063449602435407685957332986350432745}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":855925423565846080701011005655362839},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3395478787257887955981428611675349519}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":30878238919159800612911158574085070913},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":121536642657073557445283179387860666009}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":756801986158276179515090480919041914159},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":376198019548991760965825469200579936407}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-64385288747844075406645129067848604479},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-32350260774544004524620548677086000077}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2786633742534894895109048143331308455029},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1398420411323397828421667394455274102963}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":318459201236621581855527582928176290561},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":158783539410731401947212185061393020321}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":296476850691839733841433431576262784147},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":589498770645554813078174544072281373007}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":164627099244496634242105300130524006709},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":40350986900648528365794927334862789633}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-43439990270343015054386940991312051443},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-22796630899332935074898358458312749057}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":12197654488364685115602944050060290393},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":11695879563443514151319275683966910777}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":69903913701067724413826180435925015791},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":278954457692324431088783100119232433313}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1363060608578021857851789028661994465},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1262407970641196648935939152597426621}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-272918223252169759564843617894532473313},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-273589972665817064189135047520140550035}},{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":22513991798809486123041132374627463601},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2872289381228243927286174846539337764977}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":38675458398679417071210004569637397073},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":19337729199339706488611582967828974093}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-814492264219753049085109198073588170525},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-101811533027469132211353943818012247425}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-231753606283059685239294082829485198011},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-463507212566119379111497270767048880411}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":70811130148476044656669938749130566549},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":70811130148476034456353485684008078825}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":123972981054633091788725858197592612103},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":247945962109266173624080815715262616819}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":420847803774408957726207676463773119737},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":420847803774408950889876861128407004895}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-429444123920027743926125566622341230805},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-107361030980006938011438870800390837123}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-249817106323725597108388196278120790165},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-31227138290465700859464442715833322789}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1716564566166682740742566216663528763},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1716564566166679224649541405805561823}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":31220941100431846218792723372042440855},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":15610470550215922583735427119458543969}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":749549519666926465104890171331850000409},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":749549519666926457796032767885680987291}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-32101800458133944457072475945887797883},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-64203600916267901063050183436992669487}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1401950623550793962239259403272234273177},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-700975311775396984302480425368340640899}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":316982482679271556051348174576609491369},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":633964965358543099367914853243890819345}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":595267791316868616337462692454238443503},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":595267791316868603863939926931476112083}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":83433395599990176168585266862728153805},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":166866791199980339834246523009600674767}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-41956364403907806874070378900310058713},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-83912728807815623145207040302766939465}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":90803346358427479460485947493242818221},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":90803346358427468385767030117908711619}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":278526034317431625522581160657640242739},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":278526034317431615248730846881603705739}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1374955869356224107538283423475325721},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1374955869356215148983491868969351869}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-272478081267548217796274772938515094397},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-272478081267548226583112612332306750077}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":180518680556639642554877156179580996287},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":361037361113279283837397990100776036385}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3682652797278357},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2489332630467975}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5960168719673643},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1396824144311345}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":36419073779281},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-7397210491492765}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2368392177979567},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1144859027818549}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":918580575215941},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-396195697553457}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4481955894345177},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5122103540555637}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":7943357036328025},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-146588616380049}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":965937166417719},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-287675401407909}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":96116721928359},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-188708427916657}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":86371445431417},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-162450448755513}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":546354222107137},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13231564481405871}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10631265005413},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2192955305231975}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":791665048450761},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1449299040765403}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":313301916808671},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-557203769119905}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":529761217122507},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-265769838288725}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":44193996838231},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-143921287316047}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-298040473700723},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2855266394177425}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":899527892321555},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-126248558852775}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":53577361321139},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-342019107337703}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":8207232884837},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-29201180266149}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":251858368040851},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":40049039790681}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1033651179516313},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1127975907925261}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":4093982507974950341733},{"denominator":170141183460469231731687303715884105728,"numerator":2151428399663375378135},{"denominator":340282366920938463463374607431768211456,"numerator":4316450835739256606171},{"denominator":340282366920938463463374607431768211456,"numerator":5100156430569897173569},{"denominator":170141183460469231731687303715884105728,"numerator":2488342396475912459497},{"denominator":340282366920938463463374607431768211456,"numerator":3418160605637965607013},{"denominator":170141183460469231731687303715884105728,"numerator":2029905456658392352403},{"denominator":340282366920938463463374607431768211456,"numerator":4883663045917988983259},{"denominator":85070591730234615865843651857942052864,"numerator":879023208584980520063},{"denominator":170141183460469231731687303715884105728,"numerator":2102643370179630479099},{"denominator":170141183460469231731687303715884105728,"numerator":1827210769793310848243},{"denominator":170141183460469231731687303715884105728,"numerator":3037225756989661709083},{"denominator":170141183460469231731687303715884105728,"numerator":3182850163491201200269},{"denominator":340282366920938463463374607431768211456,"numerator":6367389842748945904401},{"denominator":340282366920938463463374607431768211456,"numerator":6236760852110934315731},{"denominator":170141183460469231731687303715884105728,"numerator":3125730753942332897263},{"denominator":340282366920938463463374607431768211456,"numerator":4698532011658350023029},{"denominator":170141183460469231731687303715884105728,"numerator":2768679248017747652679},{"denominator":340282366920938463463374607431768211456,"numerator":5136924788080230270227},{"denominator":340282366920938463463374607431768211456,"numerator":4479277271717029375931},{"denominator":340282366920938463463374607431768211456,"numerator":4393418496078239327499},{"denominator":42535295865117307932921825928971026432,"numerator":636177973214892344345},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":729},"tube":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":9685865830901840769940651402615852575},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":76714309718331298781020411107902731423}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-814144393866557657532672588563859728099},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-408358012451758931373231789684345021501}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-463276941877868284896133278280378734751},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-464943885483675167833166312142913922925}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":73193735409821120155963863514178513407},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":35248835551130405162919214266667400445}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":248091977206888098208746809620869973759},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":247009177087201302733868903023809271803}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":210526900664098583094143964754481408103},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":419662148208424845078398019592576805641}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-213977575434126802321506705605100556907},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-13427633280531402306099627897943249463}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-30781036736281039108005610315179086799},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-250235788293447214289168504918811462215}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":215077375592260802454584812759212865},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3413125996948563469658607679868164509}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":31273247050675164163502798537002820603},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":246212680294715156299996832122329156901}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":47084808722071420217331549506354672021},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":93628705016499545270368886424754850845}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-32073033670731001812406535021456222113},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-64474826996254771505309069588508081437}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-698693585536954606309777113870246221491},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-701236647690249052555990729143497266379}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":635518952492971620196531608814917412971},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":633758017892763785163272117775784243725}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":595636872641233706544004857098397455305},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":592239680330525523361727530710725006223}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":41803068676800543589381255640067731503},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":81979638020176392692996037846246870389}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-83444354683023714155376925207993250897},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-5486240197385338902526204528868572019}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":47202563410889533001412962997862327035},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":90367457043198081120500253221253376515}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":17445450234622934444873923453651382105},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":278419527511424821877193546158515936459}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":707341614270772479024587195022616115},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":656703379054696650491397751829097423}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-17023231974680662830767761659211453621},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-273091879417260666966629674285175389193}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1444640109852095709750583994146350924875},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2879858571542352478282704859187993617933}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":38950579070854488739536722910203430159},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":19475289535427242294100921833104506883}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-812574625294688290211543093415038346737},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-812574625294688299022139667486704455153}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-462168256811322456876245929222811759011},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-231084128405661232851305891698980751469}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":34334041329882170832830839951009342871},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":68668082659764331215517294641030291283}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":62190246064547078747825599639012026317},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":124380492129094152416503240719730711703}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":105459463861613945916087060822994816573},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":421837855446455776653180289241329664693}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-430705339111197892033602947947039078673},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-430705339111197900344325129116387683035}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-253000980214103099621040954020008009561},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-253000980214103109626482648650907851989}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1724940888464507402588320393980434759},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3449881776929007579695526785376197049}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":126470351496042772728662033014507895129},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":126470351496042768417985030629438551407}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":46639841323977051986368486686510644457},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":93279682647954103028576914378872416199}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-63954091903462235533771668002418227029},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-15988522975865561983995019307601846387}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1405992393210720431477425070842932370759},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1405992393210720437970731603818675585199}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":158151980906336512213679031939882081687},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":632607923625346035847694859270537402177}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":597908567226895159403774607367240702619},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":597908567226895146636055906515317534405}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":2648015715542031165726623733368495033},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":169473005794689981815005316148489251687}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-80456674994762152672579105820527787625},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-80456674994762162293116809799948596337}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":43793590874691125938316309808724952295},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":87587181749382240552428823391179589097}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":277957716599620067006869148911764648115},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":277957716599620056471046495202698631437}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1426717269499668480933746637317530145},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":356679317374914819683902273390034927}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-271896793391791066000335678975753561505},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-135948396695895537509532226303942592999}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2895735420231164700187500376062037597527},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1447867710115582344892306685215697961453}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1968159045730247},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4345176432069657}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5654121749077955},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2840582785615583}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":132472466471155},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6972192486747535}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2284891616789597},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":530370591387055}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":215676506325373},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-26474917456725}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1056979146851115},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-623149922721015}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":7774959866671863},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-86526632361593}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":516586312932889},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-26895216166457}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":48926228235929},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-94919177364845}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":87875157286333},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-21425821854233}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":128725003946415},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13164080823998097}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-4736556420025},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2131119694290427}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":782138606764047},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-696965114316179}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":143234563822401},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-617262310340123}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":583030683099411},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-226583274434503}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":677343097222021},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-71703866048933}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-632454824120983},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2799347820846529}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":910300989226051},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-788270555189}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":1494532730907},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-700013013957411}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":133303349850539},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-115008147999945}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":988932198326133},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":165860398336739}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1985906041684323},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":558727963357263}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":4151330738496732651317},{"denominator":170141183460469231731687303715884105728,"numerator":2202647019841782853719},{"denominator":10633823966279326983230456482242756608,"numerator":137911853391214532095},{"denominator":340282366920938463463374607431768211456,"numerator":5225070438109468794687},{"denominator":10633823966279326983230456482242756608,"numerator":158723353606435657387},{"denominator":340282366920938463463374607431768211456,"numerator":3505579370467340214509},{"denominator":85070591730234615865843651857942052864,"numerator":1038839289960356196363},{"denominator":5316911983139663491615228241121378304,"numerator":78167503486691755039},{"denominator":340282366920938463463374607431768211456,"numerator":3612740364229658499531},{"denominator":340282366920938463463374607431768211456,"numerator":4310676272821191365099},{"denominator":85070591730234615865843651857942052864,"numerator":944158381302794886349},{"denominator":340282366920938463463374607431768211456,"numerator":6201103148527260274095},{"denominator":340282366920938463463374607431768211456,"numerator":6493305444941325516237},{"denominator":340282366920938463463374607431768211456,"numerator":6503509752675085002619},{"denominator":170141183460469231731687303715884105728,"numerator":3191929416163672799949},{"denominator":340282366920938463463374607431768211456,"numerator":6395748819314266506335},{"denominator":170141183460469231731687303715884105728,"numerator":2405133884271606020791},{"denominator":340282366920938463463374607431768211456,"numerator":5662100962587488165647},{"denominator":340282366920938463463374607431768211456,"numerator":5267910964891764182377},{"denominator":42535295865117307932921825928971026432,"numerator":575137368077016221247},{"denominator":340282366920938463463374607431768211456,"numerator":4509363975280165817549},{"denominator":170141183460469231731687303715884105728,"numerator":2600721037818621255125},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":16,"numerator":183},"tube":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":39017959686787185788753056572800364961},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":38637402700000771553719844631585276569}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-812233118822392628490043916713682071553},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-407371640187507663801015088384795609889}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-461929961030485236991533721756456596595},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-463682462736745394902604332012561718119}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":71084440410871525870464861618826794239},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":2135979305841147304141113597527742903}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":124452688589670307978466249667845704035},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":247839360434813457809319517290879056063}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":422037024088037441556292749974639086179},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":105178917046001446315068773864177991867}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-214639016727180066273592501942331436297},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-215469469055518123168295314531211599573}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-62354143789278389882231455303852146549},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-126710943411616967661774784821753685167}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3458342131723667114587240877859490829},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1715163843978328743244643613290471671}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":31670205686131586725625841351293135959},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":249368182505054991065851289567110965757}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":374987184065259437608024720916044147043},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":745725883494594774104456739028728612873}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-31947850579082552842153645364265368847},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-64237812000501544994021616204491023637}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1401443672302061326902493428643670595939},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2813026369578775360540306347659591481079}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":634138522409384327419425049934357700391},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":632402951900972174252138044321993779413}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":9348004781642607841937176717510676341},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":74366744543660543566047499405486869159}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":169821460562914242547949978797032444591},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":83269247302049397544139736061108391529}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-4999152152886328405133316067785824311},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-84348983736886108552215260904679940137}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":45604641728813590082989584060143892035},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":87149912465630173111046964048861381133}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":278601525734256402259979101978576028317},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":69461652891502158721499922742060357023}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1466639169702019524548004280606533181},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1364768835984459107254101356673747773}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-271785616023168384015686748958260355539},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-136277510925128548989746632031323911155}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1448354023567470224518445573001943770433},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":360920567248991698027152056386932946033}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":78443029266675428684773606306870653085},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":39221514633337710130121408405538755125}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-405353315430909329159704433153080169637},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-810706630861818667341891731258268369407}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-230380727601179025683087223387382629755},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-460761455202358060390226532692313061939}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":66495630770471430732637866702929487653},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":66495630770471420027007899188145924093}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":249562360362293138051683188687744522721},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":249562360362293127684712832558550233403}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":52846412032215147242775538234145136187},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":422771296257721170751474970510551803131}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-107977805587921241230547963000173155181},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-107977805587921243357258794979607473859}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-256198248569347375326558463202535691747},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-256198248569347385575604027404726047671}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":866550089483191128751301241404493609},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3466200357932757090717967695069760265}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":128064556536649830555335534211331558091},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":256129113073299652273542116636295358345}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":371494070179980659537447634588154329163},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":92873517544995163908539266089818205545}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-31846776739602154806716036813252957805},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-63693553479204322274010696267839853561}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1410021745700511690509222395018178627215},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-705010872850255848566475180038765975565}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":631273344215691701612243655540905280985},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":631273344215691688326625339025956855649}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":600500874521375339414299090216788395853},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":600500874521375326345613053507870775383}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":172103304278159166136476423427782873751},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":172103304278159153050550587363866259687}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-38489819454423201598226763775818014717},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-2405613715901450407698987424221944539}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":84354282038333868577484425115504864025},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":84354282038333856997791698679527872729}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":8667214757726816035404403889571133459},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":17334429515453631395540342063699291033}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1478798339846030504715747393288297633},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":739399169923010526280671534044130339}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-271275343554436702691546847192668154049},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-271275343554436711948133060487385600621}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1451555876289108382531712164463955450519},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2903111752578216754430583863848339592413}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":518128998963949},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1889825001621691}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1343468888949009},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1466363286404021}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":275308361381005},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6576796908363009}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4401410580938839},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":960091273460907}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":50366044816379},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-461217679800567}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1001614882874229},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4839473155223089}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":945975030220065},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-78874579772601}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1095722988950549},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-145797042413069}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":199073946008877},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-47761257458717}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":8629951704623},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1435184528863725}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-102896484089089},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12993439569833201}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-17464394634019},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2064290248732659}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":96575732678507},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-677929789682229}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":132544810667223},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-84607488282311}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":317808354421417},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-385467688810807}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":646720968421743},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-290154996734385}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-665188245336697},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-685797160762009}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":115284653989213},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":11467172399899}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-2010258440183},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-714414573671611}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":67611375647627},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-113072675771243}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":60611216059539},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":85248239107501}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":475673895371501},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1095445599631591}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":170141183460469231731687303715884105728,"numerator":2106130716203449546965},{"denominator":340282366920938463463374607431768211456,"numerator":4511237279174989713027},{"denominator":21267647932558653966460912964485513216,"numerator":282001404953247396169},{"denominator":340282366920938463463374607431768211456,"numerator":5352813263097738042813},{"denominator":340282366920938463463374607431768211456,"numerator":5183484544527398713343},{"denominator":340282366920938463463374607431768211456,"numerator":3595360244714961283179},{"denominator":340282366920938463463374607431768211456,"numerator":4253417840621457870795},{"denominator":42535295865117307932921825928971026432,"numerator":640565270167634937019},{"denominator":85070591730234615865843651857942052864,"numerator":928035855893946546303},{"denominator":42535295865117307932921825928971026432,"numerator":552320469248242949343},{"denominator":21267647932558653966460912964485513216,"numerator":243955267456379048035},{"denominator":42535295865117307932921825928971026432,"numerator":791286037079992154583},{"denominator":340282366920938463463374607431768211456,"numerator":6623726900826632927657},{"denominator":340282366920938463463374607431768211456,"numerator":6642808289648278414531},{"denominator":170141183460469231731687303715884105728,"numerator":3267171253906129991707},{"denominator":340282366920938463463374607431768211456,"numerator":6542962449593975728967},{"denominator":340282366920938463463374607431768211456,"numerator":4924955996011534242237},{"denominator":170141183460469231731687303715884105728,"numerator":2894922726203964490921},{"denominator":340282366920938463463374607431768211456,"numerator":5402147370526515411457},{"denominator":85070591730234615865843651857942052864,"numerator":1181519269503721621307},{"denominator":170141183460469231731687303715884105728,"numerator":2314146353502934677237},{"denominator":340282366920938463463374607431768211456,"numerator":5316418877567003984103},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":735},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":78576642088903169763542795869128845201},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":38913052184899251222249670847557120809}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-810371571358319596579453570592855657921},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-406409704532697966313441283692956230509}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-460515290379452222650843238300642480581},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-7224248746065577143012629510204853827}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":34472507159925596942559973316314067695},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":16543924429745667922634320381389223617}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":249705106403383500903683450938848560475},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":62164020449402765206288371146020622723}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":422963601020804437399414030398043902233},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":210856386302430740507354936656457193841}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-107636532940937892700007797309191420755},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-432138205238214783135748774140476383993}},{"hi":{"denominator":83076749736557242056487941267521536,"numerator":-61669609252445683458761606135344003},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-256621326658873321186621689427735513459}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3475019294145715357875453803444799457},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1723544359730242246615545102849661971}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":256552496912068103691829505460241430175},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":252539392556531918296430122769945149157}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":186663603906690763074402659456018454899},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":742484871195460847140462131624061992311}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-63634317581331688585740215412754955859},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-31994811191849488376336697727241230843}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-702743511032153035924309625847586948611},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1410540733528449668136677442073247004815}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":158194685220120044411845801546039749181},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":631070568329138889720712424136875552517}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":600859150740144280034029491826199281347},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":149395181153577977397959154753554244643}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":172454739740688876679208839795335462221},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":169141702022912326830093813276725977677}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-76507725900791153438598248378890823041},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-40447723558157248305142769545534355327}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":87995110871377443598971922971187587601},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":41957909825712763187789445816417006523}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":278038007395221366378080394520226006353},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":34654387429901046583245992579329459941}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1518908002175486709784224107761830165},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1416473854757900675285762736535145707}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-271159281725654248903569470997616582547},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-135989369566236472293726392071125474055}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2904075855073545225380240941909484427813},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2894808705248677963607321417800605727299}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":78977275257369798460726330701954751767},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":9872159407171223738374734209130706093}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-808888957670427860568778782229941502473},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-404444478835213934905140478360145894939}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-229643980395367488009699057516858357765},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-114821990197683746311366303197608574811}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":32147222435094109581340366050801690857},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":32147222435094104097869308236661988285}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":250349925907224269840015468689521100319},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":250349925907224259260534899216805508199}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":423647981007490291815764195604887073215},"lo":{"denominator":41538374868278621028243970633760768,"numerator":51714841431578403862384587831123155}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-216530658246556131111529908659967890641},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-433061316493112270931149774238762809473}},{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":-2026628741631003873611903294701478685},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-129704239464384253160299735705956832049}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1741045209943317879992924139101170665},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3482090419886628131205523143891880393}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":129666161072615378756712234348606225499},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":129666161072615374227698747748628609797}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":184950408210896500391411907531350352905},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":739801632843585993496721496964055330841}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-31711050171809837684071725159387122045},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-31711050171809844146183056652161492753}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2828078678979350203640330786417217919763},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1414039339489675108577225197770447563665}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":157490705162024051151810095541657079309},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":629962820648096191036508293751416429459}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":603043879981715364651346509408514974385},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":603043879981715351274775845708983594805}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":174757758371275665279618920430661742435},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":21844719796409456486657461792734910979}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-73483129621665442797153668217809558961},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-73483129621665452882515223556468215075}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":81106072346209043337004442087122093765},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":1267282380409516117119631788023488435}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":34588111663514106988490404599551288903},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":276704893308112844828491961453237644259}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1531178922723787945119014520819878623},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1531178922723778236532680549502817145}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-270613081546775136568438349663101262505},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-67653270386693786517250340047485178121}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1455214652606245376449751415695262317673},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":181901831575780671376910530036672274241}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2162511630344273},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-409234012187959}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":638361598690129},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3023538080168605}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":829479289462095},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1549528749652769}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1056178185760951},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":841024594050327}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":754036854008391},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-125903155279991}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3813612299201887},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4674232034537179}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":7317406006187717},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-112969587065041}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":576232951311737},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-80529892401197}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":3161127826817},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-192327239474139}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-30863237788149},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-186367939585749}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-471492245464469},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-3187819040948451}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-5068385275429},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-997396318368305}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":379678620090863},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1326935476153549}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":986675960565147},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-730830261179917}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":685607991498759},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-5068142456511}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":615974391122943},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-297354248678321}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-694888295645217},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-671946431808857}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1868043576481369},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":95118085370461}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-30374383715583},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-726684661133067}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":137028698826509},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-111197704542989}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":950366144866087},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":174153065339733}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3640403122830007},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1064238475328417}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":4276860429066775455401},{"denominator":340282366920938463463374607431768211456,"numerator":4620747022029740298883},{"denominator":170141183460469231731687303715884105728,"numerator":2306515017540607377635},{"denominator":340282366920938463463374607431768211456,"numerator":5483469365970065205833},{"denominator":170141183460469231731687303715884105728,"numerator":2644869827955810115941},{"denominator":340282366920938463463374607431768211456,"numerator":3687550582123996224193},{"denominator":85070591730234615865843651857942052864,"numerator":1088510315817904221929},{"denominator":340282366920938463463374607431768211456,"numerator":5249137308347164683873},{"denominator":170141183460469231731687303715884105728,"numerator":1907194982623722517627},{"denominator":170141183460469231731687303715884105728,"numerator":2264506385995728530427},{"denominator":85070591730234615865843651857942052864,"numerator":1008614290608709151989},{"denominator":170141183460469231731687303715884105728,"numerator":3231055177184998552059},{"denominator":340282366920938463463374607431768211456,"numerator":6757058761415480436145},{"denominator":85070591730234615865843651857942052864,"numerator":1696341296363623767839},{"denominator":170141183460469231731687303715884105728,"numerator":3344142413432605666029},{"denominator":340282366920938463463374607431768211456,"numerator":6693179156380071326669},{"denominator":340282366920938463463374607431768211456,"numerator":5042679781220613532951},{"denominator":85070591730234615865843651857942052864,"numerator":1480168279341015965377},{"denominator":85070591730234615865843651857942052864,"numerator":1384928822379111906185},{"denominator":340282366920938463463374607431768211456,"numerator":4854293042872456845989},{"denominator":85070591730234615865843651857942052864,"numerator":1187570279289219990453},{"denominator":340282366920938463463374607431768211456,"numerator":5434465887319560372949},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":32,"numerator":369},"tube":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":9888730177152908309543275342637871873},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":78368939027725659569564662574516541329}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-808560426904484600664570573757384036843},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-810945097968189119194927415669369212531}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-229517042677918178233859871935170873363},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-460953385185304916381616176139090236469}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":66776098152285321073642814142132813323},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":31985712167073208831796670974561406091}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":250491000243746409624384645734309401831},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":249459178153242763024749297516907741849}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":423833390214471169587614965999887216913},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":52831660727260285248987982457036216095}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-53969869595042508312206470217917212009},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-433281612673789050743052662117863687037}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-63948578123187958885066995520121353619},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-129916836629353616701586395550982465815}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":218204690155029734564447482796672005},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":432926785233987432696507153151772153}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":259758091512781835349815530245202968563},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":255725893246690520820622848213191928815}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":371698596030702326829563603044636492393},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":739306675046971307816807839158652975739}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-3960126824637194931404802926638403869},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-63730389510872011537514457561245258807}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1409517872911130994465263799700174485715},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2829113201609875909809699503561408545875}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":631441220361482923218566383671662343623},"lo":{"denominator":2658455991569831745807614120560689152,"numerator":4920019210184146149651086754399335725}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":603396575616025627715317345792004158909},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":300089564977651535318934065949315574409}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":87556091130650750574460983490105144505},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":171768984502254447706287100495492116923}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-73009738061847519642698523894055932151},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-77420739002957401202330828228443286209}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":42382011994022083784277150274222066261},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":80666604490941177657855548418074703105}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":277436037658615268184347242487955167747},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":69146095886260929417571016117547363179}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1571469408317398588585042616971448099},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":367125388615078109361899607357997309}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-270492059191363945741299368416095733935},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-271362375150333685971114582072975947537}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2911385062942335666351354286446100148005},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":725548123967773107720957898606618681127}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":4969040713641589085068592630083254903},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":79504651418265416670660216454275890499}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-201780568419015630184448522013229086787},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-807122273676062530205570073313329468649}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-114437237143934103843326074532211661631},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-114437237143934106201454331999997324283}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":15516305272823667492351529939213107955},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":62065221091294658735150083509384656633}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":251123514997535270824206398031370536621},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":251123514997535260028289429693369006949}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":424467791573264421939275466220376579267},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":106116947893316103593717795983041781491}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-217077596402697236009820192848246810331},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-27134699550337155058387483193518921647}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-131315611488207975533666249285756005495},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-262631222976415961820606741880784329891}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":437194726931307890699075647686290911},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1748778907725227643224994869252378951}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":131274938044352781823545438868945362227},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":32818734511088194295363904927821352485}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":736677986412649481682638865019338971591},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":92084748301581184167768916300173897493}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-31569916071199309183592640502620402643},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-31569916071199315780268533793313037923}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1418045838136223678794256762994633555869},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2836091676272447371375309401261605348521}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":628677928991443508198976888359261817603},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":314338964495721747168225583720674398461}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":605536770500970763742835160909229897721},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":75692096312621343756414089119340647111}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":88718213317499779093739039961144483495},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":2772444166171867882726904695550474317}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-69968658462276118308732154233838634305},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-34984329231138064317890938523537866229}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":19460996552835487109611066944649060795},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":77843986211341936329109113116879622217}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":34502396881756733057707353981807425359},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":138009587527026926550131000327650087969}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":791919491893068497947438948508782331},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1583838983786127024233533193578033271}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-269909362868093164515075209005143215141},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-33738670358511646783236400355094143675}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":91177796678172175951585886448136132483},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":91177796678172175604354743160792709375}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4465153723036809},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1411499613144367}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2436431616828237},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3112826209849279}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1098133293064229},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-366743293443699}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4042346263539353},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":712510544473911}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":702281587129533},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-68596043882599}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1827118873856797},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4490939996310669}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":439105621584351},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-94739407813079}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1205427073928623},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-20253089655377}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":205460605005579},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-96911290283427}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-119289360142611},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-384542549372265}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1347930701318307},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-3108145748582881}},{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":-292446319527},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1921853485769765}},{"hi":{"denominator":1329227995784915872903807060280344576,"numerator":2908084092389},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-325858346142531}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":920393152525299},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-390800327509695}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":732975737457465},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-33456590785105}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":291950963090067},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-153525298293267}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-719338950888283},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1316564994623891}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1889814807004625},"lo":{"denominator":332306998946228968225951765070086144,"numerator":160411848735}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-13686970164987},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-184160586720457}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":69403567720001},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-27389578515095}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":931090429835725},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":87939939915745}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":434521066164379},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1023000036325613}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":170141183460469231731687303715884105728,"numerator":2172607494368526715601},{"denominator":340282366920938463463374607431768211456,"numerator":4733883999785484807873},{"denominator":340282366920938463463374607431768211456,"numerator":4716253031922577243597},{"denominator":42535295865117307932921825928971026432,"numerator":702140794150734294359},{"denominator":340282366920938463463374607431768211456,"numerator":5397957858644031669673},{"denominator":340282366920938463463374607431768211456,"numerator":3782198068555232714519},{"denominator":340282366920938463463374607431768211456,"numerator":4457276065115524074957},{"denominator":170141183460469231731687303715884105728,"numerator":2688318254407277183725},{"denominator":340282366920938463463374607431768211456,"numerator":3919571108079899998475},{"denominator":170141183460469231731687303715884105728,"numerator":2321044554858620639531},{"denominator":170141183460469231731687303715884105728,"numerator":2085119112491413694607},{"denominator":340282366920938463463374607431768211456,"numerator":6596674951080514200125},{"denominator":21267647932558653966460912964485513216,"numerator":430837307105294562971},{"denominator":340282366920938463463374607431768211456,"numerator":6931262009462052737995},{"denominator":340282366920938463463374607431768211456,"numerator":6845760723663020491263},{"denominator":10633823966279326983230456482242756608,"numerator":213952426382102122563},{"denominator":170141183460469231731687303715884105728,"numerator":2581761952255549684663},{"denominator":42535295865117307932921825928971026432,"numerator":756833339319290170061},{"denominator":170141183460469231731687303715884105728,"numerator":2840349037326173251263},{"denominator":21267647932558653966460912964485513216,"numerator":311614409260562188469},{"denominator":340282366920938463463374607431768211456,"numerator":4875407619312529965011},{"denominator":170141183460469231731687303715884105728,"numerator":2777848533006624137509},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":741},"tube":[{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":2488633564681507225545326532471637117},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":78904053167098851983614253943593427127}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-806800352132119753410219758029531990191},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-809121024952462104965843312374712129349}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-228743761680484496286480925720339656951},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-459488009394042317764632253184742992677}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":16144589776312376524721685164477415129},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":15434804188659159184206664323467532013}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":251262892679065828044992283425828142133},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":250248485154797418284484078504800409367}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":424646276842091027354533038475334483419},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":211768529624045100947334021913958395479}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-432916047751569565528816031711600224543},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-434368735166996532471253885595932536377}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-259002923671240010287115735860838862805},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-131529238123262432819597296135659847999}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3507115224642663023729701136332317413},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3479309886024846476480614233729247885}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":262977972947457304359636661904934975731},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":258927249833872242243815365652068218295}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":740202776567432218350603985864620629993},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":736191339328970050501040430671451701815}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-7884866689304114199546991708376737921},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-3966264374456694231439480566494716717}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2827073765334774466231843472126797349917},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2837122901780531840316716612831979792825}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":630127556516791339731406358782489587207},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":314240098914919994244873297411450071525}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":302941884833379795869283348417870935637},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":602728336683377102334354639783896757913}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":88896922472455615450339417589804462137},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":174420415418649476447990900671128966499}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-69493982113200661211362843461699690595},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-73926368233717096401532154922445079523}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":81517446917296077890399951069368345933},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":38701850603212866178222431722964539905}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":276795008167293077365344688750889496047},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":275893859575490862791130171405120903373}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1624303197966196286636013748912333011},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1520831781030176230965643283010286987}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-67445826168092750575985124883386572473},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-135352639488632247688115172475826893917}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2918637086342343789171177558555339526241},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2909517329531395959014945249457022344085}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":80025922282861870801588888350063896623},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":80025922282861861966754205437507106971}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-805407238285433424711883387084747964129},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-402703619142716717206654808574568942185}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-228072807893057048888109480862794908691},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-57018201973264263427464237630333819899}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":59808680913070058736932700984955995861},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":59808680913070047229179248418967977877}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":62970740073578150514320069688145647045},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":251882960294312591040906127202878645171}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":212615318456120115973515469096693618421},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":425230636912240224188321682894989462565}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-435192451020755410675580413353833260247},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-217596225510377709900964927974512777271}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-265866016721857052270656773297852013453},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-132933008360928531642422113295939060657}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3512608695225394474593462401703993499},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3512608695225386419030555364597623409}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":16611331491397281646245384999172439129},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":66445325965589124206050765845829095625}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":366808611764114526727303192750417945945},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":733617223528229044833163396357283192915}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-62846833225645183526328265903133261981},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-62846833225645196994510076157217314191}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-711020955060267851185757731506506726713},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2844083820241071418808711124778019284285}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":156855056820055106768237250876154856435},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":627420227280220412911782860265549531093}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":607978753640294222100715088939358637025},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":607978753640294208087019704792318055827}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":180139354186214085749667882424977152175},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":180139354186214071743789755488666353277}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-66437738254581664972171040532976712099},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-33218869127290837773661310099746252425}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":37284732454447813902900292475301420755},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":37284732454447807710988823043734890443}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":68823279106553973982486142852575085869},"lo":{"denominator":2658455991569831745807614120560689152,"numerator":2150727472079811595934230321979007529}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":204594828283453851313546173595170583},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":51148707070863142779896005558304447}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-33645443648082415395249398264397871629},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-16822721824041208323093829420529954577}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2924893729244051080241742260733199584569},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2924893729244051068881282540342923135127}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4569665407099403},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2424337509619377}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4698969953917911},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1602312451300269}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1362988858152811},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1406361533075755}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3860689367448493},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":577066532388453}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":648941034701199},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-596539991999375}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1765479572472701},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4275988265615197}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3346938220563325},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-156075681216575}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1258140742856547},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":8341295028795}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":104267151610725},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-48878265942371}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-10570983869435},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1575984257258683}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-825840126163639},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12049979939546989}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-27291937257407},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-115443636932403}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":183311957974269},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1286452053822555}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":863320293982869},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-208835482462659}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":780105721649323},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-216125199685441}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":550802978450289},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-79758606729483}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-741534960410385},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2577642091297199}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1909387974182451},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":228041657032899}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-75191232110985},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-372095928261215}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":70246771720883},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-27133399793733}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":455424490004193},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":11051878376185}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":828111583750827},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":977582993597805}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":4417413844454820035435},{"denominator":340282366920938463463374607431768211456,"numerator":4850709163234766700895},{"denominator":340282366920938463463374607431768211456,"numerator":4821743975441045142989},{"denominator":340282366920938463463374607431768211456,"numerator":5753875084471576478971},{"denominator":340282366920938463463374607431768211456,"numerator":5508186453034338621217},{"denominator":170141183460469231731687303715884105728,"numerator":1939675362087746803419},{"denominator":340282366920938463463374607431768211456,"numerator":4563171218283694367247},{"denominator":170141183460469231731687303715884105728,"numerator":2753546557129615841623},{"denominator":340282366920938463463374607431768211456,"numerator":4027781251494869689577},{"denominator":21267647932558653966460912964485513216,"numerator":297366302804841477995},{"denominator":340282366920938463463374607431768211456,"numerator":4310716295421932739631},{"denominator":5316911983139663491615228241121378304,"numerator":105220156175373674931},{"denominator":85070591730234615865843651857942052864,"numerator":1758209772381513332225},{"denominator":170141183460469231731687303715884105728,"numerator":3540291111144211515285},{"denominator":21267647932558653966460912964485513216,"numerator":437927949622378726451},{"denominator":170141183460469231731687303715884105728,"numerator":3501469314274726357669},{"denominator":340282366920938463463374607431768211456,"numerator":5287574871779692452967},{"denominator":340282366920938463463374607431768211456,"numerator":6191910628758407955535},{"denominator":340282366920938463463374607431768211456,"numerator":5825181210598181484159},{"denominator":170141183460469231731687303715884105728,"numerator":2560387862045938251415},{"denominator":170141183460469231731687303715884105728,"numerator":2501876337648592577693},{"denominator":340282366920938463463374607431768211456,"numerator":5680228692763467521969},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":8,"numerator":93},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":80156705861401466776445707468276196191},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":19858050231145908331393234857651651479}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-805092005192422345976394605226569654287},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-807347859063133661786589570011749809751}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-227938402026702088327641342069085795651},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-457956964633773341266987844228971626175}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":31176245084468821274017947524332233357},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":3717487462031744797608634020597960833}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":252020616237941776658036550656711414725},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":125511918540967267979158763559886411067}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":425402173163456192548215195911294936183},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":424363971396576439022277404579039229767}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-108504243114212667155257118606908323643},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-435399175942288702607147584917213299915}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-262224106685649311726210038076729452533},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-66573817398328926284358660206382945387}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3522545980608192579445532604053221177},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1747390676327575571391909032331727905}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":8319114624577550748918377428711489097},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":65535752580571497768436786508553258115}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":737071220089078193987449094614615308733},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":733138883324791070939346800860875192871}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-62785112755180520133032805246250166125},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-15794811351911272096453829800528717997}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-177193089283448458558102616534510099137},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1422555952953947771759179238362096793047}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":628839327634015957752893471129457050837},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":156806335302072865553431911406631993513}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":608319942646388915297437577328077941251},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":302613764575739921400871641667786142893}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":22562471391039622767594016788445986087},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":88548027512315470155803714924761801035}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-65961970646233227778693802391286098333},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-70413845997392006508791663364277164645}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":9782101533914210299244943822577700721},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":74128551671596342838806724759391235441}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":276114313732793785242374850218850997307},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":275162926945394577435214668773958308513}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1677389322671009664276005192499558959},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":786722250843903365447740252458751011}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-67258095160530302185327906371690785693},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-270006805337645614879733378346643511865}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2925833336389618781860858988113282303399},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2916784622291719712392517646793484604561}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":80541860674987844064596988302951934855},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":10067732584373479384686966729902962251}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-803744502551728643893845473213477164261},"lo":{"denominator":2658455991569831745807614120560689152,"numerator":-6279253926185380108097035714516743339}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-454479182204853421045671074882091877643},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-454479182204853430904791813676145905829}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":28762785380666427110941867325485325825},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":7190696345166605304282614550902058867}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":63157023235257344015813752051423501329},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":63157023235257341205575993958283545129}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":425936453059142630992711421960360143419},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":425936453059142623034590156517378310531}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-218086359676338363611124546867690740309},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-218086359676338368282903973789470017615}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-8409761896485924321282454242469790907},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-269112380687549589562205953848457048295}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1763624748944027568807291741361543723},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":881812374472011714844446936197547397}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":134513058902645425557813040385479526177},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":269026117805290841362827786179718621601}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":730619343760866574410901391927505306071},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":365309671880433282749462734358376775973}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-31271586216030806885432243012176701585},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-62543172432061627519797691812104699899}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2852056457355251229420169307295440496265},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2852056457355251243771141078684394235533}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":313095627464921332911867969783759970449},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":626191254929842651356911785097908041907}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":610369058182211289226417197278417455039},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":38148066136388204680198091047838238873}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":182866572422723952561585869318010602409},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":182866572422723938236295210492201388103}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-62891882568426923561387410004947505169},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-62891882568426934391231057077123256165}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":71283956771820098377695959626343364377},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":71283956771820085712712535685939546859}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":34315765059715668344206768771500919317},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":137263060238862667403574366869720935357}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1689918104234558633895996752011140585},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":844959052117274057730665115398054089}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-33546876098021644788430608000830166525},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-67093752196043292144560822091970449347}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":183252713627707183144376479485181881801},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2932043418043314918693662614577008323819}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4642996376227989},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2069899405226635}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4538553075942825},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-411571813953251}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1613947534142471},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1351815080501079}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":919320645217273},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":217868756255873}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":593752922262283},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-646063834851525}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":215605411154363},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2019458655230047}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":6323975786265921},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-471506584635819}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":325820510775871},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":80257100323159}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":105754814840521},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-98697064924305}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-105147257644461},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-802926712090189}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1851544317680297},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-726301861654763}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-11701311404265},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1770138592886943}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":719731228568981},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1273184709414393}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":406082315273995},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-884369330931547}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":824210651278095},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-168191944211109}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":516629663595933},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-83222837684641}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-761082261752923},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1260799241214793}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":962751751218905},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":288384585643359}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-23333715933129},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-748999932446103}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":71035114422435},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-107471408399639}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":889755380872787},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":88336822541351}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1575553830059535},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":928776031974973}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":4493547270783973391111},{"denominator":85070591730234615865843651857942052864,"numerator":1242820908389634801787},{"denominator":340282366920938463463374607431768211456,"numerator":4929556858793098940699},{"denominator":340282366920938463463374607431768211456,"numerator":5893809788349342911683},{"denominator":340282366920938463463374607431768211456,"numerator":5620474896277901355495},{"denominator":85070591730234615865843651857942052864,"numerator":994764222104886612873},{"denominator":340282366920938463463374607431768211456,"numerator":4671776029180593826435},{"denominator":21267647932558653966460912964485513216,"numerator":352536443595765029967},{"denominator":170141183460469231731687303715884105728,"numerator":2069559096708543342051},{"denominator":21267647932558653966460912964485513216,"numerator":304774903094760360603},{"denominator":170141183460469231731687303715884105728,"numerator":2227991538481320739553},{"denominator":340282366920938463463374607431768211456,"numerator":6874465723675234907025},{"denominator":170141183460469231731687303715884105728,"numerator":3587742444618253938973},{"denominator":170141183460469231731687303715884105728,"numerator":3616705614483912604863},{"denominator":340282366920938463463374607431768211456,"numerator":7171623374055205071933},{"denominator":10633823966279326983230456482242756608,"numerator":223832653270387419997},{"denominator":340282366920938463463374607431768211456,"numerator":5414920943277977537165},{"denominator":340282366920938463463374607431768211456,"numerator":6332490893410743511533},{"denominator":340282366920938463463374607431768211456,"numerator":5973252380383748385117},{"denominator":85070591730234615865843651857942052864,"numerator":1314804302122447223487},{"denominator":340282366920938463463374607431768211456,"numerator":5135398855639752337551},{"denominator":340282366920938463463374607431768211456,"numerator":5808179417427136820449},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":747},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":80671910777900990671629500469773775743},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":39977072891706534944217363983681891023}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-803436035905804341163796040784545012473},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-402813130386029444609405562939214282599}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-454203149679104532892775276550058583481},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-228180722676779807850242429781981681333}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":15024802432832754775490476799741591649},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":3574620096795088465729365453617869675}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":63191000480814218364081256656057441761},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":251785066779985448550304027022837047679}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":426101018522477507300464802846423415687},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":212566963922218040810152890216913775245}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-435061327054721263364710004581873578215},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-436372566715062736473414090102447142977}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-132728699745171684398809948326751003321},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-269543571805480203527988660897978819193}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3537573732612461052711041693764317163},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1754917401091189063199694986288258965}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":269458686817948607608431883835011421057},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":66343176439044898906488854105531365233}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":91750318493757301264494882245561948777},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":730149303731764843502432335526921862513}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-62480633611248489874606540003058168671},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-7860940258961159445423530885668586511}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2843084071179877848346326499688470727049},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-178317597611988338269585672554063079345}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":627578094039184531391522984508389287727},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":156499856612385872051445794167428480853}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":610704325601655313293238427110782285313},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":607675912311254085286328735401486113045}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":183229990391278348559807001661375939885},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":179795950163429152097565616780696037481}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-15603804228067371980037076621594957331},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-66884685070394140839230877523063163859}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":37491780242007116122189727634387127475},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":70842604732828187858590754286083376105}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":137696676390401173915689784715742937593},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":137195494617468914408514795709326906819}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1730707888899868096427464679833212281},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":406579954827120488698312636105582089}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-268238656249236046711524900364474303691},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-269266315066373031664831978791037964909}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2932975219095525183843886835379803451739},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2923995785927220611663215396205600515997}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":40526623410090972471653674211894466947},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":20263311705045483948971656269751829547}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-802134709319965239061362420989960534173},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-401067354659982624626353696021082136033}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-226375445269155520370376773797588073729},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-226375445269155525410127436225758092981}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":13804165401414395617954030669953904125},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":55216661605657570397756578301212331165}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":126679371238964537502962802612561176337},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":126679371238964531768087317295492976457}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":53323150389453179404009763088492113917},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":213292601557812713534670232904677113161}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-437095654486592297642480462623837612603},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-218547827243296153604383660529910333657}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-34046227512709489703204770042229891575},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-272369820101675929180009714112582567939}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3541486940639835280791257544197259551},"lo":{"denominator":2658455991569831745807614120560689152,"numerator":27667866723748646667377655279746889}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":68070953486482455571111204440415554949},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":68070953486482453072223406042099758089}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":727684326094548247168319379070776172333},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":181921081523637059489010923006843601277}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-62228902897280838230368607704215135357},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-7778612862160106533274976092227588163}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-715002735813769504600559614381606006329},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2860010943255078033045112010412018497857}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":624992532151073778861572689945553075023},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":624992532151073764081898159531218985527}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":306353467340542797962227205534196518527},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":306353467340542790622056095841026851723}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":23202262344609205589842290531845751109},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":46404524689218407516843664819772871733}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-59332604984041394363199291399259416501},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-7416575623005175681813164683608172453}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":8498614564194724007910373205712333635},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":67988916513557779110290974509365088837}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":136858797406849554252142100087821111037},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":136858797406849548127140246960332460981}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1743297834827512726418569934842362245},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":871648917413750961962923589719315313}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-267543117025533523045993611210253536281},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-133771558512766766793428057622270618011}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2939139960722237655043603619050469531809},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2939139960722237643164260860072969909735}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4694082022640517},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1755082770068781}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4393052936715735},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1691495324271311}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":460957634238513},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5215865936567679}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3494430142567839},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":73517086815709}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":134309922830291},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-349298685408553}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":853006644554641},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3768679770878227}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2962274953862085},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-167077909748495}},{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":10477499613191},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":116934968152217}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":13405912516079},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-199542180311473}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-60302042931577},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-814223259246317}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1978097000973257},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11153330983338423}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":9021556005941},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-845856943461867}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":352417504219507},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-316020900175675}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":383502629188295},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-116114120810383}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":432604336564871},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-61898408734039}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":481681533850751},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-348610079282767}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-97209197139629},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2464531287959077}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1938474423857181},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":344160399180827}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-108740841120235},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-375849640935071}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":143781351206655},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-26624322851473}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":433844942607961},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":87619447419331}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":748069452638441},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":109705039785933}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":4573707137089994453203},{"denominator":340282366920938463463374607431768211456,"numerator":5095668597504309239767},{"denominator":170141183460469231731687303715884105728,"numerator":2519873566289966629193},{"denominator":340282366920938463463374607431768211456,"numerator":6037028172008403990165},{"denominator":42535295865117307932921825928971026432,"numerator":716859358424817141343},{"denominator":340282366920938463463374607431768211456,"numerator":4081365229096116794111},{"denominator":42535295865117307932921825928971026432,"numerator":597892516598402271035},{"denominator":340282366920938463463374607431768211456,"numerator":5777185164794880549553},{"denominator":170141183460469231731687303715884105728,"numerator":2126841625907902272255},{"denominator":85070591730234615865843651857942052864,"numerator":1249443725794364552639},{"denominator":85070591730234615865843651857942052864,"numerator":1151533313976177425257},{"denominator":340282366920938463463374607431768211456,"numerator":7017914750149081320135},{"denominator":340282366920938463463374607431768211456,"numerator":7321435791983492665413},{"denominator":42535295865117307932921825928971026432,"numerator":923729552156006826865},{"denominator":340282366920938463463374607431768211456,"numerator":7340170615190424367893},{"denominator":170141183460469231731687303715884105728,"numerator":3662840708671015347105},{"denominator":170141183460469231731687303715884105728,"numerator":2772826084802973780269},{"denominator":42535295865117307932921825928971026432,"numerator":809561901051394306493},{"denominator":170141183460469231731687303715884105728,"numerator":3062500765824134137551},{"denominator":340282366920938463463374607431768211456,"numerator":5401246236238380559535},{"denominator":42535295865117307932921825928971026432,"numerator":658803863223956082655},{"denominator":170141183460469231731687303715884105728,"numerator":2969835161085001838943},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":32,"numerator":375},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":81182670093926283692125621124791751343},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":80470659628439118564759079452046885909}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-400916542950566190387237329674878323179},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-50247305136223292761039799009935403355}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-113116951361539034702245310714525727627},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-227351334255687676124385383116798855741}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":57819261178141616870687086636721329655},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":54882357010053990382653568978237805161}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":63373219781266362915892970938614343829},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":252532005587247577395496430264206797143}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":426742779335528002703044111441212310649},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":425846861250655358626984161281505282123}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-436048736205336683153664982956152879823},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-54661070959842140479938261068676954027}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-268702324528570414944646383770447316111},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-68200721529590512077141975364320997421}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1776102587833252163193703870070573841},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":881119161200387896316401875242708129}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":68179630839310399429315012182015105595},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":268615850521740757323446423430011393119}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":730996762295449949489243165620420425027},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":45451411059351012419114089430643280689}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-62165547069363309193478234157701960047},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-62585130805694774000499854018040921611}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-356382379822205372242702002407956015127},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2861033226353725492727148897382548617951}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":19573293672255022011822345690504285291},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":624803971688980318832523839008988500729}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":613036171421851939944717889802627050065},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":305036356133347822715943148647359328559}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":92992259145687002404012699694793547395},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":45630033498218482709859075092594542519}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-29427617044183684377774091769568028657},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-63340399066211330572973598825679973321}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":17924784782945228111230334196476567509},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":8443414441521596471583445923662558625}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":274631527794208607037227273785102862415},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":273577454629376004201496039853171039177}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":892119585113433936072040271300836407},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":839718992895478515692734420352008523}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-16712594235416050641427537147480693631},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-268483175563897208391065810168683347927}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2940064134788846108021924171211672008525},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2931152227293811453212744663595487552679}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":20390216876354582460445820058972324911},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":20390216876354580131450788657654317871}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-50036155832622226415305908399588964761},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-800578493321955633092752804686813623125}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-112740501707749790728691836646111619929},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-225481003415499586609759000563912415115}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":26441374278043775694226082747488451977},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":26441374278043769510592964678558878429}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":63518684186326575339837149567682014373},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":31759342093163286207058336625483698853}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":213588438613354870561491342691532336549},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":213588438613354866375163168677037518615}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-437960941539356725930217780847659887617},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-437960941539356735724851194702352465837}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-275637825095285776477325475397568798221},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-275637825095285788311288471525517606711}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1777664004986410815873203121108100365},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":444416001246601611072900883413719633}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":137776936157811481830859977690624152137},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":275553872315622953417586964295106502293}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":724812131111664088378977294864455376723},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":724812131111664078856439543902929327221}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-30952030942602552448086170692794270157},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-61904061885205119225278221750700181707}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1433974321203581912570094395025373243743},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2867948642407163840081781095950926836395}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":311912779681250991982654330149858224021},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":623825559362501968865412537572771846329}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":307495828005585986685157649817821439847},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":307495828005585979172584590025332940101}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":188393936357260885010759682001827317617},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":188393936357260870026488202992276783499}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-3485088648097782082745352015793772891},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-55761418369564524683648100657059563001}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":64685804552768461538569771055873143045},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":32342902276384224145271145107832164847}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":272866952028218545772930822199411149871},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":272866952028218533211888292723299002715}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1796878409496484080753353733886488553},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":449219602374118246709908931440713855}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-133333628391883314222760210175462491855},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-66666814195941659815848180216120485073}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2946184751778864315252761313675708858647},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":368273093972358037887888667721089270873}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2362337848833933},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1475199524070329}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4268483821201867},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3468135086699015}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1026784751503181},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5061564854688903}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3315257277440403},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":154286019501269}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":479457162802559},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-189004561248135}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1713809798049285},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3463653483915093}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5492890517765119},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-912596259689251}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":171430419529181},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":17994083975479}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":108716603940573},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-25220104126047}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-131578839881581},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-410262089889573}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1022827810530925},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-5328660761567747}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":33712350224671},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-806217330630359}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":689231849176979},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-629296389311547}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":727803069389913},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-969808407254187}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":112930230145591},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-83157140349183}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":446185678654701},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-91471859326255}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-790437805491309},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2408064351654893}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":974559172694945},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":49356852126109}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-60752431824245},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-752599096942765}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":145839811296451},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-52852181870201}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":105699615528541},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":42903946046981}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2837214251803657},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":824882301358749}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":170141183460469231731687303715884105728,"numerator":2328993481432512572491},{"denominator":42535295865117307932921825928971026432,"numerator":652990658354655142879},{"denominator":42535295865117307932921825928971026432,"numerator":644046471213063790953},{"denominator":85070591730234615865843651857942052864,"numerator":1545907884395825150995},{"denominator":42535295865117307932921825928971026432,"numerator":731430041861965666973},{"denominator":170141183460469231731687303715884105728,"numerator":2093162364188977405551},{"denominator":85070591730234615865843651857942052864,"numerator":1224328376045989390481},{"denominator":85070591730234615865843651857942052864,"numerator":1479245221079658047359},{"denominator":340282366920938463463374607431768211456,"numerator":4371581389990432777071},{"denominator":340282366920938463463374607431768211456,"numerator":5122065806597731003425},{"denominator":42535295865117307932921825928971026432,"numerator":595158071205976498491},{"denominator":340282366920938463463374607431768211456,"numerator":7164552117109050078001},{"denominator":340282366920938463463374607431768211456,"numerator":7470795179037776274417},{"denominator":170141183460469231731687303715884105728,"numerator":3774973606278866989403},{"denominator":170141183460469231731687303715884105728,"numerator":3756286283246498871395},{"denominator":170141183460469231731687303715884105728,"numerator":3746067666734108643599},{"denominator":340282366920938463463374607431768211456,"numerator":5679860425388906516579},{"denominator":340282366920938463463374607431768211456,"numerator":6624012963288340216165},{"denominator":42535295865117307932921825928971026432,"numerator":785065118648867428305},{"denominator":340282366920938463463374607431768211456,"numerator":5546956733231974298139},{"denominator":42535295865117307932921825928971026432,"numerator":676116976658276057261},{"denominator":340282366920938463463374607431768211456,"numerator":6074824979787522123377},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":753},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":81689771538512796916648532327235887189},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":40491260925739253391234317570211891063}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-800283788704528293378677790988896901681},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-802340367166124911016488459070196563837}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-225336019972641332208544456655714685839},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-226490936968768213543636656300153096861}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":55513412490093097774159887202039094587},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":26272951822868972375361122089413784637}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":254207075522428274512237834165297608739},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":253264483250762484538834278838393184983}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":427327449066251373759399416983466892761},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":53312841417916706901861183873764612707}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-54622356630634687779068897812933363525},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-219073433730112728165921990754075348339}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-271958388924756986064751359028731165973},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-276072700693946301673619369920787576689}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":891611817098080375752116923036276545},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3538713570889549581248325429656406243}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":68997663890304998374404004677423255567},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":271871942655342014376813357863919338415}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":728053844410575743816888105141394124311},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":362179330625150388665600423317118930043}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-7729986030162223667545910131145736955},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-31136063373972818517868378251559134053}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-357376960656357768137377603914158167989},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-717242066323255219532799272811457225599}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":312571380350641293582815844256358673065},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":155910118799798626031260426260024472653}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":615314755386288202320880819627781110193},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":306208588412475978340013394166318481595}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":188763356106873451141231681643570668307},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":185268625717984761059168323216480105051}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-27641767278118502272127501520657325197},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-14945625424560473611133282606843400039}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":17101250563974890183561346500581712793},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":4015259052030117126538836539691767863}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":273828245753472689231610617598189586377},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":272721736355736881958346445571739198905}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":114872726156166828982251982252817265},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1732779414419594441726937542146441607}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-133260159517983613321523429932502680323},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-133828380623298228290306349709968347507}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2947101477577613005411721197655867275881},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2938255347738307047358987488986089840657}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":41032757642644210709399480142629931909},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":20516378821322102981457269354814915651}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-799076481220418290952975816586336304417},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-49942280076276143854075819427122074191}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-449113820927231198375415117448204558439},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-449113820927231208910400899366074619823}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":789447663454963920694515094576125907},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":50524650461117678256996039936846248899}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":31846987722014887446019324089597192995},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":254775901776119087627698108407368428469}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":106927873135002232172995387669403098411},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":106927873135002230026001389845167650599}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-219384146992377252532084084530612788611},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-219384146992377257546433657081448165491}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-17432241931411187758685241978132432143},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-278915870902579016259074726622286109769}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3568779952751010855194485265254314585},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3568779952751001869351370607541026961}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":139417878632820145383710360889699315669},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":34854469658205035033590044727655237567}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":90250337882823456434413995517259495977},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":722002703062587641632348080388416763139}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-61568670641257955156912441174278614905},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-61568670641257969785904729741251767737}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2875870927756181413915036571516017769943},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1437935463878090714581187600265207579835}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":622691816600004016124341887739918492593},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":311345908300002000348334965620457377603}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":154305629478172437881196498791532258347},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":617222517912689736146954493665951759079}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":95597036949013024320387370854125544865},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":191194073898026033316581714865984891205}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-52179834171478168886139723250803128141},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-52179834171478180521420164572370767831}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":61376086340402109844901962175270075979},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":7672010792550262036828741440477267669}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":271973610137977341890936032237682113179},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":135986805068988664505562378332689911329}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":462660151057646435000943354114127857},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":925320302115287173556346877568610093}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-265746818889942639858549346122847530743},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-66436704722485662740138939714784507089}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":92286849346243378949058522431949074047},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2953179179079788113942331772326882987231}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4735390003537295},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-306503534759919}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1041425181635655},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3540737624379423}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":278609332166353},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4944199269897095}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3141576793581705},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":22129595945723}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":420788612781123},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-814327464457859}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3480258420846627},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1562692905683619}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":157187510282821},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1188061310680559}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":696391061755883},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":81604135201075}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":27529027468859},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-204020272883947}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-274937080598689},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1644154723215147}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1031336174195387},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-1267750875703191}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":61487787854605},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1532900038792501}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":673337566221785},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-313641760824671}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":173199781660975},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1006805665157625}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":469332622799719},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-2832958527225}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":205066234519005},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-192211423354773}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-399754370160675},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2349054535437529}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1953737987550221},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":27481056927981}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-16431321328451},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-375119059096501}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":147717025217251},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-104980645790935}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":411113404708999},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":83318743223731}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2685472922379771},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":385614628117061}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":4746481960730928812121},{"denominator":340282366920938463463374607431768211456,"numerator":5356114793904632980297},{"denominator":85070591730234615865843651857942052864,"numerator":1316872326105492854183},{"denominator":340282366920938463463374607431768211456,"numerator":6333724903334414086583},{"denominator":170141183460469231731687303715884105728,"numerator":2985113812298332969127},{"denominator":340282366920938463463374607431768211456,"numerator":4293984692826354788691},{"denominator":42535295865117307932921825928971026432,"numerator":626793307940001938933},{"denominator":85070591730234615865843651857942052864,"numerator":1515013703174789260733},{"denominator":170141183460469231731687303715884105728,"numerator":2246460672601305163201},{"denominator":340282366920938463463374607431768211456,"numerator":5249349497370257057171},{"denominator":340282366920938463463374607431768211456,"numerator":4921477902207500984961},{"denominator":170141183460469231731687303715884105728,"numerator":3657247673544786626431},{"denominator":85070591730234615865843651857942052864,"numerator":1905917087638723483657},{"denominator":170141183460469231731687303715884105728,"numerator":3856917564223552983965},{"denominator":340282366920938463463374607431768211456,"numerator":7688915258753797619635},{"denominator":85070591730234615865843651857942052864,"numerator":1915524029035868806371},{"denominator":170141183460469231731687303715884105728,"numerator":2908819722943943130877},{"denominator":170141183460469231731687303715884105728,"numerator":3387567629152593808025},{"denominator":340282366920938463463374607431768211456,"numerator":6439905328392377362563},{"denominator":340282366920938463463374607431768211456,"numerator":5696445413481824141527},{"denominator":170141183460469231731687303715884105728,"numerator":2775501439286741881769},{"denominator":340282366920938463463374607431768211456,"numerator":6213769515625910618311},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":16,"numerator":189},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":82194008507025722892684361802188706153},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":81490518505239720262816353589440083681}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-798788769777254284042102423761285377953},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-800777351493589116320602847256208234317}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-448817145617365458765155799268955904405},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-451200324743625141492224912689812850383}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":53182455839476511546632104082504666337},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":25092691502793454982416360203125149033}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":254906416974635809730383906871486023347},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":253982327830936342981587002329798514371}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":106963762045654658258901654652856400045},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":427101524898275410496406305858922390729}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-109462839787568426338139951949872621609},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-219473591520551955564569768041080621345}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-137612542340628056713030579814098187449},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-139676244410776371969352157561448676287}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3580307224175754061927566399032316213},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3552552541728041647100500230560222097}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":279274545745611327252724187087100579259},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":275140464156735356324793939296104576457}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":362586878460205947081905658581072832447},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":360778749416466918157735548192133019369}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-15375919054701546155779461817225932187},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-61948549181471667514407152493013482653}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1433477687296291825069955300888006517223},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1438444026369192700071346241162162154645}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":311985843268095401383163926042845505891},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":622510414799302614756135936424968629935}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":617539375709805538998630819704624660347},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":614708576044657116050340108733667876235}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":5986452830847006414951964562846830647},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":188041430331722721665157684634738444303}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-51701629194119113096889354707472519925},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-56212506055725125971065739340238485071}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":32551304843484177180339060528212012935},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":60934558344969426139594623249938453175}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":68245729643500051691556001040091720209},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":271823253116183596833292186749832826739}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1891861873982489637369709606935661725},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":446581172805062228639629040324156581}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-16599655119170033154006154446954905307},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-266786453992327318018869859965840463729}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1477044317424341999486051214829918378125},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2945306542548884336895443442869809073115}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":82567987732608697095514622354363208227},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":20641996933152171854232677843353306437}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-398814645800860571141526778247232379071},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-99703661450215144158457202290540359683}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-447207646980751488949123400838215492945},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-447207646980751499719450339806261260759}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":6017901188570228617001102422302620715},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":48143209508561815961171497066153939469}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":255462061678434392062990114417890279315},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":255462061678434379880397904941824698973}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":428189093143788836354698828965662796631},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":107047273285947206886475752306534893415}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-27469840846411076565122468227075372269},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-219758726771288617655272434264986243291}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-282203418063149452576254712100505393277},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-141101709031574732494622598373411627775}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3581850267602620174620366806309748789},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1790925133801305469494207423966925735}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":282128917786147705946250657032052517277},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":141064458893073847593417470511265251979}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":719255971823598019082850991024940590479},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":719255971823598008909088665252024584033}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-30611367133254542266218050184150881587},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-30611367133254549734083321638843499705}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1441889590185444062441848387720448842529},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2883779180370888140444023772377299725003}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":38849547682630713411118492098921314679},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":155398190730522849703676634324583799189}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":619398839536379059848225199315603782443},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":77424854942047380513706229853071052563}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":97009242657603662171455594290887528617},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":194018485315207308671599205704510080317}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-48589361717857026953684823278038420291},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-3036835107366064929491001673009446483}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":58061231689499491877141842513164994781},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":58061231689499478017230520355102609515}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":271036993012300065523433713603195914289},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":271036993012300052316929405179042304547}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":952282694393059685411280726084653969},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1904565388786107671198548497594219819}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-264781202565899818443729133920543009167},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-132390601282949914918588671636449151625}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2960124623389768041818019617674791575331},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":370015577923721003638094056930284577109}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4741366267274557},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1014292650107587}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4089151263087085},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1805985871824891}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2367836010140143},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2434201905167991}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2975704389063423},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-100312766826363}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":363435460007043},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-873543482917023}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1784321393393329},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1379083073420315}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4541497751832529},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-743918810637743}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":351254220735295},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":175014928518827}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":55742564664953},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-51599887964779}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-275384064063781},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1638160737551721}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2033094500205131},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-9617263876232325}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":96881251151429},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1454774419217119}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":164583333419951},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-314121911617461}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":663477808593567},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1041016099833457}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":971494622244583},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-5136447681743}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":374366899615471},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-50759810587135}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-804233327052759},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2287112929579447}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":976562361003335},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":239089798883231}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-138603142264167},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-744628396037579}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":18680746696651},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-26067945528719}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":797299280406561},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":20005736831953}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2538080455595689},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":714793992198147}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":340282366920938463463374607431768211456,"numerator":4839289077661016300167},{"denominator":170141183460469231731687303715884105728,"numerator":2746149090176712845613},{"denominator":85070591730234615865843651857942052864,"numerator":1346289962841028161461},{"denominator":340282366920938463463374607431768211456,"numerator":6487417123147555568231},{"denominator":340282366920938463463374607431768211456,"numerator":6091295486248561328137},{"denominator":340282366920938463463374607431768211456,"numerator":4404394746465294797841},{"denominator":340282366920938463463374607431768211456,"numerator":5134289673780696711131},{"denominator":340282366920938463463374607431768211456,"numerator":6206494627322181719959},{"denominator":340282366920938463463374607431768211456,"numerator":4617815761294282689195},{"denominator":340282366920938463463374607431768211456,"numerator":5379707176616424262689},{"denominator":340282366920938463463374607431768211456,"numerator":5086877370801769989625},{"denominator":340282366920938463463374607431768211456,"numerator":7467864495626857433843},{"denominator":340282366920938463463374607431768211456,"numerator":7780162541057710945147},{"denominator":340282366920938463463374607431768211456,"numerator":7881593815895248705541},{"denominator":170141183460469231731687303715884105728,"numerator":3934643594680879438467},{"denominator":170141183460469231731687303715884105728,"numerator":3917827800607970166091},{"denominator":170141183460469231731687303715884105728,"numerator":2979542430152627549187},{"denominator":21267647932558653966460912964485513216,"numerator":433122182725404317033},{"denominator":85070591730234615865843651857942052864,"numerator":1650812962799862479541},{"denominator":340282366920938463463374607431768211456,"numerator":5849811879618409700017},{"denominator":85070591730234615865843651857942052864,"numerator":1424180946512371192893},{"denominator":340282366920938463463374607431768211456,"numerator":6356632669473025780457},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":759},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":82696179317245379150371377874348076643},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":81995441503959860011991043791025032649}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-398674323251083063567813572956514918505},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-799268462855779654390722662736169476567}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-111726109817270078573700777376382330175},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-112339826944534215966922385732062225919}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":50827207187775039581970005738789930185},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":47801639921201553006759611078634464371}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":127795363701164986022246206762294788971},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":127342682797714494679582703797226191733}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":428325624092318442271043877567360220353},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":26727703481303963602562581347502239917}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-438665964467279262257692287376889092121},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-439689259642031690322451102021230687577}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-278501888878382922168847941530406578167},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-282641709120343741870007240528506683821}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":224612031414529522727326616742482991},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1783000390270974796104248778250404789}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":282569640904214368448548589051811454721},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":278420881305798714915406109662398255009}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":722356445873148171152956506051273089635},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":718819017767542974376511089118325126999}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-30578456974665849987237280389550820253},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-61614421384805333098285859870271032491}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1437439739259348332315080377065453708723},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2884793970893544157478918925782987686861}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":622833657637779628199406650093881587319},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":621415247260023507448759028753273895613}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":309854677043406620549536374621376793507},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":616946202782231568930052465024193416469}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":194393893709806074245658422539505423981},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":190838538363383806546684302657924470279}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-24055513340770489898394155717345895847},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-52631923892582313935268148498671015797}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":15448356592900764747089298935081640235},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":28810013029796783776902431144392483443}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":272094963540226375332639461516972944697},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":270881429517736040915605170923087885073}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":60809836703106653609094008854395681},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1840054585311814506181769674334253835}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-132311698335293624348059784012994542635},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-265871643580982140101048669196046050427}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2961026986803193565762272630083335050485},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1476153600221927087425613616165915087015}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":10383635841412132675042441450243459711},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":83069086731297051527319868474162466537}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-796237534916709560311289568365591005775},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-12441211483073587055880775960262251819}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-55655603001668441296364970953644555031},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-445244824013347541381817381650806858747}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":22869645415372190448255139095727849369},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":11434822707686091901716300766228002393}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":256133038508274558305748590964332369157},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":128066519254137272938168506535629779277}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":26788109373764333845792652973809528363},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":428609749980229332497466699288653469225}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-55026023753634735915726174637227747177},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-110052047507269474460050889543594063703}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-285499912625005229310349334998236541871},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-142749956312502621011566550909244064061}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":898636674154140023514377327657763975},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3594546696616550601294424527220395653}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":35679098478222477484111995354131293595},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":285432787825779808846448532379525558545}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":716571854746921383127440824518134153799},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":716571854746921372612292882164148116663}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-15216560402921711748999111109832252469},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-951035025182607222586912107461789047}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-722918697271006121836936214460314833235},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2891674789084024503228520640889519269973}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":310264917905001706705913019422283661411},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":310264917905001698652593044998522929371}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":621519963987029699116722544263477986277},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":155379990996757420752290684330444002563}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":196867129569663612143306738183966428837},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":49216782392415899029372453359651978441}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-44991507534427189418257585329589943559},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-22495753767213600813423732570600973175}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":3421419631759056543649779257860106789},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":27371357054072445260630972657847275281}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":270056530799228585109328547173946254057},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":270056530799228571568007420360556995249}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1958633934918172315723692519378889057},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1958633934918160301405981429844028241}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-65942453963396902780000354975416668995},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-131884907926793811406193700052146763353}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2967022457935734650003114555442502064521},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2967022457935734636996021093645787064589}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4740741267759727},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-417252149252651}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1009825784658155},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-459331528021425}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2470029111899565},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4850336965201715}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":353951923527483},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-54183979370557}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":19347924385905},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-933452456351409}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3687628885580081},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-147851696104675}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4034346166085385},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-903014864844069}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1408511918207435},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":87912735634823}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":3525389706017},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-208823995399257}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-267368552996341},"lo":{"denominator":2658455991569831745807614120560689152,"numerator":-12670814933329}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-983007309692931},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-4544192952350207}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":135858205029343},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-344423313427129}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":20146456915911},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1260656591138211}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":638644695528085},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-268925411047955}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":125635875149177},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":21590528972501}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":169431101771479},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-430323642944751}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-804480013153185},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1111033965446053}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1946457356151669},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":15940427754387}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-71490340102745},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-736412984983781}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":18904760329277},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-1617789364645}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":385360996823753},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":37972598110573}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":598771886898897},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":657537903498763}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":85070591730234615865843651857942052864,"numerator":1234126760985277368265},{"denominator":170141183460469231731687303715884105728,"numerator":2816268094783957576655},{"denominator":340282366920938463463374607431768211456,"numerator":5505445146827786658609},{"denominator":2658455991569831745807614120560689152,"numerator":51912664167090773387},{"denominator":85070591730234615865843651857942052864,"numerator":1553676291859228285589},{"denominator":170141183460469231731687303715884105728,"numerator":2258802423759068932425},{"denominator":10633823966279326983230456482242756608,"numerator":164287317510947789123},{"denominator":170141183460469231731687303715884105728,"numerator":3178195633533451162115},{"denominator":170141183460469231731687303715884105728,"numerator":2373190662583618518975},{"denominator":340282366920938463463374607431768211456,"numerator":5513223037978883160221},{"denominator":340282366920938463463374607431768211456,"numerator":5257570409991350361291},{"denominator":85070591730234615865843651857942052864,"numerator":1906195552110845843909},{"denominator":170141183460469231731687303715884105728,"numerator":3970193469426261872417},{"denominator":340282366920938463463374607431768211456,"numerator":8053319117250590872087},{"denominator":170141183460469231731687303715884105728,"numerator":4026889705861307438777},{"denominator":340282366920938463463374607431768211456,"numerator":8012908077779756013681},{"denominator":170141183460469231731687303715884105728,"numerator":3052147115555923565967},{"denominator":85070591730234615865843651857942052864,"numerator":1772141635805799893347},{"denominator":170141183460469231731687303715884105728,"numerator":3385330133345271120129},{"denominator":340282366920938463463374607431768211456,"numerator":6007158728156466444659},{"denominator":340282366920938463463374607431768211456,"numerator":5846192680685512822755},{"denominator":10633823966279326983230456482242756608,"numerator":203235808191360482861},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":32,"numerator":381},"tube":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":83197086507450682526616033070857886063},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":82498087868737354626965675384916790651}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-795964028118182352434850501711019628687},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-797814320877669908915747298192359155723}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-444935262637633358863472147182408748919},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-111865033532496712175861979252200753173}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":48448505885993956734094728787468371897},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":22697771055836339376617818448008782843}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":128129914329550330745980884364269163081},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":255373420902804793034668586498965045335}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":13398101595402707518621910066934323231},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":428127964487222403873680996435608237517}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-439422407206389358542369730332491833477},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-220186435284134011769133670570304903097}},{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":-2201470811535619337785334285551074503},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-285939805742461048633842021851192849755}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3606910801379855696280308712800050651},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3579065763849583743733759729723912055}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":285875373028528133167314367826830729955},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":35214080622679844704181042224992375751}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":89950230338952108322223347115734591087},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":358071566915714195814214460057769301039}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-60799588131509388025056904222848217595},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-61269750503731289628512170083671670229}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2882789377114676879219157307543966913827},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2892687409676789335864551984314251370585}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":621730135724170786590359095701767277663},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":620356407703377066465726876710528105231}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":38864002264646249021158140561209973941},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":309564686618302803153220452059294520357}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":98622761222488448966019699029196504989},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":193659925634121798753772517420853837515}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-44513232816946680167494686277028766001},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-12260566232267325237529599544541831301}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":14619730425453045825497041414127865309},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":54302021578685269053524936422070052241}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":271163803736106014715668236953621276305},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":269895696498046522793323005648390911699}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1000051681774172856784521673714610109},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1893950058256970110935159936609969157}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-263606472490132474508792851191299268219},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-264911728129873980429220064859634113315}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2967917906026096674659455287250982839873},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2959258703096842624043118807219195563699}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]},{"domain_lower_bounds":[{"denominator":1,"numerator":1}],"duration":{"denominator":64,"numerator":3},"endpoint":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":83569617809245040063865350978972189093},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":83569617809245029987387152132560802219}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-397450906684520716347640760042982503259},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-794901813369041444249067721773596410337}},{"hi":{"denominator":664613997892457936451903530140172288,"numerator":-865677180709544103513720452533501005},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-221613358261643296127924745213512060255}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":43313782115268665093184708519931671961},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":21656891057634325740537343521301470363}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":128394326066749548428792864859422550789},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":128394326066749542088271753411113852783}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":214486780365293385109471990586985728171},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":428973560730586760951607595973534931183}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-220420150583455967520046335302246898737},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-440840301166911945806320978150866077697}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-288804786347180390151587223796091223405},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-9025149573349387599102081808116210125}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3606877217333463375361129509482463609},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3606877217333453617882876548645580499}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":144373393305219415495021211514500654129},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":288746786610438819690072278523779778525}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":89243782300837703539164853396741800457},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":713950258406701617445976430130053863491}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-60499165190150893056651696585120064401},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-30249582595075454313700358631434878687}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2899559150125464448003532051671123111865},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-724889787531366116053109835595996349763}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":9679757040021602865102058610869863971},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":619504450561382566908311785117619076343}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":623585258866494654762543044313625406857},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":623585258866494638277570798935270698285}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":99869975208041299723760266460669999805},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":99869975208041291529809518608804894937}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-41387774673497635738614194754611814805},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-20693887336748824122674867214424919037}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":12855502534008751889067077568786413599},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":6427751267004374131766744934478694301}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":33628957543421996164247530896808307855},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":269031660347375955429513717329689541399}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2012827623622255045475867675100718307},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1006413811811121354146147315444754193}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-131356038019417366129766521970124085595},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-65678019009708686064636534571837371615}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1486937024001746859354596620627780596571},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2973874048003493705399905065564131133559}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":1,"numerator":1}}],"local_remainder_bounds":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2370045659634889},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-340461273085219}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":251014883443003},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3732102894781075}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2533247181135461},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4907853624000673}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":84925953770483},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-10168160816517}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":257432794036041},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-993421535892617}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3834162409667731},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-977678906254463}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1756537401082177},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-66801131383079}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1403377508269205},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":20985918476927}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":228106953924443},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-211212927595895}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-250397044826081},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-798233259752167}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1857022590552879},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8562247730041415}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":88886982003269},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-650920082766243}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":633485245391771},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-316328764069815}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":308839525280753},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-555803713964193}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":519587908406729},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":12514639809827}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":303749517307541},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-456435904536777}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-399271600762325},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2152902124776391}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1932542835431293},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":267296401145203}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-144559833560501},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-725161420574551}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":76477195907147},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-25699801198451}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":185568819066637},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":141682960394931}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1127841774649081},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":597613221187441}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"picard_interior_margin":{"denominator":1237940039285380274899124224,"numerator":1},"propagated_initial_radii":[{"denominator":21267647932558653966460912964485513216,"numerator":314889774307267060833},{"denominator":340282366920938463463374607431768211456,"numerator":5776889226673300767347},{"denominator":340282366920938463463374607431768211456,"numerator":5628408588814533234907},{"denominator":340282366920938463463374607431768211456,"numerator":6806053489232830973617},{"denominator":85070591730234615865843651857942052864,"numerator":1585130121505285933419},{"denominator":170141183460469231731687303715884105728,"numerator":2316832648920053587125},{"denominator":170141183460469231731687303715884105728,"numerator":2691555664208841464335},{"denominator":170141183460469231731687303715884105728,"numerator":3254919539643366761701},{"denominator":340282366920938463463374607431768211456,"numerator":4878738906820477681385},{"denominator":340282366920938463463374607431768211456,"numerator":5649984399217873425739},{"denominator":170141183460469231731687303715884105728,"numerator":2716833922954685262907},{"denominator":170141183460469231731687303715884105728,"numerator":3892686885265905038487},{"denominator":340282366920938463463374607431768211456,"numerator":8104452695956280308077},{"denominator":170141183460469231731687303715884105728,"numerator":4114554559172893431977},{"denominator":170141183460469231731687303715884105728,"numerator":4121242814065274283605},{"denominator":85070591730234615865843651857942052864,"numerator":2048487591939788545677},{"denominator":340282366920938463463374607431768211456,"numerator":6253367092657657385763},{"denominator":170141183460469231731687303715884105728,"numerator":3625533238212320739775},{"denominator":340282366920938463463374607431768211456,"numerator":6942232974621594953695},{"denominator":340282366920938463463374607431768211456,"numerator":6168591658645307300911},{"denominator":170141183460469231731687303715884105728,"numerator":2999753123438696360913},{"denominator":170141183460469231731687303715884105728,"numerator":3327321629405275487215},{"denominator":340282366920938463463374607431768211456,"numerator":1}],"time":{"denominator":64,"numerator":765},"tube":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":41848768087106713379676843953211352527},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":20749814753854363569829027628782741799}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-397317757801094089517105065289594893703},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-796415537062767504081054054020852736923}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-110727745751354503706310441231379333183},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-222752069840447633277385114098976361683}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":46047214279159324749592065503397751959},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":10741994948752471554693548645750118827}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":256913540394199263769692413673911874225},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":256046316076505132777075301648851161751}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":429096030053315685362509799678937323929},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":428555718860997515512461910112063790307}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-220060226848685919234269214401062346647},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-220498908507216163520624054780037139479}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-285083657519382888695381137884364061087},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-144623104287803147422531553412032806685}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1809835024052433277929706575201391365},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3591755213117848828564981102530879805}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":289191159426436923771167538703831963497},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":285015190981262351632590864765822262933}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":358454933068181684606376879143278523481},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":713529752241943508359624422801351370889}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-60431669129545278389507702523680772149},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-3807157965189745444903583669797829677}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1445343229138143057093400119850380950075},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1450284883176834922898123209453356486247}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":620662561011577864771337967559356364231},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":154833827248958337794054670652622301425}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":623882792434619021511243469091180107251},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":621257427492853089842264877991950748857}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":200121318524730146793177635536147751699},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":196505553019100646042413388516767570043}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-40909749848270977916277565088627259791},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-22722518083111168797344282695689747737}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":55160568847462350261257028948078897679},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":12745505363571973658162855730982565671}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":270188868471706412051261574554674356315},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":268865491746928142631931302946416589287}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2054408897427312731928789653741010439},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":973996136208571682340612358093112023}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-262543127822026182134291729902173763291},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-263906114523761116221064697037753862147}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1487381378544064906691642801303216061573},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":741540606174144904349359036990344868533}},{"hi":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124225},"lo":{"denominator":1237940039285380274899124224,"numerator":1237940039285380274899124223}}]}],"time_step":{"denominator":64,"numerator":3},"validated_end_time":{"denominator":1,"numerator":12},"visible_capacity":[{"denominator":1,"numerator":1},{"denominator":1,"numerator":1},{"denominator":1,"numerator":1},{"denominator":1,"numerator":1},{"denominator":1,"numerator":1},{"denominator":1,"numerator":1},{"denominator":1,"numerator":1},{"denominator":1,"numerator":1},{"denominator":1,"numerator":1},{"denominator":1,"numerator":1}]},"horizon_complete":true,"initial_form_storage":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"initial_phase_flat_certified":true,"initial_phase_storage":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":429600645348889814742611372466280256727},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":468279803900694775798420278408722790443},"scope":["same_complete_conservative_sine_law_and_unit_held_capacity","shared_regional_storage_channel_kernel_original_structural_t","positive_internal_conversion_transfers_phase_storage_to_form_storage","boundary_storage_inputs_are_not_conjugate_boundary_work_components","cumulative_bounds_integrate_whole_time_rates_not_endpoint_samples","primitive_forecast_readmitted_and_Picard_inclusion_recomputed","Taylor_endpoint_enclosures_remain_supplied_premises_no_replay_or_authentication","phase_flat_admission_requires_equal_exact_represented_lifts","C5_phase_minimax_excludes_acute_unit_winding_entry_below_7_over_2","barrier_is_necessary_running_phase_storage_not_sufficient_entry_or_arbitrary_winding","partial_prefix_does_not_certify_unreached_horizon","no_source_selection_damping_new_trajectory_or_physical_identification"],"steps":[{"channels":{"boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5188180630954459171021382756589065},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2279495843385720615745361474567423}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10913873889959255856079983088256999591},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1214510259171187631600973869927042091}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1020971499566808962208259486340863704221},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":63767547390688866369460760396782018409}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-510124209032079451853971800235215526969},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1020978594200918259628385974993525678233}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":22850491028130538621439075887541181737},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1270309451804014903175674076456370117}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1270312042558654157169538868845230449},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-22850537569565953554796732083981134593}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":3032703843246056543860093255055659},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-24261461337620386629913577276125969}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4243261321303762038568637795068799469},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-235980406756457370186570598568787889}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":471961832185202732704537135464862727},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4243270479055339656517773789099882827}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":454856097813487752692352778736955707},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-102015052041565741525442763768090171}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":380650098087176266992711743058381},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-761300196174352533985423486189391}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":102014348695948104094795941120165415},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-909705866299113957301722758104237603}}],"form_storage_rate":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":4972814924436207418469705811553779},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4370286343754587015927081508395617}},"internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":4757406865978440635971865127276111},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2090875204837902061256561319662733}},"internal_form_gradient":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":182041096727878095023667117710061605},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-19995541449554297277002562762407939}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":159964513150578459273972671877668557},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-728165213702915845665280454638606453}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":161858961243204180898476939503995175},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-71216222453238528131402523959032003}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":29684885195251546727355138617757185},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-59370034108420776766538526144343713}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":71215966722697453216269860802483227},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-323716757800690219057333152922657243}}],"internal_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":8570652377339157746224296208242655171},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-119219185620954768153211093669315929}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1907511389186126899107032378623412413},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-17141344523018139493755555918698230305}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5715890301325494156510697138782660395},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-640979476098726744216716314663906307}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2391695103477814335944456325100285},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2391695103477814335944456325328457}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":640975056847876135561061434750222775},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5715850532985670155203733636569958105}}],"phase_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":6069995401626441499678414560252270105},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12130708309300161974510407512755741463}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-108177890037091173581692898176995476463},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-108345413350729658282485784405267087407}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":108346166134051766629000754008036660673},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":108174458548966044154066349750510145963}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":51521307531150908277811556053759433},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11334413831764936784689138721318229}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":4724496213939706282332451167450743},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-1181129299986199220662196536820677}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":11334373130985225146968531441552465},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-51521122165661717326836221601456253}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12152646745062056668374509574970770527},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12143364081700987577807120798457652477}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10935856990047483316157790343569161013},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-304778457619955700846273736171868689}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10915965730349738486483911520322945897},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1214743544136068216369167863179079139}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":486391934151980547283254633430225},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-26712841914676413465765954780087}},"cumulative_boundary_phase_input":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":63948479823980014781718650907755857},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-56930168398649420231295650152830099}},"cumulative_internal_conversion":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":55750861710684851202795294460267},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-98009775226776659121401311859191}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":35704443056352381846368657922281},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-425812213136061309024296673934599}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":80774401565336741786484132398709},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":80774401565336738857023641243163}},"phase_integral_residual":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":35568628272650213791423729114503975},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-284512997478200084290283708405045331}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":227172850888866811290471820407519565},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":56793212722216702655646725042215179}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":12762067314863881636126214032240873713},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":511685848367066894912870608573906047},"time":{"denominator":1,"numerator":0}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":44128989438273175700538881110322331},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":736312009732587794168891960324365}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":20596141564493685714511422277482334091},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":8464800842328724898799390149626249279}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":255185874947554437477591240102946999525},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1019570528291539339000975381910111421317}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1019497756884916554927698049333226072623},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1020737570254477565724462596653565462247}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":21556374298218298449848033122730802799},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":17728278117804926041467748204113036439}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-4432038268408231668147684201947977543},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-43111905647719726623090528599473739439}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":40894525190742225214021517517755749},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-40894116046392403354648874811300669}},"form_rates":[{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":500466012749290919031812795286805469},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1646823306413605376726347644833449699}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-823407880724171621482899622544694881},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-1000920128208313421616368500782748897}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":858484478427577120752266849387954349},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":352326261395033602619751769484266961}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":690829064190862901008465672193559},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-345416714165152575783766698254625}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-22020476485283116153675310435790453},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-214622195614218604522661197111423345}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":84612000371487136680877358815431809},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2823287715868840678515494451978535}},"internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":20241265185190235843637181482128771},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1350325970537510664496539859271581}},"internal_form_gradient":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":205170006046397723882946352621308205},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":33300208897172115830233138126891299}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-4162535365568122755545240862883281},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-205169283001545131001912966527596117}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":182415723901124316957409199977674727},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":59112438704768062595819202286199407}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":50383001826901563168323252165807157},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-6297845193466203131288041092528009}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-29556065338673320665314734112582231},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-729669172439591843522616314467896931}}],"internal_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":16177874078370857212308410404603386599},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":3328402472332922012378406960575224771}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-3328398178564763190181552575798719835},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-4044461758863208440302784082747383875}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5394017061297883231695858778537050153},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":1106865594465394743381946390893448215}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":8681214051793306362126833689963681},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8681268893186950425383181900968005}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-1106869874475395655553241446050526395},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2697022052155762840406311668642126301}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12168544842741508569673265632423954415},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12146645976039900786647567535054576011}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-108005639228881187269870041548344649587},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-108290116032750849314909509847885358973}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":54144743429025231445236789508878988445},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":107997918556567542312491991035773268645}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":58064728313100664997376417849975407},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":9408036818080512233550258721158457}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":2004675947139844255648197454518183},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-8018665546941441043684777264644093}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-9407987793993785188826681181865543},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-116130455615533604400646757786048131}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":763200105545196878692408177772154997},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-3047325500933210658083521865393047847}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":20677475155071340133466258777901377961},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":4225484275099558128938936848510232517}},"weighted_phase_storage_rate":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":2574107894337481624598172677385743269},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":8448145262483247417199358202568486499}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2554938314071035658246014685476585},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-37822116746275548159730197839939}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1477031974427481636121472126519031267},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":339857371085509559399925763110900335}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2343625504797063419963348119631709},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-8678311339457711680781501488959}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1362982679894683560179166841787905},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-112753640658672560532375874483263}},"form_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":645223658895288582648155318996065},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":645223658895288570586667410821939}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":570004546905605989854249738098009169},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-569548395186520982967493780983355319}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":907518292486318485834212153089277795},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":113439786560789810500087683942703973}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":13216661146684860041338372406354569601},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":1477066687672839466968195252524987103},"time":{"denominator":64,"numerator":3}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":123352363874710983056667717788325927},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":21586774897277251614428088350077845}},"boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":15116495468261984029060490876177750609},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":4525091338705694950829730909880151463}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":510068188914473935152181081779611437373},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":127301852465143847219068307239133355083}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-63642291752304971793226320082344793813},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1020095832455533608944270665440752783455}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":63246655246696374333324827327716350555},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":18939935671060760991175210170549713031}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-2367411830826873865652162724046727449},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-63242608998091626683077781808721637901}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":48807130931382876222440951054736299},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-24403293185801860828749905069166533}},"form_rates":[{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":734571374055095347692329317310649695},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":1760831051562067958693763000591549779}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-1760793295020241228901441519582322097},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11752670888541325035303898693276514143}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1261011202678999351469405057474332963},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1509011345940590173714141993781494215}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2502868726482363724814181288114107},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-625732265210430904447601570257795}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-188629222923141626104836492928648987},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2522085066455559307966043771325038943}}],"form_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":118328991892265162967801661891927571},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":41429655032209013187959729553419823}},"internal_conversion":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":7081477290244557297580703269901635},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":19842685161721569431411431214832101}},"internal_form_gradient":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1563783715300757849108253100610789195},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":913834672876353731262910645101582509}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-913832827944230815044068191380300765},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3127534312255602298426389764285380287}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":695244348762965866624990250406735471},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":406012961101783209073959338284992711}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":74035939594963857843888731776691559},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-148067701399450977073870476901908569}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-406015059141244390485296799196409799},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-695262870277491803230754458605504125}}],"internal_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":23762049151104155019992244311828866975},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":7125473851870168866828616436707059733}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-28501754068279081878418476289987009203},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-47523704572408536642124561297922646129}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":15846334121723096643735069896424859317},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":9481397917181208305647030317083342375}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":7862994004016635463588851031625511},"lo":{"denominator":2658455991569831745807614120560689152,"numerator":-122862242968699367967859737706667}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-9481538895803090504095342729958924099},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-15846727833010621183869965921762392789}}],"phase_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":6106425044027425460861197359755264987},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12180726087680258073275316989975077955}},"phase_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-53862661620076383397352123861224631089},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-54071435284660466716885993642092588465}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":54069284383671026922980732766706745927},"lo":{"denominator":664613997892457936451903530140172288,"numerator":210372399228814286958020526970854429}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":110651574762331665884637600926450605},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":8077371214840777653186273984281203}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":23566371505982946820496427788628249},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-23565706589977371624115530380914301}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-64619303632077270103765006653138185},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-221309045105844034075891852312266577}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12314617660298191079282278702625881111},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-383827858802640050392982387794525505}},"total_storage_rate":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":3804571223752281016776953803812070601},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":18073851818714197428602213060719010985}},"weighted_phase_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":15099955903116858904140013553356354833},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":9016211081840994207707126665582795581}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":8337080370698112989027313956804363},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":974057956563595621266586443569959}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2894203424577042638845893146160695387},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":594155998546413681340250154356714367}},"cumulative_internal_conversion":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":478420842030030087071804723253621},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":447706310798933860187142416119709}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4647073206976378566563070416132613},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-9475270058040752558631067989121841}},"form_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3258271892568920954101970845970995},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":3258271892568920911772560769870229}},"phase_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":428435451604605245252143386868962273},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-427889922562943701453930321716383207}},"phase_storage_change":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":127345510426847335736977387929955959},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2037528166829557368217658217895689555}},"phase_storage_upper_bound":{"denominator":42535295865117307932921825928971026432,"numerator":1764797230807864321182563983244215789},"running_phase_work_upper_bound":{"denominator":10633823966279326983230456482242756608,"numerator":90415875373607649097672464416514249},"time":{"denominator":32,"numerator":3}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":268299304364103107750692432516180461},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":81491973663484822559750934487049049}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":39791959758196847725681426263714266653},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":27663506206409318086382182436167295721}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1019089848173215250045209620028294395759},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1016824316170577487998616723142574059779}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-508298503272979646581425211267545257131},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1018989957969803167968969043925423718683}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":83169330551214714691510941312227873229},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":14458258784529696285222895257142570449}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-57828483543579844544559824512613886579},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-41579248954824648578233396139190198071}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":358642188789271011760939754568717341},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-358637607879958690667449073630884785}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":15468354131808553916478306839397606447},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":10765644331869611904407529867754022461}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-10765108570541083020885465909303186285},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-15467085938546370074587915361491516955}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3322958355427647501417290095302053817},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1154766253274280934611427466706436263}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":499134222927663835995650933400923},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-499161599654928414310588014089909}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1154805773037660597398536036597139043},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3323136551551437747342160079262812873}}],"form_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":257622502045499124819799989874478499},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":78300786851285807877854657804030487}},"internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":123469938609213599336232978361382649},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":4694427602390150957431830668324413}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5173321309048641428357819397661921017},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":282454254365321528060735206201556727}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2259617494810566733037823226907045731},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5173220021571492157428290349010300647}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1150167589048851230162439295700209985},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1004183676159569121907203016434096663}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":195184919386969872437215351543681601},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-195170294366550572847090781202584475}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1004202308175407796295197723469893939},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2300448998691437847904595926062748275}}],"internal_sine_current":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":15654118139907629274859016097193441985},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":5453846536795965887692957346252935787}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-43630274457345316153334800304916157317},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-62615352761288508137792411190926648217}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":10439381557596318433250537441206054897},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":1813902588949945753109622580052645503}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":25089222526476781558172412024610361},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-25090598630880841248252113417227685}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-14511717331592786647080279660331412453},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-20879882754459432094460207824063692743}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12267610317278055762546803384432115993},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12225388161120512084129058026795931133}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-107339504344030616214980531624788006277},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-26972259144216619867343172419053108301}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":26969609913016802733247886285786721269},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":107315396790718824697471821419780357157}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":366109714362424757076229212772077599},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":79910397916493239298008294663065357}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":31064644737429368694550386787999013},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-31062317093136817261022129115422959}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-79911880605203485055392496476006339},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-366127829472543398425240760275825907}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":3113605867621785497738546618242814661},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-3103049183355071497860737608599310307}},"total_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":20099710825279972449948059921812801707},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":13824031164570332420994584130916602943}},"weighted_phase_storage_rate":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":2480261040404309165641032491492290401},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":1718216297214880826639591184139071557}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":20913610262765446164841021731000323},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":4793994222039446678754911497650383}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4759451538242519875987210002272301637},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":77657464078695754624364534700274085}},"cumulative_internal_conversion":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":2403755027136782041365089661679695},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":4416233323390480938448157833482727}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5656634417127807406273234214958773},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-4905038525043540069128553167321339}},"form_storage_change":{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":641359261865173200929673055032833},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":20523496379685542219247526355152527}},"phase_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":572791900116063635137159792871012237},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1143642694385832239077049584979786143}},"phase_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1805696305266648580961531989428678817},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3611392610533297155971712259459032767}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":15459253746568202445923993106955563947},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":4755035304919129395048761844438818909},"time":{"denominator":64,"numerator":9}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":498223579985003586993299234717800885},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":12586020366579564236163650933379089}},"boundary_phase_input":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":3077738351024092370889311664401817173},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":37125126865916924766771145474446313231}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":127200910145049671818634686806999750415},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":253701028656185512367669456750473448111}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-126808114913444513191733581907423449423},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-508712008389033557963211719443062456121}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":6425072516288825000614233380258299001},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":77508058395023316627171956797191895547}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-19374286878936083566681612052665060871},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-102779008441628173008300562144503270181}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":570450462893441302977496953591977483},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-142610535971087390804172874130914281}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":19141840233688676011967262630091578563},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":903083224141443606933705081694304651}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-14448045930570193850106000537913013699},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-2392405095987612654178971292401329971}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4118209841301725509692020962186385341},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1552324349229993928086957164309307085}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":182757420486120564529474032762173},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5848846498469324262880278832153689}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-776210040236785811158356237933843471},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2059291680065364228914186444693211075}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":958069290629254459592751739145578243},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":193806719812087377536601009390097439}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":459832003523520731296594280586051117},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":23280312733817516104579546327441917}},"internal_form_gradient":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1943122630393541511085374914461156523},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":520817885631814669361113161781491417}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-4166482136706901035696352401998370183},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1943063844351584980136487329094604299}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3456694432950946313294665840487236837},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1851966715639999822313612016770360611}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":60504025271948154372337211860239181},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-15123677368732766154276861229677865}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-463008838157426087044164494860798031},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3456959151664752589440642179300286257}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":77606433702416426760338642892340309079},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":58673683487037988063599963963472771413}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-58672477346877352430653967477419530323},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-77604086133543060015432667190378865251}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":25875475566749378272882413409819942739},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":19507083086118022147157473947845982153}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":18372779826822948636147075725609085},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-18374693191565614967742439530695893}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-2438535760050524118028210006075891659},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-12938911227383862260501494384731651461}}],"phase_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":6166099459797106651796619742496359367},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12280057032829477814770506107250014483}},"phase_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-53424686941959539944331385020518192171},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-107529401996926399366331493724928971923}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":107509963508853234539747059321064977183},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":53406704546277167431861636206096184645}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":137537501440594819463732789627541165},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":147374828617884241703433854843284927}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":19259029397975011451638468258708295},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-38512128175373580630019665564083187}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-294760581151958906226657878504295831},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-275096068527105237731537908592873867}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":3157264970208668501027694632154545109},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-6288454837530423387763619846903577913}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":49955563072616871798660542417998559091},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":37165127521309634745695046171339719827}},"weighted_phase_storage_rate":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":3062343361374226083691736917428311303},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":36777514081685459990621844152559524949}}},"cumulative_boundary_form_input":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":5533480071820311163143990419799655},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":14233509496974119855877649697684699}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":7067755301510589154154193750573664517},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":1056319793089529999105515638630860413}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":40784665382259290610448574195908707},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":13146350598572049477665487706273445}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":22501677894772436424481883910883885},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-35170967966503174592385139705371061}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":49881537990318605758025021314842029},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":24940768995159302661607678924467443}},"phase_integral_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":359140126880135547188494133187596163},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-716776968207807109567039211211991219}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5621055014496402894565590513077917597},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":2810527507248201442771224920221704317}},"phase_storage_upper_bound":{"denominator":85070591730234615865843651857942052864,"numerator":4308098142370028436833285608902429377},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":7054608950912017104676528262867391071},"time":{"denominator":16,"numerator":3}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":830891074656078993656466974968378929},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":200112142692046271405293233854623623}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":58560182974548126575216003855687842749},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":11614256958463217058561684573959199239}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":507846710767739289581352420964109363547},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1012360757234439752737907993301309469781}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1011888249468937261662144957742071068899},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-15865683388923887653485584606960869123}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":30516194450077307710751157625117469307},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":96827440716727285402435178558107741235}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-48403133674219940066887229142361073871},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-122025999693279354606832641997994425505}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":828578362411023099904866628954242809},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-207141174414319483786110058871259443}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":22762649639243661664831451917351789579},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":18083403372234642791213428758720432857}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-1130056515817516318529260641529337881},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-22758091091752820514218388850177387611}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1226558369865413493835199642493342043},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":973204337395420417541253897211236627}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":4030749411574752030509430553401425},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-4031471597551520727393960556200265}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-3893195066806419499053075298923217669},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2453449622095199885662863310566143149}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1600493731534124402179856291579738093},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":385950620401989624754141412400338889}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":769574863805178190996256085317336621},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":185845541869504379732201597458124019}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10917231648208667110046252234740379753},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":3314425397280079243086722862221558221}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-1657173041538994166701219003267898359},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2729191883636936869634585801861035117}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4856301960989994741243970186503095123},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":368383164734086281502168922299662723}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":288388151494077741121477945685430689},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-144154399200700071230527095215748633}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2947244033931898033149332065940198063},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2428412670044283004824445996440947279}}],"internal_sine_current":[{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":5779258803021843974144512747344045459},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":36802310420806227832220526113361261063}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-73602240566772307727455493716015904331},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-92463955657454579590354069448804757425}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":15413387055873021856664427809630368617},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":3057411596803175277432131609594310441}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":12662972739864622888229326097823681},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-6332620777011882497724080130525401}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-6115416510435535898939813614580101415},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-7707739308726934425385367930112123583}}],"phase_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":6202904963885396558580736493464184603},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-771498673766009004277729064747687819}},"phase_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-53128229108141213018417299456765612303},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-107065076221545777700763091275607467455}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":3344823642410983820579316253407252285},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":106206372829251935531418329836898322301}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":193226115559605583978312012590190255},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":14657500404816451726100632006585385}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":45898399839416833739073570290532603},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-45885770402467564627801043886818487}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-469068456498359277438705276771631615},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-772987760609070933615668703796861077}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":1604563063764455848191810840685190429},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12774659697847252572056252381046954293}},"total_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":29846878314676303781295905744513783817},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":46616414351356952996816218449609267385}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":58093262897818483160411955197447829541},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":45844513110552973747307935624808589607}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":83215859699066192132798812810040003},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":32994022874353457800123890371555663}},"cumulative_boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":4906381939221266293683721965654516073},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":6402952352069973194902378412140791509}},"cumulative_internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":38429243561563509156699039097579431},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":30569370148838085077559387467972571}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":4913229832120535863383836587366575},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-28602557571018690725162232423105817}},"form_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":51434615840077914892376985269230417},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":102869231680155828995872426158987231}},"phase_integral_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":432548459847301939286092720842098303},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1725906803957640581214573583558632233}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":8056287704336053933733351217314025859},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":4028143852168026960537655480141213671}},"phase_storage_upper_bound":{"denominator":85070591730234615865843651857942052864,"numerator":4857174256714605297222568745986438151},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":9782194508293694502289884543841059575},"time":{"denominator":64,"numerator":15}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1282290210230950170202726685893213153},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":347736262708775574145445347800572723}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":67713798598742022140985650495351138027},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":13908026518776587146128900715173200233}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":253338600179419547917993539759504485101},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":252375442400592454712490721400726262293}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1008876114866259898629285277493321628359},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-506468248764443433327668672106050085265}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":140885656065292970575140346052805975475},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":57858237048158040553192652338754946037}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-57840262423355095680443530743138732887},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-140824382595839457381004584782237337091}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":141320188705246956617185429723129789},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-565270307923248423935794456402566997}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":26320212822179210802150736432336058025},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":10828623115233494362079999937294674547}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-21652993965459827688356099355937170857},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-3289124650502877890666662264736097803}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5685518786775456436622753221264715501},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":4672520442890786180632733944687590859}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10630095360161242731911456872432855},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-5316553642508923166700990025325767}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-4673175138482032917269007154757990495},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1421647356921309390608296907133057447}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2475108757007650850878926092366212277},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":672258730361947850042198210635029733}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1192767866339442377753258648181980307},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":649074721948124049650551958980028519}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":14598452437868446092274478466331498625},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":9639187990862861669153844090061674847}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-4819424796580789767449691363992385579},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-14597629162439843410893365579758094433}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1623886030780940356103468052789663051},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":4286387468919845009733033486330462511}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":334397886182978799757212162553800917},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-334248633495004275424875633585286857}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-535846130744216452607773224506138273},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-812059183988466769156578834882353809}}],"internal_sine_current":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":26794126415985323103310456565554252107},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":22099565716886230167382349132724884817}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-44197067731813984118085651809709528205},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-6698110845901440037690102269188412125}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":35723168104761056079216194660907921437},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":29358311794267641820530378759833822853}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":66790858980883014859117800783856363},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-66809783462888355590900100457315185}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-29362425367987238568449799715631595805},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-35729895139994658234123274272119586949}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12487544194812875078019198915253294397},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-1552037186021093021257971215865107445}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-105562520550169407995386507800233257757},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-26624372927000985817998724235694390879}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":106453186707628533312331161967037891841},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":105496223873124900708046570649703154261}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1033797955266657439644246353272445695},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":341099876842875609892410181713694141}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":6652634568187760559594666107990789},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-53197322242441186645316368185715575}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-682260483556864617597194469786536801},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1033945865719483141434682991159874389}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":13074412560063532402853975663836380921},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-6501572479811961344916325975262020883}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":69401991160587432135660469220130327299},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":27996471924674524810677862615360154707}},"weighted_phase_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":33463441201789890642390771563882057511},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":13662106597156288480317832202362562487}}},"cumulative_boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":71661606651820990680525813105642185},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":65594297503301167876259391727859355}},"cumulative_boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":6493424093879282437613073149139308371},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":1126338415542572910600193412029470819}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":132769480857788379770582077328689189},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":60994747740156399904929010545161407}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":31381298368182164152653512916775205},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-21685263045402116587510356115448437}},"form_storage_change":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":47337910494955474021623857026642793},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":189351641979821894781592279078179811}},"phase_integral_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":506712318533592479406427123061111159},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2021066322401243669494380875164477473}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10904787117617164822656673711151521999},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":5452393558808582402913418206284488931}},"phase_storage_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":11018507332175893617044993887597316969},"running_phase_work_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":6462926720009204237660608643866727667},"time":{"denominator":32,"numerator":9}},{"channels":{"boundary_form_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":466577313641673416688022071060248075},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":551353707223673945418396390388009119}},"boundary_phase_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":19169673694972833851648003036077439669},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":64624598916297013847874064583844502085}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1010597623987122118694134005506274441041},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":503118116320053770081888689379564761871}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1005439374595736986691860621346077421895},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1010031209720005264018562974194680187671}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":79596317965952115144967205715532297257},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":134103788545663538878786290227256044233}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-134048175605961472834583925608411889815},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-79551341688845376393483586719714969135}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1473484380665600204519398572469041549},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1473454135012760320046118447186921241}},"form_rates":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":7451102859696354734855797230796511531},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":12580345440173263453319374891840453183}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-12577047803059862561772756297323846849},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-29793797889348704233504246450908469945}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":6454589899854958934934389186515553527},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":5442279816043929200127675511039588917}},{"hi":{"denominator":664613997892457936451903530140172288,"numerator":26456206692255680678501008259591},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13551313739074845869980834418198191}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-5443317647725578975375583009376308427},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1614048024963917996459658666599780619}}],"form_storage_rate":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":902798832218766464021826879834746773},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":534413959677535481326345381273318011}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1744800719156208578599411688039200985},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1035003533762117760731116166093927305}},"internal_form_gradient":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":4701316699629755786386084800741273317},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":1648581141685015068218292558051818391}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-13188015540854399924310836159331695751},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-4700979526142398967280194914581346439}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":4184952464222708757278582314152218163},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":2933163228397513226340742379268477029}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":379872669664416276005095681500307703},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-189807745173408217654557624118196597}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-2933520811518738055972255905872892295},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-1046428653511964449231147732260259899}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":121707324130063384889785330010160990151},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":103030136341157530261934276971857309041}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-51511795142840802274671638499746045543},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-30424311584365044341988740538941626873}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":2534711526414902279448788421867812531},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":17097426288863619337697700147484358675}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":42554687788156707962652343810835221},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-21286353844583984008915724382577743}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-17100686733250353012644126949968515133},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-2535340708883879989724923172610484229}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12576321284346508579586660486072592273},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-6247989853561100539518194004921041885}},"phase_rates":[{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-6548104965653886150420724173402461611},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-26457094772029509700131052994757594995}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":26442086973520987933556851826811402013},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":104685273286865281763729078261374826555}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":333027935642826181723418469706943731},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":233413713347423109309269762343913023}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":15114653280651632016024267503902179},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-30208840881474756470787787036046801}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-933768675632310757379436024407104881},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-666177171197701456832290447743039329}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":6670004239809008983118881768298180071},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13259636656740870581214210935083731331}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":79067314810362379704948620901216880465},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":65285367377717158492129889493467019645}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":75456119481487313848861313381877893373},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":63147711539007016566824507968373747601}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":230806459611455746990055764535080885},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":117283707555520600259234053326735209}},"cumulative_boundary_phase_input":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":2072645250695746402801268358442892085},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":12039985398542005808920644073603477587}},"cumulative_internal_conversion":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":13409813410514728555776843762845421},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":109510538385255669939200080830814249}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":46921187096294191262545207847128241},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-124726854046326753172950092320259735}},"form_storage_change":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":80159155033341163180881137462951485},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":160318310066682325354767586210173943}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2326858574663047853036883115417711845},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-579841127135974392232614692286050437}},"phase_storage_change":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":1769035869829602250633137211101957837},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":14152286958636817983540488017568120683}},"phase_storage_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":12522077471966389384048426597872401385},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":16471651467180715552470946786712322431},"time":{"denominator":64,"numerator":21}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2594529136253200786313427265673970619},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1635397994217426147947737741605668705}},"boundary_phase_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":21357601897614985252531123183624737819},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":73410248332479367758743551758857038333}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":125928970621367417977031644038709177031},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1002574302504040827286337137578637095871}},{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":-7824923309552505413633446097001519257},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1006698285359027942048358791257482923839}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":176918431282061534412468589586267810205},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":75960924280601957282442351693655026685}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-75920785582008128539802496037561365203},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-176793571649397074441028251119642775103}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":927046525481154377277913143905702833},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-927025553571737838488872416058585961}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":33205646264478708311729671148922779095},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":28584077580823911826230455555095593983}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-28574528031701882891185930154613084481},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-33190880936034655626466820268807098989}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3606006935869894973287591369277250509},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":6200656967394444334109129766709582995}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":16800034592429792077960592270683295},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-4202548090422784548234214223305803}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-6202197915214957876738286921913232295},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-450892906886686456237602336528572493}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5034401099900723085780984602746918029},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":795053705373487900960838931257444225}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2439736792384226494507673291472978203},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":772455027360494091638710286664921829}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":23525480512258795270907754213640380137},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":8633405694886545681965887501452351031}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-17265730861668878677939790846793894905},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-23523402351947612066719957394727911701}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5237191356876077873690799654024476761},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":7682612662334156223403026642009341815}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":424733653054953607774477037093263885},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-424319209822982410965575358081952397}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-7683833758702833000551400886869016983},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-10476734749030846057221907717223865435}}],"internal_sine_current":[{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":1062792279722667790979897961652015015},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":7342295990716713608107266265880584997}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-29366752717138623082030116818215211163},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-68011555747531454115763624605946929921}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":45314419594090810882349549014972134937},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":38959876752393504852900484080588790683}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":105557730511263662037984404202977507},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-105621553657840272388639867854344379}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-38969558813098485950532734194215603789},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-45328699002590747589862126298486532337}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12670963680791015283411598661618123513},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12581889400728954743498866842465607757}},"phase_rates":[{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-3246259573922692416768849135156001667},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-105059764559199801105663531567866008551}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":26245513650715968699575269624233486525},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":103776108608815421681599362160272866623}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":416762446182489145138421774113236359},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":611362890535433575438139637838626065}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":67598460381173958972820794481130033},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-8441562461521845245887391419059153}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-611460062296966811694779099137360341},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-833712061385443333501324613269146241}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":6815114997045042863368586115643197317},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-6770556885104596054623179478219822567}},"total_storage_rate":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":11084484540098359954178557716468637709},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":74483822956503949687191561043733276761}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":83641475220886156547647477129002183643},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":71303608135009998083348205318703499861}}},"cumulative_boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":176212506436662266924248833806774129},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":193942988534462450944284259964500929}},"cumulative_boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":10292856180684390478629866232236387511},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":7740545394563488086305874031149950629}},"cumulative_internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":164459838355623136911238342871661295},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":90964098600150995515164585102825335}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":133440885903283991542385017489602863},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-86016308973261188549752277694870449}},"form_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":254656035819024216758499223829877231},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":254656035819024215285734898983564975}},"phase_integral_residual":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":164407277612536385009886196726886243},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2621096609952166934011165500965342259}},"phase_storage_change":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":4445671888554078014736862631046689639},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":17782687554216312032218237793301782093}},"phase_storage_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":14217532191431192120995343155339620677},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":20403784164168478966229403294267124351},"time":{"denominator":8,"numerator":3}},{"channels":{"boundary_form_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":869007878700016611748184444352030099},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2304678338413316137631153190518840145}},"boundary_phase_input":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":5871633983242061213601956116210850367},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":81966470903669716683728114771306905423}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":250966673500438444434654031274884385029},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":249631811606677337993228216412892403119}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-249335497491308467292035711886142690263},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-501474772709254895952504568343649227731}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":48500017677655999717200321622322173387},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":169107398929327643604796088074243704757}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-168997622154858997462162520744738908103},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-96917159572407703022434054307315532303}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1134415595621475176844880296818602655},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2268775002798212918723608774704940779}},"form_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":18257448183396102901387977736706069431},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":15959158215949653734969540615177162691}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-31905210684919739387131738837455429535},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-9123811055876855997465360497073591893}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":497275325498557568445215140259339053},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":3473129829308707244975207934313301879}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":20384680583274311140045163383288945},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-20401631251687993940833220374378673}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-1737108928716529799680545028407987011},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1989874334784824801467186096404536565}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":6766414771148699501385961434998071493},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":2248717979544393144447845860704727849}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3290179447086932760626562718706276081},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1096452620746216505032523825421013019}},"internal_form_gradient":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":14372787011377420814009045324056668771},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":5465455103008193519008943732462344677}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-10930051647097687557675548420824631487},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-14371262470041421223426847843653705987}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12803426434448080064896096708020547679},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":9730385872258760615053183649991747141}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":29306571479669662392783061136217355},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-468271728752031676330917794848601511}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-9732329040469740263110410661602295237},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-6403441440834590740320776964373458527}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":150144719806897078855087997458135825219},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":131715646322900095589185710614188156689}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-131701904342076288598776096116162840335},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-150125254285793378084848417020186230339}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":49991568300727732600268540456828251823},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":43644636626879228957484698783977222311}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":128080725532378154674875723149499797},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-128187229723101879557367792890536249}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-43658309191528686711696458038925891589},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-50010996733815058881823484068113457327}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12770200762174109488018800060620335451},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-6336396880977434907269911399239135459}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-102897031255342976984403783491480920087},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-52096976590711973103009477969366910107}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":104096822886236402414371330508616510899},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":51385797578306059429421896915216711183}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2037728605555852590373783131139519315},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1548639009761525403831456107717148477}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":74628571457046208052986687876094339},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-74527760341073050325385282687671483}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1548948274587561849787367529411410441},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2038278716216627125971921217429325043}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":6970878873911280045573522793196645359},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-6922147279579291491350958252659480827}},"total_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":49106453494952796456253156774109518143},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":41788940343757231440961059565731382307}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":91446492218756893411120352113220964793},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":19770111182106419148256606852513327229}}},"cumulative_boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":257681995064788824275641125464776951},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":37746848205948330611968070721258945}},"cumulative_boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":12494718924400163433730599775815456399},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":19323269112736494142161503442204912449}},"cumulative_internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":241573419146723123488423406591339641},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":17795039399703736773570517427429415}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":22796496503664679236393079219102321},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-229443440350860032490862458384747435}},"form_storage_change":{"hi":{"denominator":332306998946228968225951765070086144,"numerator":751042371164222526527360818712657},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":769067388072163863037266605727485749}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2938077145724251280932334427669010431},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2926517798237767935394031166393972539}},"phase_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":10889099710083649588058495528345621799},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":21778199420167299143690040106398069619}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":32192949334372269392188429587343699293},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":24704717218405067079084071272792042157},"time":{"denominator":64,"numerator":27}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4517265407624980092438958499550332355},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3119179435782918584101159843603047707}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":102204926458923219043044647941744251215},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":90272497892395374711914700024962229249}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":249978352717118593410763039139059717311},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":994107367642313884093227998294726247105}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-992709433576773577959656295715632631615},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-499399064380985420444738366591022677687}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":105189642098465020248759460154680812699},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":185601853329386830202297394338473032355}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-92729097931216021655527230274211580141},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-210167194484956685273198320739602548687}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":678473769141584386449915522249271513},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2713821922042304267192760117883134099}},"form_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":19861885572084745769674711596950597397},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":35154939899037992069720607943877680729}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-35137717168945200374228390374098031605},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-39698548704877126335512828461899752105}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":8686430557499510500558611497668461511},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":1919436667991254952816513400608788029}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":24289908886054816613655890777354545},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-24316831229276085440664017084085955}},{"hi":{"denominator":1329227995784915872903807060280344576,"numerator":-30002733908410513693829460624217217},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-543156203664283882525980321970573493}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":8824728686743839171108997119012998889},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":6110611529867966932643688869394526231}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4307168044285291107397490487727327975},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1495827087197291520604087593206432565}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":34450795156061341494818580530970106433},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":6740118397024579540213204600179861125}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-13478946129073305041928004095337316783},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-4305812284637922932238538844929360351}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":15350971689159411975657341867836278085},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":3001056910815801031611488714290853475}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":256157391692559804820787306626470241},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-511387456199811498507961812829024177}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-1500894171806275790343288382228615937},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-15355851494067384004397682449174715353}}],"internal_sine_current":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":20501054825160653700498048993947378669},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":72862824721619280156530907492078862951}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-72853493251595262229290835028262952419},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-40995703105824764406437699190715276561}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":54578452850716708497679574760480123097},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":48240705081537580771653824358432103587}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":19077249828198812513148123724741765},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-76393578348476611168854627411393767}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-24129630319173594706704620431294034913},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-853187769591717890100083970432016369}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12872689594169443007735816286866714517},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12767383702667413042949242497038388547}},"phase_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-50911362393937618217431746689978125513},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-6452094556831277624480672321823841009}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":6444715730632510399296572728188120971},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":50837427644897197306321314617641485727}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2443183025593462628653194548198852061},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":477633041856428029166414775244532713}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":81537430194795397559225577226125775},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-10173730186173764706407032977953635}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1910997812006281634608515528035410439},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2443959670665890468443462551736246333}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":3567767700211268121836540768637334431},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-14165691754819009243952687313607059801}},"total_storage_rate":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":13457843516127920722920252867889326835},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":92556500111729189891530919127687523769}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":98838019442279526612253025824101615791},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":43222944290930611479443615129146498769}}},"cumulative_boundary_form_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":181777701527999647596089607648993933},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":448186321699910953525486433438964421}},"cumulative_boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":14890146888281176380051958711950087287},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":23554792451442527331782505005875016945}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":685045340369319267636104179794897781},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":106238604955001467108440372675493423}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":60340427144493866945054274985596933},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-297653696383425573861488815863650437}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1114502450097892289739465024083325845},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":278625612524473071039743448631805769}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3249751770757074030031986558626877179},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1617920237456032418044588998088349755}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":26119498881830282094178387384706996343},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":6529874720457570513895244484255375343}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":36299424617046968903254482442520816539},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":29355339356742346891670155933198200881},"time":{"denominator":32,"numerator":15}},{"channels":{"boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2860983540396262064398166009403271441},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":510614160040600007222053476762654937}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":110187715785330654711147584715105999317},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":49154744785248243663375817700003203335}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":124447996397038930274088908834957010077},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":989327925075364620650189398312339296523}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-987708238830774004257051408246760739951},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-994258392810583552876249435095582516173}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":226002828990956871667317807846510004307},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":50337905583719671621102498181615207513}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-201170444621087914303800782412623423129},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-112869894269797130211614972128233440953}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3185290654626325364863624912958666219},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3185197664223761474680947352949833567}},"form_rates":[{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":1338267324561324090320135354750793437},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":9571536851268854321613988829740542997}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-38264319960088168760276291920796046761},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-42793162473381940683008010818197967455}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":4700406445011351379317076440548416555},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":8393832062749948234792723712306211607}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":14252674049773003744064029041644479},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-28546361508073024703842588172069973}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-8397712443087947571657088884161666907},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-4703010507916160801010916928463236929}}],"form_storage_rate":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":2805619492638322410574176811144494797},"lo":{"denominator":166153499473114484112975882535043072,"numerator":3924251294606551961279597744550575}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5500097234785455762585231514982868285},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3952274035602164219656654517518073473}},"internal_form_gradient":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":10156314527979160468797170257810488427},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":32548311047813451660402856652887388311}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-32544601464074148235659312122415438329},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-20309702372093509417770669259338492679}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":9055239579111275846111126463544336019},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":7249098331080490167527408040143892395}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":277446846341371033803285756136160687},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-553583626797104468909544429615291545}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-14502408640360673452758364996356811725},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-1132321262336088914850413633544599579}}],"internal_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":88804543682815479176744605005485058969},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":9967925995702742730537522904961769419}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-159462274822578929885217067224260141581},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-177576266011159131952331353145529199165}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":59067049426135111736631477281353254859},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":52740002287603395491912003620722938909}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":89552192177553511329322288770347059},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-89681039600480665597251113518827713}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-52764383436329381482907957774781440359},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-59099773045700051641640821598366879997}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12977036351307901750171172587720270861},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12864295036685244535009058008832116849}},"phase_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-50330239657232298756947336881610259077},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-102181257122144637135800689200784863187}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":102041002488296406209260505670672112103},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":100489246328013503427099882102687227681}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":720593069948466689767604742976900777},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1153729832350668866181181639334560565}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":88314074080973473058742417184001803},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-88105570619498187575020170364992081}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2308130021852014194278875914901783987},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2883432417101493130985130277197872287}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":3653625951687733893026555125803535567},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-3625417375431428616690357091079288901}},"total_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":58504453328786111478317141858660894217},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":101408013364397464373182488369595386595}},"weighted_phase_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":52893214343509466657168788236371904623},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":93371146713043245956481872188755808995}}},"cumulative_boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":497664006512074079460843246988766215},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":319833315857567978116878243612480011}},"cumulative_boundary_phase_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":8736335738499931799922240114355192073},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":28163049775059550175223987915250317257}},"cumulative_internal_conversion":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":235715599562471876626821726764929933},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":305108632619428658115083585605316693}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":311043844474934334188742979756305583},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-47157833730638508262894543808254673}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1560927741428927606652666638191898991},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":780463870714463799662908525285607389}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3565706098910059114682322506862736263},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3549232213041148145283536484412890467}},"phase_storage_change":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":7696473368929930445849755878763333447},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":30785893475719721738175256801797244439}},"phase_storage_upper_bound":{"denominator":21267647932558653966460912964485513216,"numerator":2545917058494333576778799492422579035},"running_phase_work_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":17167562844380434941729396643105067453},"time":{"denominator":64,"numerator":33}},{"channels":{"boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3545472090610470603719959480360388299},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":2602617633164510066874426240526393487}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":117876036059673580453447016300504173203},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":53031163887817788511772932738814121085}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":990891340324474023678990028130008156105},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":984203650909279927567575139448545560865}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-982355652476687968888435470947287439963},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-989345746291869218278913852606313642213}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":120410316496841813996648901457354562263},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":216308920369730670188714175293764497981}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-108043782620463353606982208434995444005},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-240503300056968782322223440466668766225}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3678219350042619989201337219915695941},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-919526438050804003938199481710340833}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":45809765137007264828773606790726358431},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":41305183570055125881382851961428639561}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-20639181641771892090140340595831446517},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-45771735588632129808241954141422138595}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":1262257032462110941710246775928149823},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":9094145174401873111351495963094759437}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":8109333804718486442720772078734999},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-1015524173820161162513821805385353}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-9099109998573503940772203302743420183},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-5052285940549835699586428132568284269}}],"form_storage_rate":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":3491973883629064139715329693654233177},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":10289236263654121688947948115335396367}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":6876397834636396497260827081455983101},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":5084440918144616435911129073648449793}},"internal_form_gradient":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":11812798908449757248877961801410476409},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":38609807899492020672332418987429931689}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-38604673932734226385918143736463770557},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-11810859984324279318095312406998132989}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":21074044157924891101133583252361766339},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":17206300562270950499039593326341198173}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":74456925250753218990257521695488795},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-148464453804975691278814362232357155}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-8606070849074795480816553628329847113},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-10541445136046039817445872437646643419}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":190926231857603925987909434616792470281},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":172983263406858366582343723530596967459}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-86475921645224358009057058177649737675},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-23860643093116848267793467098714023641}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":31723979361000167186367175318127557999},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":3571262458822499196190001520668379517}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":203809788051287711905529506544884797},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-204183250177040802729206708227134289}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-57171394251447908027965972694654520247},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-63488897578665450802776030072990191793}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":13078360433840221230274601086207200763},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12958746298718101227144511227419164425}},"phase_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-49706871566393590728948626347673884115},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-25260052183426815605541885396656058269}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":100876760844297116825164345495310919725},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":12402310914270257249713807303088309411}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3354038298670625405382913832116421707},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1369233893405139922370345258756086361}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":94801501608649067373580803025199895},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-23628851696500230094017470714209899}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1369698716229318447812547099226522081},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3355446201467488705575091290868831251}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":3741155716847765289531560074578840849},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-14844895134429537181547611146452994449}},"total_storage_rate":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":31558046477338914578855239564249098135},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":13765260638308123059917415514346494419}},"weighted_phase_storage_rate":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":14033036296854925219569954935297432479},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":99832848842810862790391375999436558985}}},"cumulative_boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":663858010759439889010216347630659417},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":883662034824308775003233947274309411}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":40470782144296926283444289346506901411},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":8283680347385616962050675089878535277}},"cumulative_internal_conversion":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":316298386687117148079097044125742235},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":424275216638443105831750673268952235}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":391946686474574306760255942590602827},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-234375206845789543145986322361053239}},"form_storage_change":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":531039788643942323356747809100704177},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":132759947160985580252803014190136331}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3885966950817174058889792054030720019},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3866736917408866809292444168678310123}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":35755494793611173314776104237041892187},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":17877747396805586631244171915645343409}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":45469739173256574359092677721404971913},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":39622231711020040071780787999968996941},"time":{"denominator":16,"numerator":9}},{"channels":{"boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":4311416611589083093744819349512322031},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":3240368192682109663440140675745096341}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":125257946468064247940028138810105774007},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":113512830939954225959425990189381503217}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":985849573726799423029158251887658974247},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":489374143997336498487456547487977561715}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-488334076605390435912835616627346806751},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-492038389714441461835450196378584429535}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":254794543636852032703560921108071563917},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":115214915803007565520185165664581601829}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-115083501559862674223299342165635518631},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-254420662758496103098617130910263867001}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4189732424220529672159535017511337019},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4189593068644852536690048428853620823}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":48674097980904079720690843577008119415},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":11051249356350439642551414480748257463}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-44172938457484298640767455294679193941},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-24314539607745508703995780467006555043}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":2694392064385948682894939790112017397},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":152746788361693442963550393224167247}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":37247122659957850718596455958573215},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-37332102960819444671620036521032527}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-4891000985483370219054042501582571637},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2696389229681022812839958299662721917}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":17066087983699464797299066430300374645},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":12875757078258845596742183178649192753}},"internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":4221258461862765972971296454239084757},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":399726198382169737391203128831177809}},"internal_form_gradient":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":27156210420943131200471590220412988257},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":5641013062424138588873190123503800599}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-22560609609485823508665170877256536047},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-54302417663697030807758956640528504483}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":12118048735173561606654991155698990233},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":2515103892100074981984544912324954961}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":159078540033117896090651567421672913},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-316956419765448196241275398470065169}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-2516085284355406437987068173590273849},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-24247536111516740044009254727836795405}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":203948022273902102373401303831150894617},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":186192453884778535615224856174851511333}},{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":-1454321357162459603494001638711987441},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-25487201410521494434073706123951828791}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":8464682315365533559960005431428677123},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":15355782021648993600805620607676081843}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":234030573831763004408490490149925701},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-234564520809536272287568084334072697}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-61462131058779979377645590772470440493},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-67767652761476343506182158774732540041}}],"phase_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":3295543694821879453885171879838355867},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-6528063538938230347623658412647970591}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-98085691885872459627387248481168530773},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-12476705991684335106066585235896469253}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":99626279167351422498937549383957571461},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":97866044100606874335493070773503094317}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3857294713662724899993270362538522515},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3202329734539135205693112497818966963}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":101272543944450690858219038936285997},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-25222590475190398830341064281939729}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-3203579281967520043269218607889922649},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3859115229947123877786075430067425061}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":15325009453897231340016879689685435917},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-15198822396910497084254022406970237435}},"total_storage_rate":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":16914822097401959578290393903819641477},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":59340978647165958521631877551080090317}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":118252488795516211829024084800256757171},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":105806200216073071446521571923510987881}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1731911328855356318059009509278099025},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":37107704777758017373460847988294131}},"cumulative_boundary_phase_input":{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":1448195262030857434551034636038456549},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":38455635339852822190050793649641399071}},"cumulative_internal_conversion":{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":12976066621469553924081618899124087},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":574172541031756757353451846580643913}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":484519386648638120878859522781240729},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-286268417401525520282818878694667537}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2820311021600408191536510351567940747},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2820311021600408179775818970976647087}},"phase_integral_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1052674400564587680272949239019035035},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2094253444180427220920994675523968335}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":41005396414563070008860143386629656075},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":2562837275910191871817763456813836567}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":50498331190717573782023598141796751911},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":45193903302923924390926204660069321741},"time":{"denominator":64,"numerator":39}},{"channels":{"boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5156553826387044030820786150883232733},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":1977355332038884953634019020200318303}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":132319167641780300321569238851791604175},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":120650097981438550943399144414962371657}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":980473339864974153440163528972845853007},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":972978007593187375781066061600915813469}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-970664551232285731759647671322954822597},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-244617197785435200313896394144295118737}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":16742845474975082707731915367532424125},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":243677598497519333695408992991704278723}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-121686746147216729607783787547928817599},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-267454628079447674635566523679365975789}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1178756665609281201898061277755516831},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4714858400287678494431174995951459677}},"form_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":25705776348941378482645328257085554779},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":46980316172219875474109525185462879945}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-46942929269195837970175859339492205701},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-1604980673527276314463738072270051817}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":11437977858073387835374549242735804317},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":10438549672812577562308082426004238095}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":42332447337559213999245259210132523},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-42450627214442484399921108820511367}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-10446160742146406444999825157604049483},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11447605886859200608982121440466606247}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":20516509068223580993545648445068564603},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":1975085996158733173274309486462347447}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10202438716783455818984078585883773787},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":7892061077630916371417327253245224067}},"internal_form_gradient":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":30894745125297629209922568290699370707},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":52085663194416160887486059601167032967}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-52076678551890187642088810263785438451},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-61776872349596457344447319546647050181}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":27588058801952974353618957460940969591},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":1452182211855362311705558170545107383}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":337979824263142134583991558909652805},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-168205591409283298444918882557412289}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-11622592913185901675380179503170026125},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-3450316023960111673291362892880697209}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":216656941196337628969145826627061146889},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":199101449952395815232340510404066828515}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-199053192895839318970086631012986398755},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-216596139258813728282494663247398169703}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":71866934421692147921618740062711993227},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":65587341932480267064242036193628639971}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":132991305564152828859752008379732485},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-33340644649292864345358931071488143}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-2051098865359078306973447411043881309},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-35963714555348134427286067220933699041}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":13283576229898895916519306499858449269},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13151620344087007125319926588499290761}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-96680104415765823107215530320900682003},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-98504991898479722902833752803275515557}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":98293255973345580685507330331972623503},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":48217988936499751194462901972020485473}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4390775928640687848747864726675530095},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3697951636590446158718322540013127201}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":26895579848404586432191639552191845},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-107083005313932329342451249426474645}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-3699586227356736415622008606260015715},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1098269700884852314333791883580407827}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":15688225253183481276544800278241966873},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-7778050552611073086092175125906100359}},"total_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":72123872281388786017240010387002805871},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":127076174189332242211026460901745868923}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":123731235494553991040934372328937047139},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":111275486220062376824831985010047089347}}},"cumulative_boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1107669125039570847974229105461701047},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1558200677645547484757125701912971873}},"cumulative_boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":26272354684097944741603333212204170507},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":22055554341366377132761314272046380121}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2139175842397327393797325902801185033},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":189785680634682839952136363519644713}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":589104650329352195616659443708299409},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-688923319424106704226724398824879707}},"form_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1832795386526181199995438026889214493},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":916397693263090596379764928724926855}},"phase_integral_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1134980440445585444456902689159956565},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2257284660500329090854306847750352329}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":46511854602117768649552913397931401469},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":11627963650529442145470240455187619663}},"phase_storage_upper_bound":{"denominator":42535295865117307932921825928971026432,"numerator":6973670710002848481112048863654377527},"running_phase_work_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":25513211961559213381794787758125591655},"time":{"denominator":32,"numerator":21}},{"channels":{"boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":6077441745960535795101414351189400121},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":4743353174930613739766399406390856711}},"boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":69524537645210278414827304987350924645},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":127463620196628919949002293122091051969}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":487389043077001098199638445430180870733},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":483454508742048523584185841117977819535}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-964363756026651405955045460553155116241},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-121567488270725134111743909263531568107}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":140031216769386538049290457399487874253},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":256020625667959154799864070109318162247}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-63919294087914932747809106756010528859},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-279575892815987013592551212654654410731}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5249915744247658880988832218246536021},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5249715393110795681402981821667897503}},"form_rates":[{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":3376086466464897372667146612033111029},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":49626285969891192473300452340223437833}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-6197958305808651672812864339158886649},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-26979047346019551214930110728329498989}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":1509783009927515489403592342672889919},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":1385172215595355474025622877820707013}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":47680500008819648624720422942681513},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-11960226266114468611887905951874087}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-11090552429179501011550283092465342517},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-6044847197371094922807470423484153991}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":24314757722836197324173880511960237269},"lo":{"denominator":1329227995784915872903807060280344576,"numerator":74468005911507677863570648927757563}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12158641414535689624274239244795033389},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":4789067814363655481826124740465993913}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":69663055504036579000507757927450918131},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":59464018199473934404558338928982443137}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-59452571569507358706640042507912731177},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-69647452855092899637396564403941368275}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":15560952485294726265224089945668381763},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":13270458766609648128736001211518660765}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":714537791713191399451319491701020693},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-710518004686445562563610585958872891}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-26554038398215127098638311877054461375},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-31139853171530622587199069287641033299}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":229039411625869104961723650514123811823},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":211696100615910037395890838363196733249}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-52909467596790874573297159625995179379},"lo":{"denominator":2658455991569831745807614120560689152,"numerator":-1788806006583206015496983418484447193}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":75889971400047496557680826897111773197},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":69626349703537055759787019675914352971}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":149792708547195879833183071856715675},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-18787079486448449015171887731880455}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-69683996071525512059275903572920140455},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-75961790189335530914427531747439916635}}],"phase_balance_residual":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":836323593976481543612190777053342317},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13243850597081578205682256161976532827}},"phase_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-47600376672789803297080823088546635227},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-48558919465504721912774254024445560253}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":24220393795933920215296889520737607159},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":94932348209773578927996879802728271377}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2476602507252769450462148069960080575},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":1056029554901551057671877821020051421}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":7107638848570096238550339932030447},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-56541226300819133496456309500385765}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-2113103235063966064872673693781835801},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2478030779702466361805863462465388273}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":8025293731031492459080947443618483765},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-15913060204383995226463248219781384767}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":153000914008553132346696986822109732921},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":135290898577957633193394190457299264765}},"weighted_phase_storage_rate":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":32171539071429233755630776577537373913},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":116227089064611667660320104331793328637}}},"cumulative_boundary_form_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":696274603440735481684803951586852089},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2002890037795292522860225646262114689}},"cumulative_boundary_phase_input":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":7382829346554294135574590783371561275},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":50085965879449734888132111034190778303}},"cumulative_internal_conversion":{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":84659754959490245154224402106279757},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1967260552674055421038290102575844633}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":44121739612648930678523797845577337},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-409056074097449477219996827455579793}},"form_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2338049212135865417377448257183598357},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":2338049212135865408617201509418600497}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4873615798985011005970003279189854483},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2422452350014619845175511921458178561}},"phase_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":26125234759865529024583466722989840281},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":52250469519731057973207412321480288445}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":61319025412226268919380972489705682509},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":57095374219760297663558436164396645567},"time":{"denominator":64,"numerator":45}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":14138911475698806617270791645567274843},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":2801392351300937073899896707549864215}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":145439185849820640881982928144270155739},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":16743124645571312557041653437054357135}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":121097485606100828347868043940937422941},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":480279017546370800409391706901602831295}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-957785178243204757570675295949036769213},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-483154449271667397478914320562906144323}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":291299811149074227019928098902259435543},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":33429125098700199249502250718197442091}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-267054058652984813011615317470612054175},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-72690258331893963747395010819339509817}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5790296618935326509214416573723339935},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5790060992064536031629336170435601173}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":56487613483535402019726745062489800293},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":26069408841460697610657008206596510355}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-13022816395176277786642906909007141977},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-56421460124893864502614885728216203733}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12697474849898556835105572778818384193},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":182864278672166186010406973580111525}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":26639027225414809865210394763342155},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-6686392173796245421364961496629553}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-11714209343252852718658128533760269697},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-6355432391151709158031316542160160127}}],"form_storage_rate":{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":889136422497530799888448508781422073},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":11330375811020851600493282889567891483}},"internal_conversion":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":894493821150464538459069394000256831},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":11456499495781910791616348877082709541}},"internal_form_gradient":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":19478295048226920765731603292048656529},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":67243975425530358950438872436212810063}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-33614849259636116890747596027253158397},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-38947115110030143627459163942180690809}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":2176834333842365558685559444160716137},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":15015442034404308247228096124026401047}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":93999776900131041339477983271342951},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-746935500072552073979247490488835735}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-7511824814927034734499904536146595733},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-17425611872406171864556933625629761497}}],"internal_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":120541701733504738400118943173134347339},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":55990944752242197201955225290868904833}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-111947276570314641434311634304874989441},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-120499350285976106723276692729240281639}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":39890293707582468760490236452260044023},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":36767044766750336043681159272082464645}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":167377944460283319373417645548285731},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-42011841064437145257119227411934975}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-73602548030752157373627815042144539383},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-79864718841715291004286991319855341465}}],"phase_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":6736820402451232216713603261044872871},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-6665743714733318440672059959987340579}},"phase_rates":[{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":-731652560687173349977073103778772127},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-5978495681648401766012212306450421335}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":95395265943290973680989332693763392309},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":93359329173131596641638536387130013717}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2771631556185324667995535706476803497},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":4779563644970541611023625117109718605}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":119684233145529709098823743073961729},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-59439238503681704887782596483613119}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-597772025467999712966552715467748667},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1386686132947130004972387473263673025}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":8204267890606134559456430834445842961},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-1016634173681603193077793416468055161}},"total_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":80779551175493258935422837997762999931},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":71655975273306898205004512563174274003}},"weighted_phase_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":66553368415532766137207661857260246763},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":7540699932785755825563903709200797815}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3447859889186323486923784164733374365},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2528151103664218224216456278927714229}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":65880096609144695625939676023735153751},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":14091159405384744274255682768271540557}},"cumulative_internal_conversion":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":211248907785408515548717682056321553},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1252141983269416244697653228094548321}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":208799687650531424100334546838043261},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-120026074118460418325073533852839299}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5867633820805176410013100922468983915},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":5867633820805176389102678806811804821}},"phase_integral_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1302927433938282999951716035320586713},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2589723904940145186558952815988013159}},"phase_storage_change":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":7274545604090696606006264037683420529},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":58196364832725572763426463935570030791}},"phase_storage_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":33531469665766522677671376227836196229},"running_phase_work_upper_bound":{"denominator":85070591730234615865843651857942052864,"numerator":15843953160651465784136092391886514277},"time":{"denominator":4,"numerator":3}},{"channels":{"boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":8126885053809088088395003109516784245},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":13056716885311956414961238750489691647}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":151483122746761025773642861295956971737},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":70043949906328889373399151434516896711}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":240623835275938502907652001204872902675},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":953942196074081904900812589041552756825}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-950948613506731648166303124688608939731},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-239948768302695698565492432328990047173}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":18848616361929450953926851656233997725},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":277894447847051741202953206548417679367}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-277485916520193962279601216095417654735},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-150496208052311855928684079661207427843}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":6332194720345476459111394305185050195},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1582980163879014728905929552251653927}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":58819029648436723116045682767834890987},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":27257291096997328538228708306446513733}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-27231309124288491923053799764970486671},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-29373249542518546056509424756834558787}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":6647363933629066674845532302902562223},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":12303462514040259498988954758759653531}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":59111543962012988371221869988091881},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-59389217809398006465581094223196975}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-12316231030646459306678454626354056269},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-6655113542537540780282552908223178205}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":32917040644063480035494481379620765281},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":6645798087235494212435557828855595069}},"internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":8330671448419929794287971652697713747},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":13528129038406047161421848323946023439}},"internal_form_gradient":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":43259725318598895397898067655222198133},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":75405724396598210882026998836274710517}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-37694126624448964802624499256196360713},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-10812101157748550268131536483464163731}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":9675471176549217775115255699450984075},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":33696587123192175364764874653106144685}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":788294206247250523427545476345411799},"lo":{"denominator":2658455991569831745807614120560689152,"numerator":-6109491314822664790721335763012903}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-33716743063289361643702816135461603389},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-4841015075869913022407517447592664165}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":252778432513555929506208718015128994119},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":235893384955459960901908222435221961225}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-235812167634790630163841370387722224741},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-252680293744392404417984859525460003171}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":10441654849813412897298363728946097983},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":38652467447826287588696701834085792191}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":185704392253410104301487617486490703},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-93288365186224445283342104354519783}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-77385161851587128367087164297078321679},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-83630623256167528242453466557385676273}}],"phase_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":6779846938443165051890398613839890833},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13413261721566739727185948211293128939}},"phase_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-46018205895540968574492947225308455975},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-23530782910739771224109041581267481795}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":93838478067411939655794162287753953093},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":91721185140172238784823474780187138613}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":6159596257963857456736810165344677913},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":1340744601495685959044086944607718901}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":31365229883737990432646990135274127},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-124461535043971843280392837531489737}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-5366186323481875169744066396329135265},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6163771831256667106844161006688433125}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":8379337369398997067869048275707713903},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-1038248032415561638478473214928146287}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":169903291436767729297497638170938912875},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":151124924335730215734777296076140199635}},"weighted_phase_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":68493125396352124631001578395659073797},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":124541731986788238885035064760717819359}}},"cumulative_boundary_form_input":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":526219420372615686901351963281321611},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":785046176915804045291941086339229631}},"cumulative_boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":36490433993949559354539592573491568401},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":31465628962628655237889450760036060647}},"cumulative_internal_conversion":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":520122871606988083374247531917694439},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1569207507607057975043477798187033245}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":976914532751158234879432071086153151},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1115224080208339820707497246299914197}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":7255514255628490366134152012817138165},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":7255514255628490341497298715292214203}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5554088761910230141272051471452240857},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2759044629186683451289224775207291995}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":64324363714311635950056972736182806639},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":32162181857155817928206890000097243161}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":72996358797991900962124015670738201393},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":69842452972685002758992229550609070311},"time":{"denominator":64,"numerator":51}},{"channels":{"boundary_form_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":4621521853367421177418751660038633259},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":7514391230472431874792789628572988683}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":157176561433655801555166623967450264507},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":72944006501212655013538060095726846055}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":477970750655633446206306699198936989959},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":236769741058999906266882137417061048315}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-943874129248214759325666928944282445649},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-476509074585517706070485515182012135587}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":310882334647755806620113423998814874965},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":143695112961127117595160483463243609089}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-286960157945777656780319828186259699779},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-77564512727535645183119401973106791319}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3435902138996299405087579719451395427},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6871488665711126599065120831449184063}},"form_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":30504584988462555290359821245859359019},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":56750998504141840683574898005657132149}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-28347687793823067521506584084941279925},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-60930995351074384979664756505910519095}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":866825683827014504090438388844212037},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":6440499000930811628895442163347451455}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":65167138070952091116654241186747017},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-65522780807996977049102132602561017}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-3223946205284431340521041662496896101},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13886959505683926832989862456003015915}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":37692957476670789156242349344589713759},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":30819107209390660548396712863091235115}},"internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":9602254230816051218893413527192943071},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":15792370737733326596481610648540945539}},"internal_form_gradient":[{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":2983158894842333920401788416963364593},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":41964474723934513026673840097289771379}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-83907935277349662475795450509516281077},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-11929304739791374293886322330261860131}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":21365412681471990040338803726422631333},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":37529567488022695339477339573230322809}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":25730707851719182100672828197787789},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-407850311985450883741015401857490777}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-37553901913657775252443526635008122359},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-42761833851736066906769800475477738419}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":264115545955600901984516358101824345955},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":247475334031237820675164564864379061097}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-123690584185105978492844658809067030437},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-132001525601202408502967371414525708123}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":87142822408124723719100479144380680153},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":80933697387106562950957145031727861853}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":409457204438349639142553165703849483},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-411691773658355199658990708827464183}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-10128325714090260947707900530045644251},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-43627169963755571097967422455818851615}}],"phase_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":3409536017744853281322360374205046259},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-3371994975564475990326807518243123591}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-90359463442629920731689538166029109071},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-23130851344539586242483111109111425831}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":92215457755223025649199951260674422143},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":90022247193675263417041241626152085813}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1700205519727266751585662867088803261},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":5973016177819697465033710793326975509}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":131045419003345629339007753145714897},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-32455696597028096797223969952102639}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-2988444560973411283798383928593583055},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-3402878616589068629744819924704532701}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":17097810625073236094159384529878035287},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-529604088877195459970847953080523057}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":178014606088443409870821083978477704763},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":158715318003055231545774496109028059719}},"weighted_phase_storage_rate":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":35080412152943155178644683658471997751},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":31974052698416142749344445811484206151}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5076290710487316965976831642507816625},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3844658885520006669429588373035636213}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":80348519305101734406977620645457367951},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":69769758534745996883298094654046513111}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5061194306994909468765237773515893925},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":242417649596585352143564443470276457}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":565531716889875658023403458540743067},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-641540152318551421831082572880360457}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":8854404712845123619773426385641545659},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":2213601178211280897769976067565747409}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5900595222703123292191159672936354519},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5860677461102158168956831785646202761}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":70609159450454210706724016553466973705},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":35304579725227105301861878882143370939}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":79094329304905618946455189206151511171},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":76469836911556368772680589549932944639},"time":{"denominator":32,"numerator":27}},{"channels":{"boundary_form_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":5205196284448166146143235424837507187},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":17108552004668018353799233471200205301}},"boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":81258577685896221808114267654916886151},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":75671479919399517067202760789090017833}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":474567881287749064821411978873153930305},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":234996510894302492615794806535595147063}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-936581955570518092177019015042605244757},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-945998145412174919387303522741377379497}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":159602186460601148735215036777641901849},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":295910977983485519705229692087526678219}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-295469626538264153049306503259091532797},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-39818924030058295243818972531301832369}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3702761651290647573300539321739649833},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1851290778354393381293053039171236335}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":63056304431522375075542094913863844517},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":58846215194365855069373864304807105975}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-14696981258175185581735123544887217233},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-62973471226580596962182153861466267091}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":7210090923931452307582339415422788893},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":13435164221907029600638751247094835665}},{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":558053270646840319562063187460035},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-35939623579524275118752972476169841}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-13452105907495032122932574273603948301},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-14440308416438618120846277163094167947}}],"form_storage_rate":{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":668141927855358853134328373056519779},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":35353061026300481740486722973249298143}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":21937439001925390681085993430584214735},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":18247008075493653100196703760937760889}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":104717037225761636050773348091464743979},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":46396469571178869483520338597000837485}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-92768059865975686898883850753455883963},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-104686113372680719758845605749293703649}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":46907348037102895151356422588904383499},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":41521176956745961942483201624335844433}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":857223952398680993827881199973346215},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-423970834658866184884671636676940847}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-10387526739848386039605906646700754061},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-23471751723499614959779552167886753773}}],"internal_sine_current":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":34385911921571794243166470152406878639},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":129350767027532995813528733734617847957}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-32324189208662039942398456486781182093},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-68739897872238781457890531303133375989}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":90604674713349981283024870021506369413},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":84415626438631109716272424757258194645}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":56101633772027844842554235103101375},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-225815314820431941856642085243122897}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-21130518547149125829363959703153540985},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-45365566836654423379254028629098364825}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":13707890284647293328392386720357710379},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-6777268060095087365842260696990910949}},"phase_rates":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-22156198528714787237809940912000120917},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-90860795553769622987776265745436562331}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":90530523806265551941813051132664392601},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":44133445141127049824664256205700337481}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3732768153718419830423284538908381109},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":6608300555659419536395492713739381477}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":136431429361021669782666206251834547},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-67477054062755214307137785601879145}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-826613113573055483171049875502569857},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-7471290619641354970321070410110360597}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":17422982660796850894104175694190556199},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-1079329269198500667247965242563769587}},"total_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":92937247252131951691154465371785398583},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":83034336101204548762417016564081743829}},"weighted_phase_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":71556705560760468390855957433976765655},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":130715611176108615784347310154914189515}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":6052265013821348118378688284664849223},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":1161655565184705007440981860499536459}},"cumulative_boundary_phase_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":21991627740788626300372083309526456507},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":38431979888594850804174176739011851141}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":6089511760210162156941143715574528991},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":4734010897084130623368751584318380853}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1297529450597708036981250244107476581},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-731807082805425809140804073785103345}},"form_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5339081304210329345056964635212001635},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":2669540652105164664259555963167292881}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":6251031020272371253529856350347394607},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-3103510514409231992931555672550509595}},"phase_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":38512739518625955352468533056398283949},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":77025479037251910592256470308686425985}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":85331855980953989251021980448590964179},"running_phase_work_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":41616250033035187289059790826893722587},"time":{"denominator":64,"numerator":57}},{"channels":{"boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":11620669521693146762048186239387840121},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":19281208368202128830183793054191779585}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":167504280246706742879125937385410197991},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":156453612060625230813489889270692537213}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":117761973014203050949607754335966938249},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":466340646570459047674690898845106951891}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-929109068420830020874680732216779170423},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-469376708232942960570868748853653721517}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":326540315100013909718289289770396521629},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":151726267346664632730945141265229175195}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-151506180460702799635819408917124099855},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-325871095356047512291759710900622610535}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3964991494126492809533396628374834863},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-7929575299087917500834575183463541937}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":64959409755286180476668575279941206369},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":60799085893539809297920521437994356335}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-60739360987760928212257744803780027701},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-64873157478580513095417571737618673571}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":14946967729005542505089610546022240213},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":6982637138919931118485950864066344577}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":19472113653506201396454225915712199},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-19611466612568668816249745854049039}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-13984496984545774657913137259050373667},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-1871198490287775269500270310892220919}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":48099534087911184986380573948308045911},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":10041633486857878744639981822422845601}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":24854770203133138955298129994379244099},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":2611042841432008817141248454670824575}},"internal_form_gradient":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":57133051308532542524790980843151800875},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":50988346465252571347130606607935512367}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-101947665103238306588130783095815195569},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-3569708878432889871931509119074263161}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":25611265660527084360386450054061088891},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":11415654897019249372761855075011968627}},{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":6951421298106391570151476893281201},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-878691549055232951493589483420541671}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-45696529148356847570550245413769787985},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-51264158472356149064659974549302726125}}],"internal_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":142843849153097364860044503795480635753},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":134782675035514609496186049534786031317}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-67360657466814764740499607019220504265},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-8923250296674980345394057614996056649}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":93914568021775055664711073503909786219},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":87746406153256432513098594342166582261}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":489387593629764727747624108020476895},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-492889915489337902524394324251160129}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-87867185981595243944559647436628812733},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-94056694887942189756326085096994376825}}],"phase_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":3441591402479137896675552600479647055},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13610355160889012501458117703229012779}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-86836548715577669817458336916055803103},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-11142425512305347928158129499688275187}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":11098480978091074909847400954520076369},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":86461281921219498787666822861233389115}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":8152319057425202637347431871993445107},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":7267431621967259774431939672713257923}},{"hi":{"denominator":664613997892457936451903530140172288,"numerator":276588265276977988135898873443031},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-34962025871303739796098807440237435}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-1818207124025967627077862324788651147},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8158944224321747035811897213732753747}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":17729921126492468787600861301655610447},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-17573502988299861584124550529679907217}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":193464741555319828431274543626539927245},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":21646514537724146852387219916813246377}},"weighted_phase_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":72682603733704321722446984839115940667},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":33251395588590414960134458011203647153}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":7141702781480080627320705744607459235},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":173450903218696713083712273169168297}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":95818274099718883773947361553046929059},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":84197722842531509302730692037587414963}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":7254579113482028045470743559061056059},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":1428287990655283482449179938704985017}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":369029408830223928792524780553898211},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-828291697010892123454513439541002729}},"form_storage_change":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":796231156308770278977850726153057401},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":3184924625235081106470605606146627459}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":6605094649572461482117559945309188979},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6556883758475807227427132310576226519}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":83548238378621942739377508423835547883},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":10443529797327742827090438685956345309}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":91684061393186906273643845986717381749},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":90105122137097749844150641798226988991},"time":{"denominator":16,"numerator":15}},{"channels":{"boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":12865024538265526755916210964752417527},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":1345661861739484933146007999446274099}},"boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":86069671581483156334239793029687418429},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":161220478987751784822924797517666416005}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":934839401305364684937147612976532194645},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":925182645305663358319767963771483087145}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-230366449633377475291786324522402497947},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-232826339278867427792249827081628538901}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":332891456729895226359732337029774778347},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":38751959830043488671462957978500598371}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-19349457195957541088470116495048611413},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-332220733458601813683858295955085626103}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":1055258928742284172523435940688837633},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2110403362236858668441754862334985867}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":66718139032331682222176558386647124417},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":62609139449518490640479051930292283883}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-31274725127211127052127263813038995005},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-66629958061364205542378599225238425239}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":7724482037196387061604039354550120223},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":452209672808242958809248305466043245}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":84525874638621338980481092020534055},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-1331402447137931715015511983156489}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-3623081870078683905937403637685415749},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-967136188593323388647788007933044311}}],"form_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":26841974539957176401560088892322715265},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":1413696036549087056649780529617583287}},"internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":13974918770993583487363787233798886799},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":11855643931072160246298281133997171941}},"internal_form_gradient":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":62043505763901090746066710206841917059},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":111459024174580388792011437084386124079}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-111425615120232245642834275723551418451},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-62023473578605293040427081602292578675}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":13916848338608634263769615603859102789},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":12486247891134516390617425065231879709}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":921023686460863402047138297929754185},"lo":{"denominator":332306998946228968225951765070086144,"numerator":-886629269499480082351550957833191}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-6248027352599415918601696218151068445},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-55714754837610409626910161618197331429}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":295912189605571722477468816806677847469},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":280061558986210695719503354710423118187}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-69980841270199718458548659810399118959},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-147875913402565808207211743292244895331}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":97068704083369958348176330008450220043},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":90922149502503690535924613481686459041}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":132772933401472308963550902543895589},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-267694345401599956128191445682577907}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-91057979091148504641370299967848923125},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-97227134243379761514682509932112881659}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":13813464920567775189677648151726939009},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-1706915041327887795169623225175247925}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-84998886670054215005945593814281812677},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-2730105355525693633754538178411386837}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":21747985613241641546339899601629975435},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":42304383970399820713053449901517812639}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":8859740821399181345916690963998496203},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":1987248072544812103930605203780158199}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":146585472404966367402014544041743861},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-144498105273137649110498562660396841}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-1988808875479131027637277664936862271},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-277102457361212034483149612673000325}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":18016986670663202087734123477634210357},"lo":{"denominator":2658455991569831745807614120560689152,"numerator":-139518625779122582445257758212019509}},"total_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":100384027723123372920497524493220505973},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":22501376017471209453414876867217646845}},"weighted_phase_storage_rate":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":18385513295791549129734358900224447677},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":16846591871274861226815754748747313697}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":8347798831942473760687850522552998379},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":3279837649651454259269149370499045539}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":103887305810482929680282342149580124537},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":91754932795082374216305291921228028213}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":8564727748262676497411098612229701697},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":6824618581159148952887183611132174937}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1666559965786138210832753040836991717},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-930836366978477309293602655157077019}},"form_storage_change":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":3762713461562048920564558848241814433},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":7525426923124097819755871912234273019}},"phase_integral_residual":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":870310358546058030021047323336162317},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6909999314135618901237921302448991751}},"phase_storage_change":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":22538171978797040489765642973921906263},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":90152687915188161826157237235998957849}},"phase_storage_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":49063167192534988688735657462208861401},"running_phase_work_upper_bound":{"denominator":10633823966279326983230456482242756608,"numerator":3033208975916368147731098704326498425},"time":{"denominator":64,"numerator":63}},{"channels":{"boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":14134156713871891130090869334193030837},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":11919727931256617898603296659491006545}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":176425471981934081369553304741589404813},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":165645216742891914622241963104833893477}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":927384543032908637533885624564464708069},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":57344251753199694898781029645538461809}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-456829280260311641507857657139135869357},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-923675766626262803941544565461230136259}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":84565944588977291428830771943294942925},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":315605874648850197493174630047171121495}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-315214046744497560904196146432480538343},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-84402120685911029206666743314720154695}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":2234737924419647338001043597325147005},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-4469220393948905723695296940149461879}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":68332786707685842533610743288621517781},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":16069136383617043744986245827739552303}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-64218593061390427691590971866910386659},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-68244410475810949079117882617355165657}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":15925633326657412323648507035264410939},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":14950918290025477927919357002547252485}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":22832234247676391342952723855858127},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-46078970216392427525823659456674563}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-7487516207452202760922441636994231497},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-7976764186033946751088756864596271871}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":59487878739346515120656517407309962555},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":50544662032281144375677795378308709901}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":31214789392435173562886650590221571985},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":26709471179154689971445749699027361445}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":134158523314174126515440573108704056327},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":121218658764648093293389504671358441187}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-121180698665152053981020192592052541991},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-67056869942713856376281123826971845831}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":15058231877396975992996812087198024049},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":54359319356329729072362722448592111929}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":118864939389460753540798661579220685},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-935554820896226226222012156571366277}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-13601035962406925309517002492154102981},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-60286211238751844683633975498896459265}}],"internal_sine_current":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":76439390951160796397076368704269490171},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":145093147549397474344331373878721900249}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-290031933812112351810669995743564297677},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-305579933054477894289582049852928720001}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":25015926331395853229131841835292416011},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":46969695064365315157429608686124425911}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":573836635020331445942782524147136953},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-579045417267205342195649430042983531}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-94090903643865401897660089507100626667},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-100238975065049655614189805278450786125}}],"phase_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":6924865418081853631255477225316645219},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-6844979869041263196332860086241821139}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-83115963898323314474855854558757448057},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-85536856955561658831997353221521496199}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":42573685624292420449937992031882946621},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":82712274377184205212166790964172989197}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":4793184075023359953993760118824122871},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":8651554378670822624135234831257676753}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":151343541313209716374922980039325529},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-18612271784885902293240758868858691}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-2164672104587696107011483413348032343},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-1199356064866191356973446641147833127}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":9141682160280906511537113974369833959},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-2265385289087481781076926645198544437}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":207768036925966963442522784372555574485},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":186570703096978009381119630248387110991}},"weighted_phase_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":74140079093310224160933133482622805965},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":68013020532348432502720917435039200545}}},"cumulative_boundary_form_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":2418219005966990888533467380658398755},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":7677149792858216446532357802825372941}},"cumulative_boundary_phase_input":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":7009828113102255609030009581833882993},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":99519552329905432714222883941767116969}},"cumulative_internal_conversion":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":2506980250258268814542852589661584471},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":1009578130335253130662337891034260313}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1868521644425979597204470753567725503},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-519625136233704442821678890162822871}},"form_storage_change":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":4405574119991555272258882921166795237},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":4405574119991555260254641080157160355}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":7322916412550371263474143024998158317},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-7266077025531336123081038398749930755}},"phase_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":48407273870711364359762808304059468701},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":96814547741422728576100411782318114629}},"phase_storage_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":52317234453788748383553199563997284183},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":104080624766954064699181450181068045383},"time":{"denominator":32,"numerator":33}},{"channels":{"boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":15321340516447927533952227524061101741},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":1636907583125799228235218250154482159}},"boundary_phase_input":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":22545828388244225374830914350813100581},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":84868515072397771121065941878026879269}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":229936367881306968433506899980108265337},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":909708423759984677599328489195541085383}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-905726930749980963056410579189372079441},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-228970656395277047093142133340442570031}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":320232971937118174394091188041932402847}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-159946189677404193913847627899671579895},"lo":{"denominator":1,"numerator":-1}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":9214358634268461693120481927067149289},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-4606896167806875969522265918615442007}},"form_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":34775581954305499301821942843191298623},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":65802076432206345619254668981016026623}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-32873890272080643583885302243197554931},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-34765216178973814551054638984970981641}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":16376503151798786741561040165194525713},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":962838386141734011672410181574380783}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":98283596138517608659276358300670351},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-12409672371443854872265515085513697}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-15432110925133035289160250640667463963},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-4101786696777017144834963413916080625}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":65281059036382781136970913323947840153},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":28030848975667150108557103154537064979}},"internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":17316404627026098544127141549091405245},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":466815298001586434251358428037640255}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":144423235059253438582383269492170690979},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":65619179736558287237127375193208196613}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-65597683193420898425215078001677376033},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-144377229798469308448769480272552743187}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":64900364282335952000482600753020753615},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":7362210209802226325882845576125636461}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":979442722118654259598385193663492539},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-30049941038001351542334140623381133}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-58948698613048620076541450322856692913},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-64956190303666661298685991335564037625}}],"internal_sine_current":[{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":19701369364424824067671591978878564607},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":74984246948500602201937128045301891379}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-299765853687304726838794862093128968447},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-315026519569012486390796980997315802965}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":25724150996590581495097533157612708223},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":48397536007953986522063016118903351743}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":308767023597153090129402639903553053},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-155944542222336969299687433478164033}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-24240703155890365695432263212934832507},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-25772285906374043801687327078808121035}}],"phase_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":3465061420166419353772805236127187107},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-3424944316961375822989508106324075551}},"phase_rates":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-10149910054727938648222380030991890285},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-83663203030805675121017807415944192725}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":83257904054665861751162566489673563293},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":40390856109323123186464404009757958405}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10329213783998455114735677520616622879},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":9373857175773153211198907817289483195}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":77941575350282737869285723757469195},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-153043092986173291525294269527181153}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-9381976773101042636695445712006031539},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-10338098771246391088215634549308921543}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":18317974132983473812044359167802063547},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-1134808713844286870927201284922084503}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":214245525607791803705939734926327536629},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":96426184358670534065858274647936828041}},"weighted_phase_storage_rate":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":37241116642852255642242205400594924119},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":34197667691501691978650585746699881531}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":11109251697284956760441890853014323309},"lo":{"denominator":2658455991569831745807614120560689152,"numerator":69568988126582545841474777269072145}},"cumulative_boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":60305967727613837130020873095448520303},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":26868993904485680939205703998208034225}},"cumulative_internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5825666967408385998341664939436828563},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":9477070936686784348052778412387003269}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2081532723865291662556902936276457505},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1148575745673543466164056425140657143}},"form_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":10231717070377320939159226419552347667},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":20463434140754641824797107881606666149}},"phase_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3842744904371618707052268457384352459},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1906183256667925222979424610831397861}},"phase_storage_change":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":25877532872967297293561005757181796173},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":103510131491869189020071269335184445893}},"phase_storage_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":55592396012638584744149531270275719425},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":111134864518540889911988967778510037337},"time":{"denominator":64,"numerator":69}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":32859998886233869021089610031099697503},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":14282487600459511958802780192122755603}},"boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":91984450963173989235973844074939610115},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":86750158842088173514361158345441905123}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":911942070949588860612173798243412419603},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":901783533002017928666578703117881918781}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-448845408912459096215549327923541073987},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-226986467475341007542424618570974734841}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":161955441943121563083661202764127933269}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-323642046095731682331517284110601187993},"lo":{"denominator":1,"numerator":-1}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":9294724735065536723278302233825272071},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-4647050392352391084604314395516115673}},"form_rates":[{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":1101794700499277394736859041536644291},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":67187065756051613452175420290137955885}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-67138549509753456562832581931193671113},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-17623051077582092704957464538451424317}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":8400582209383037551270419319707685543},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":7916887091144693025125046505137032811}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":13171995685018099576562399540059447},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-106555002093366667912768898386885701}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-7931562247241192200088472483315501689},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-16834607358595364156759975853152659643}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":71062316279337636802810315030648261477},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":61761771318651325999194236421015079263}},"internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":19097936608561119573656627590473806553},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":4150327042919134520240806551572184775}},"internal_form_gradient":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":38718637008927662212005800497773692793},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":141495359849324099833679312483141597683}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-141447745916581007760810704074850760643},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-154823645258172683898207245677431757805}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":8707584315758550542510350893449923605},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":15887770001619688249493582867063180785}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":503284749167148640144462340725273377},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-986009934142205216067634273863600775}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-63607993277573154762971910483248906015},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-69722837529447151661991083262144002351}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":324304539354779237588032296710685305289},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":309312292700155222448321148045052872481}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-154561937820908269114528580473121480769},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-162045503334548319145706617762236738629}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":105564829419499460080551798502115457701},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":99486537299360141774810062246061393881}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":41381044877169317793833635077228291},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-334752411779765763708886088122516005}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-99670950749692322874509100844011245445},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-105774957607663740054019374174177965757}}],"phase_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":6923990405940470560563208453986907497},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-1710946170263799173576778525661948931}},"phase_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-39624752332379314667427404524558078265},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-81746934973667042996800627330781820351}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":81327976868561784845770259129991662839},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":39410327524899191120253580568711362987}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":11086840689939459982306815625274854863},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":5057234260929806699887122289596555991}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":40050127806358180153396491436138219},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-156928354956446139026999931856834191}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-10123526550281816524458459219346773179},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11096734239204625809804422202520967737}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":18149448673177314859017916373428952159},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-1124275829565375785777253389247355493}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":220214741558272685805345793448558273611},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":198840487539535834920601243953021229845}},"weighted_phase_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":74576212639467524501267739208955006067},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":68539358110442254460703503766003075291}}},"cumulative_boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":6324782072538584685402733161611060815},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":10243813692745645113846532133452742897}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":129235477733025235750914294072922629055},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":115608803009388490023794174587717315505}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":13441765491869376956713638715480576491},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":11033443577781459793143080869226572559}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2305088732131013652341036880413694503},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1254491817144213913704198755028307421}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":23582346002658118559330649883093009959},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":23582346002658118500110707528646083279}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":8049420976352640671805495405944151855},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1996393915343005596001295273372110127}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":110216458493871753738886031278180890869},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":27554114623467938393441508027551903997}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":117754280498352506585877732635763453673},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":118202034155243775957771213203696056495},"time":{"denominator":8,"numerator":9}},{"channels":{"boundary_form_input":{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":548757879096951582012990337435746733},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":30943046205253003409156186249055434795}},"boundary_phase_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":46810037523268375712521635411121841645},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":176936491885328397649769632854001816763}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":451997615483831640272459372080574793067},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":893722631122068522372074338292570391461}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-444769871318734164475202809694483631243},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-899888493915037437000666270675309793009}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":163328625530720011243668513054040373481}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-81620580088443762518369006185051302941},"lo":{"denominator":1,"numerator":-1}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":9408962084847644315558445735939762537},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2352069608961339748681045457895823579}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":71438104940161203273864020773053256655},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":17108341207961792271082271792689224505}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-68392935291473736484163128834533270787},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-71413494900825216518845350030988116359}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":1074954308261600037061840007566058681},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":16235636464742082271530477400232776201}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":112592375810651513714015280270680891},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-113977736058954763983149113942683165}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-8133847464338125415045200420283622029},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-17235543390743814153195545293280090727}}],"form_storage_rate":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":19257571499052264091911760901226970351},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":33807301237448628382304288272123634757}},"internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":20951188324268857255250688389971386459},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":4584784713263551080366551452489085509}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":165529328370812552875895654107717672627},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":151964491976978199889021000811982854421}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-151912358845295585399236529856686496097},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-165473626170723264991602621588825367349}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":37259960542601315415567742385485281899},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":34154439459458890138574444001374293697}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":516139381440422699790140193685651153},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-504383172720758873535819495343856247}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-34185852442170867359378918179746375677},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-18647110717247476604028170321274663313}}],"internal_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":166502955039111496422966586484802345897},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":159156008793521762772203049696308673433}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-318105908853632934550411707885831808759},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-332773965921875517377321278316225131991}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":108066193848938901156063488300660521861},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":102011512487976575626408228375373060141}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":88429845174240984145711574116903623},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-358071618275608759451661606739793613}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-102212941757538490195406882114583751359},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-108294112993977763403933490101070570311}}],"phase_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":3457209822160913232193251031252629377},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13668718856521828087534618230186037393}},"phase_rates":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-19315927276545909177425525544817127291},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-19948234911236413135135100014985336811}},{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":620021350057919705706697346771758707},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":76825801040689647294318586689782381985}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":11860213799527956022974827377323095213},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":679480983563220519121633163971921151}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":164292267761273068884034982107084061},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-160550150301763988895373180801685961}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-10881694799963271159122638202727373301},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-5935559690063587512577889645219554309}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":18013702431061991376762484700920191199},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-17852898349937881214689834901739242863}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":225893240521643392435688303803977442757},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":204507756005340522884228088338635914629}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":148862954525434336068041260199069561353},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":136893153530443266119619511794388645115}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":14295837782368024116844437335529361829},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":11694268983616879648650728363877216403}},"cumulative_boundary_phase_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":34503089942159514049253025178126993591},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":123902701066513258663627126127748650665}},"cumulative_internal_conversion":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":3851484849317395581098347688010098493},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":1594092230656911431035067207988747453}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2538725044341917396090902030562200837},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2716045306423518013336939458644821095}},"form_storage_change":{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":210826030259485066351735687955854663},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":13492865936607044213950444314462467353}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":8414592220309839737728732694469368829},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8348268033829248848041253747316728823}},"phase_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":58455676944776758038481234035088812761},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":116911353889553515900690309301281265917}},"phase_storage_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":62160332775572159823711427620108243735},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":125259621923382764748731563048597994739},"time":{"denominator":64,"numerator":75}},{"channels":{"boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":18709908590104641296164242497054893205},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":33305791700732527526311015213587445579}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":190188732891461621373351051782213180821},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":90026703070685031399217341966353275825}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":895922478016983349818152897888707492811},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":885543245713947484885812763384355975703}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-881292980514694907477964108928984019053},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-891729788022111263296415411106736328953}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":328493092909350728631792141332705587541}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-82108909917292062302467157301507698707},"lo":{"denominator":1,"numerator":-1}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":9570872580626343020666776536522582289},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-9570127418804939071721428279712731737}},"form_rates":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":18080264462922444112851839179113309651},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":34771648727107307045404559855197920941}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-34756711727684203126865311245933744461},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-36147239138483510376083115649484422355}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":17570526961850442620369081674194075649},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":16610697961003276720804440880095328209}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":119919429171298887039966802256898337},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-121532528401737951236135644378191199}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-16645502117268220603234900564518729001},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-17609646099536817471429398307650049629}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":83169435017904050914409262461279183623},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":73590853594441268953725458246348192805}},"internal_conversion":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":11435290958259231358279600382987784533},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":40292770736545180367431470711169155755}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":176366881254754501947741499048608428229},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":81312525018259562860849542843174410867}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-162568606780126579570594559020265495445},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-176306587001301341107825468170956554833}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":39734590304712919215904378980578160183},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":73162180386963782635155065083350268353}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1056552007391736428740221019994922945},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-257461918068706314654638648336589329}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-73230829118631387490982505964733431449},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-9942996715340106467140442631269615323}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":341327545219194645299663570414801212203},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":326937044256360477763632895820533883117}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-326712941690617167684349921832730445761},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-341077038629140994489356096852196892743}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":110398876846101479638549076400879893733},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":104368093370573703997100227055532212397}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":188368998853617065238684290510015159},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-381805698399092843539330219695285087}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-52293387166923190877086402606676914939},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-55322334818621022672471511258057761765}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":13802990968975489651713461673219272313},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-3410846690687229074554330215038472677}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-75245949285080056771228353068172879007},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-38902636806554667354111317469687480275}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":77366404203591502083416091370914840931},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":18700344890030780689435642068560725847}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":6323956458726360806861493249830476945},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":2911030663991550475151543302523532995}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":84077737305029795731862608618811489},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-81952673837110346002447374106366427}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-11655048440948090344628615333435766371},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-3164954152785713784193511952798546151}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":17925470453110087606693307388959872225},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-4441280271265527576062954579771160017}},"total_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":115642334147606338965719503267626934727},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":209843428986608793661427718457238327163}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":148115233277308627017029744073974685831},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":68126287696083762353851130105445067179}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":16049891712690334238359835069628258067},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":6627738984794358438223278601007063957}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":146927456622925319698887931264799217215},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":132342704479389980357303751937094270273}},"cumulative_internal_conversion":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":4387514112985797051017703955962650893},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":1830182684191355847250485981687004225}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2781938996603487206978362927564927475},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-730267431227617913057985768062836521}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":30678878439723050861428807983075089189},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":30678878439723050790198707821227515555}},"phase_integral_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":2195222148258312121018518500903905393},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8712458528914432471210002219645733527}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":123573536620480040637307010116859288273},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":3861673019390001264052313787239295309}},"phase_storage_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":65431262817187862671087436139264081397},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":132285995149394472920884043411303183415},"time":{"denominator":32,"numerator":39}},{"channels":{"boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":19876816131146385945052969638282387945},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":35634458201173727960867279703900121389}},"boundary_phase_input":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":24103000148848263414974448569132671627},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":182859917633676211429361459341207088331}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":221935269998687829898009929543102739847},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":13707228531292655920351041553512878447}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-872969371073907020846021805407811577315},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-883488621587802130106317126463979791651}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":329442453253592042511639004058169542591}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-164763614125723485236510029856873541177},"lo":{"denominator":1,"numerator":-1}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":9794210367365408118676295383487437237},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-9793402126346881457298044224706691727}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":73163985421440710252035912806189083839},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":35259806843326287039071334154036458953}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-35251450532933743332835167247447602161},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-36567716584871339496909532938748842625}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":17914704611504797757988846686579962127},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":16958711809792309120948977327014675165}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":1989750747071075222693830434513279},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-64603185108621667029888548838334695}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-1062267601314319248446110670842500871},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-17956662146547198998881845562996316071}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":89463677465283140777554938864203736129},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":39830341128922779410472429194532581377}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":49700452121899668388136963337207078591},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":44035008896744004698011363776816177503}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":187366859089563685691763068337239685743},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":43364163458719901330117067074904714145}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-173396225601264124719535597971158773677},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-187302298116623808161014180825132284145}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":84499632736980679569681629648421559013},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":39051088344695111408038521013798130733}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1079373139132272286815321763588975349},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-524619185500025641816158575652514289}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-19544110620083631444255112358919332209},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-84580490920723955743602784693191922915}}],"internal_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":174635975200554070123477116541457671803},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":10474663988198182629525339843738164271}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-334946959884444928090264121552700239583},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-349002851768574195145835909413903545361}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":14070176099683665889917424770160469233},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":53277364435989985348730277470098688175}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":400063125086290734417522563247152697},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-202956891735747357857925787283144499}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-53395393478968267892926390916331502391},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-28206258941293303806003897590528167041}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":13770621589994349260470024494957058281},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-425367167028353312345167487307377243}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-73200214348269646994325202035805287995},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-75787931464600999165766742046080622885}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":18835785812204177361796831064052158827},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":72751535984335238029877684293732689271}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":3362133559885054042931536588707553353},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":1553793435794131921025280264930268725}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":171787570533517222309046439217998991},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-166991473226346127448224614269811867}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-6221083627042235250960444899734774107},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13461403219172391307764576335090802379}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":8949694366102046844510360159026797215},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-17739708246098523762217804258151862415}},"total_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":118196882283527016539624729681580402075},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":214837925206980355447683723571474286491}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":146930087101770892301694520498957068021},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":135177242949134796626738865182409123737}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":17913343224985307920708550973217231937},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":1865730399721091921826526367266805763}},"cumulative_boundary_phase_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":38991520419685854619875837369555992269},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":70457131559234276384027535171856676269}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":19879765145157235159764735980282185381},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":2088200314445715249777896316316786515}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":379274499845165226191720371996490923},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-781866664511690993913090412070407143}},"form_storage_change":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":4333205214011972397796143055580083201},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":17332820856047889552410462652608894373}},"phase_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":4574098684312262742951315966997111775},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-4538891910620926793146540288671328327}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":130182695341935843094192966297425390707},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":65091347670967921447493549185173510151}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":137359367168829804436863108270182716843},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":139260479163177696481280178947689676955},"time":{"denominator":64,"numerator":81}},{"channels":{"boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":21058865636881862425113362559597578313},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":37910690475753950995151649690478437219}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":195156158652498540589162608165230556643},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":46341438153881898726476336598956596561}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":879467992669872263121436453664065653943},"lo":{"denominator":2658455991569831745807614120560689152,"numerator":6788263207336161134209579458241189027}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-864587262366308523116507202925755243551},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-875183385911362335444398673586868446615}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":329532044342400455529742694414722675759}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-164892361525785558547883683079033560729},"lo":{"denominator":1,"numerator":-1}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10092486292988265184883668739395035447},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-5045806833699324024886256062693255639}},"form_rates":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":9245906095907708743242751665370171589},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":71365443329825567682952291438585782563}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-71364608155740494974485076416907270589},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-36968366913034059155672349172664146471}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":9115810533891972679943639160966054651},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":2159935582166635135113934537649311555}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":134853518081895192729688243604734615},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-68493158023794708539913379546617543}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-17319822123765743996820533829908247091},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-9138195520941057473929355359107823415}}],"form_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":47948253002690135659221813687860837433},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":85794068270873775386420453593219134345}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":53767950664508698585966240599410488997},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":5986666154579756892301038618231025275}},"internal_form_gradient":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":99254660584264401246390964554463161345},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":184439310219127544030953170484533242965}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-92187672861883396946342769781047398139},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-24805118037255850727916608775492202691}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":89602583336121687220750346591019544077},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":20780043625727192926603965244376319839}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1100728324749308735906048326803785499},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-533463440404081545290818327468878181}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-20799931879432534616126209111151808081},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-89689173131084212915702472623210768095}}],"internal_sine_current":[{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":5575664516867115528133095031615054557},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":171535706556537844945334491527505588001}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-171405431536797314665442562588683710485},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-178277466267130117341936380082407777181}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":57276326809582944565967363956040504007},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":13571275514323788328164707517409597591}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":211827410858410141471604601919168499},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-107588801034359128506327849498350961}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-108823651891008864026925960900159427639},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-114833951662622318944591402499079919729}}],"phase_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":3432982639132484120945684854466630337},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-6786998006476728546426563357389165715}},"phase_rates":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-17782603796105068243327338474108503875},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-73744833601788846811475303167840682843}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":73297009548987009685067117493929940983},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":70680319562019868863310551056536331843}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":7130347025873628226057320680108308883},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":413405832587464226257738803829593557}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":175186353885113520145687828896186335},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-169806686998236594568938191966042633}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-6620823949172769286410911943378967885},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-14274475245636856114513022465203002763}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":8974897710823779110554238251849634999},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-17790988252481461695067707186602555911}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":241226238512929104122165472590004093461},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":109741450836890401872160813048911578679}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":145329732507548832803721845214282418595},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":133688833402907028357901172504604023013}}},"cumulative_boundary_form_input":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":2485951484805372815382866089147438113},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":260982918965932841054842883083994107}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":165114026615579287569620346735969151419},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":149603282772321408779269383456017714393}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":22400137832556080405981903508379552053},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":9475301161766565416418030006185463299}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1647467740507642077631581087836608613},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3339305092630946197537562455754298759}},"form_storage_change":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":2434277788648007300975572919088735417},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":19474222309184058365753634882902379099}},"phase_integral_residual":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":594775471777321747845019530452177127},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2360967950960920152245008301805170659}},"phase_storage_change":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":34179888122050619084701948108718249093},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":136719552488202476127804253516377542185}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":143791693420708151515731001624796747425},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":146163424292046156736784286723598224821},"time":{"denominator":16,"numerator":21}},{"channels":{"boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":22253997106302907669765294696101335003},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":40116719993175395139578786514023306545}},"boundary_phase_input":{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":6162376191806293119034470830863419091},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":187582156874467205899297225752949718305}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":217779952884722947906459240799023216087},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":860464980374147412581582131996923308575}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-214042905502483137048103214195810215685},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-866831149106924712370548010045505385119}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":82197723445600613817515203065006874499}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-329237807768833093779512171116059191059},"lo":{"denominator":1,"numerator":-1}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":654924426592255228399608807046460251},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-163716449723616533759882969121289665}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":74731295252829071806907388866761734935},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":2252632800915781120384575015678418521}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-18025522494334218220933943608984944231},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-74698840905090063159246057537252125949}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":9260572884004225186680563061026322467},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":4393218468426087426358942482930766825}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":142435529123821884851995998023158717},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-72429750775929976529347561146748721}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-17615962785552578977513371834373258677},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-4642170613342555203423237763983939173}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":102451117382254574894501211513437748457},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":91961116292731282555222614058433964803}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":57930974862436925376324534689993833357},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":6481950820450387012566085510833884737}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":209774786567091297040297934380016625413},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":97776733857158701007487726193431805343}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-97743272741107128018585766015897011933},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-209703176365927093459322185746603217677}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":94769485198545566151047874627999659819},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":88207616456598725251152006870629430235}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1120605836223951645215327765192268535},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1082905462056310344981365132843963245}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-88291995634787391412141300923223015399},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-94861338827791890849072212196237374501}}],"internal_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":182021748778837171410908266848202959287},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":21911697090154349951274697092002034859}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-175154190387491125368040386269087617347},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-181868811268186294285131036625042371497}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":29092947740420518338709403519119107217},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":55206811464089597119807394271227372833}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":894948823811147745451443374540261887},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-910179091756004963112954540998677521}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-55342179273003172400886724961356364153},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-14583809095587396038860785363742316153}}],"phase_balance_residual":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":1710782056751039493476266528211979981},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-6764727468502806046333245188605628923}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-69040373843877575272129315149296387441},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-17919953834366655829615482257849356343}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":35615937394980607945321156457789270075},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":68592432451451814210785592903690114095}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":15083032023622736926637358623239148451},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":14038678177421700622871815254627166173}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":178349958092668808913372517269431995},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-86174878593737348393721179419251985}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-3513026885181114670470411280830298487},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-15097650982758219787012095851302838665}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":18089678980650570326408022535116448403},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-17931939420483240977503149797651040945}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":245788555848293171365284034802089473253},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":223772092929923954171130506182181039973}},"weighted_phase_storage_rate":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":35834359616509649117695705822162931199},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":65905488318596335807953946061873537585}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":21973924107158880117103425090939005061},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":9291689031749899237338850067610232671}},"cumulative_boundary_phase_input":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":21794698862911090906021506622783035007},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":79198098187906029527899470456593616219}},"cumulative_internal_conversion":{"hi":{"denominator":664613997892457936451903530140172288,"numerator":49054008357876584537103742328072291},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":10690666940601012981274171039466816687}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3563576613596637367901865318378698021},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3561287828093229685896508306600916151}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":43528288558298461805127907532532796737},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":21764144279149230857102016428155550951}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":9885372747961854739324296549738212847},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-4905170088772799498268474158340292661}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":143165916844541102512126121390952432293},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":8947869802783818893067922661665628835}},"phase_storage_upper_bound":{"denominator":42535295865117307932921825928971026432,"numerator":18767632725221674876008363564475299973},"running_phase_work_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":76488128511043350642811855451665323341},"time":{"denominator":64,"numerator":87}},{"channels":{"boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":23460204483151241870498246666065385107},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":42235530925895649034409225728677191075}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":198954921124527432359893130683781892887},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":189522226403812913774356903814252390453}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":431356364560754397602599770054177008663},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":425990308848240334499636547907126018129}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-423878694136788669199696909871194847785},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-858447236829979930820048188681173746599}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":327249994795969154458075934166461644357}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-327917856314531642775070311521491406631},"lo":{"denominator":1,"numerator":-1}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":2741409325501943391121486026195499745},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-1370579136271881397088569535304187243}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":75456649528582020386799879995133942301},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":9084972921377840360830766051575955125}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-18179787574802858583411145659244297819},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-37711146220336632697812368246774612353}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":586974860092926943360355186857169455},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":2229848089694030309706097409402209923}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":37519551587784793055105023639910383},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-152813159160296436878169372089027901}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-17884590532297664618558142018281624281},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-9416716728489613863377055197023443863}}],"form_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":54555265573606044869559982473009870113},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":98132331328415713674506286662330787513}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":62176555452288281110218349612633515243},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":55909362919308667140224795112560550171}},"internal_form_gradient":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":55286070079958624617981121087895243095},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":206780064440233325444077325682650551077}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-206710897718950012657100816177559825331},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-221070156016059143879856705267593913809}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":3124748631986363553736635054502520535},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":46678050089455479314644203292061515019}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1138995900388082360872092412745383203},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1097170024107583659048822063332826477}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-23361176868444027309514023010072686079},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-100088465830037649191672195226403283885}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":370879800549540567868834805034270013053},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":357740825712738657907627956262415606657}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-178721994375676164036554923166476356839},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-92638998156155479422612630512330381007}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":14752287266478687889256027075970214307},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":56042195017631999720258969925819203405}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":58935573817083984121834586519683341},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-240038349094917551709696874477150071}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":-1755815569647747279479452408925385655},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-59166976190318165109947080544496577261}}],"phase_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":6815782551146780149161039638030970231},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13476081198300202633617295498584513395}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-66933814250319871893258790913224825861},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-34798308639821221006598027637679308577}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":69151373308090778007939826299821986121},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":66493580524241802133731280126836129149}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":15914214102408559772863317474187527881},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":7429042405627926797367163299104521849}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":181276827708167336729448211157410019},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-87310016374487955442283701645523453}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-7436093550113821714836184191291840361},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-15929574083334752918998343418604939471}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":9165004935660859946407234440385487185},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-18173521755495639840332297280945046267}},"total_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":125043883600515141350790299211850277949},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":113850904167667138130278663367483808417}},"weighted_phase_storage_rate":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":17622154506727274120307579184710101959},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":129569477006918562586051040072636829321}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":24173318277454309042462635715882634915},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":20563168575651157023165632591252208673}},"cumulative_boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":91841801415500475320021021741533278143},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":20910006342311348673621490097435039155}},"cumulative_internal_conversion":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":7007544579014706115009650302516302255},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":24002085268044619734746379349834909163}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3839523766534364672080128359495663101},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-474839872910374021315580314622776947}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":48404777610230141429992140300582780937},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":48404777610230141331976594408965628359}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10254852672850486921798880804069910903},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-10176792467673879289879149099151591751}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":149504725095282451850732200373485015123},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":37376181273820612903854128758520013843}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":156390130009908126313478185874472917537},"running_phase_work_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":79840758781478165452647832066615823561},"time":{"denominator":32,"numerator":45}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":49351079569843449999963761263636760139},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":5531375539669806065052074258453987945}},"boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":100222516864880567621313925628513385057},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":95597707783205471846258361550681559923}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":854262497630790197699064157872677396295},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":421730134925039317663332172980417875131}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-839341235865972894682466983852793956197},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-106256319062601647726841816652840530597}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":324941976926073345921546842425496718057}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-40732199751712610742522856431815684071},"lo":{"denominator":1,"numerator":-1}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":11564825011527808365327163519443017861},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2890938542396474866872863851487045483}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":76143904721857125201069168257178422553},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":36578019636459600658387874782602201907}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-9152475892915961568044984567787402741},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-9513461870205776824333222394227368625}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":19017731628015465185549621048758431691},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":18077167482560773225042337071526649475}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":157770139713614983426262758789175813},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-160834631912269140862152913117209277}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-18125637314176358309405559967236965827},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-4767646440249988864040059368949095453}}],"form_storage_rate":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":28964425185941441584825721183202929931},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":52139433369640254997547800761744283007}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":66491541339022959462623295665799987807},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":60041871414879509453559127145736798303}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":232599373029797150474792965160299615827},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":109050284717651796081014777683155923237}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-218030009729950247379232969232827329653},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-232523594040239397288760740643736271909}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":52630897578989533465776820694592803559},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":98557394892940425939163058656872811887}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":577945276579811835962474783057216563},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1109719945391072798038879071913834409}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-49324745451182044960616948305679763987},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-105362208451235051792197684578947350487}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":377357028148544076144050763619975672639},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":364537449710514740184311035942985250181}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-364222826642518346190249030287302286623},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-377015759198543541854284531529379792641}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":29872982985257821961200325841130954405},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":56791096560925221941563230654281210233}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":495649511880128117637060535237464451},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-252638449029201625951823052192272483}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-113886738055698956683702823663805671593},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-119824024252823153059520007617265249019}}],"phase_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":6785218250728504212464590292108107583},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13416443826948840388597968321246537087}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-64814354180330698791290786762458659215},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-67498876986122051704276660746685274427}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":67059462345070328254437066431104411527},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":8048168937661061804745332432350201947}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":16752935018118902402362554175814474991},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":7842948287735694744468224169218694871}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":45991423802144831475337613209599873},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-176617414756657390871868299161338529}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-490642315956568855830095233122595331},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-16768916290092728470566637933305645661}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":18685591588841366781192175583596043523},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-18530528072391289847025255207131529515}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":254132011472610758994125492752591066929},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":115632792613606647697783178656766000369}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":138274310728844992654822608019779347205},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":31746679621983196350117688947510858681}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":26486650132290720761210937025115608047},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":2829679300378416787195020054771556769}},"cumulative_boundary_phase_input":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":24134932973385437981817528001342460767},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":88121167921583151187279321087428354741}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":31146969316325525684849068194399583449},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":26816547990617096740381963434791321583}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4122171620769542852408832821513850067},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1014366358550568165274626295626639509}},"form_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":26788077007206986945175478347238812901},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":13394038503603493446240375009252158365}},"phase_integral_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":2656176595945188313948791795857593055},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-10542842885844877416498413872608460179}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":155720072910621529945504741163887498253},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":77860036455310764848829923351669952187}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":162522691527754420580788507922068898671},"running_phase_work_upper_bound":{"denominator":42535295865117307932921825928971026432,"numerator":20782864474558300889269782571993545569},"time":{"denominator":64,"numerator":93}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":51796233111797334485650778743576246421},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":23074019191171987254552607542684101367}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":201678415987125402364733344883671341605},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":96308114083538617301333134525765485639}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":211445616048875621701401409737486324913},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":417468256469723649547430437742773071811}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-830943763301210110259864211406835343463},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-841656635926620969489922931053927384651}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":321900781567689998338795640792725256843}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-323090794915266947999332435669760007095},"lo":{"denominator":1,"numerator":-1}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":1535915532524786585593900296785068899},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12286186622335799213256509874641983909}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":76793713856475089988614654882575047373},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":18379303274063241920502549644165310209}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-9201031252788993157181495923178238433},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-4797232178140675567264828324628904813}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":9612378496279356763926427436067902359},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":2286001832009076743119356115105534189}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":10343775428152554503254495651942115},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-168911385675627532516050097365934945}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-4584769340707125157470556879735139951},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-19280122933837800475346587533265324707}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":122675616323644111885332662893792481829},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":55186370999404542201750631920362906907}},"internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":35431347754673774565553497485895775651},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":64240253681101844691476245434143727903}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":244122214118600643907759860497325377779},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":229497017580314501656461226551268222039}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-28678257098225900050320322497987618387},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-244045782164340061229071052078428052053}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":55285497489548954272210372427782476827},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":51901727819567540249819649005448253283}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":146410437431568928501448743905409309},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1120557888265182714823855394371567887}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-103898156658706083166979890310534150021},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-110674412319482158522855342099063617453}}],"internal_sine_current":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":47935166869899761707601799425196139909},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":92745657039765245635828821645760794445}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-370650617625820876360197359846820787879},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-383123202762804352436397307330985895911}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":120792710669742923551065583811694962119},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":114906984984520386386065704204237581567}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1039869724654933868745817563768692171},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1061301536692447380975565010985497259}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-14403477679169224176520863312831220137},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-30285146284626462605067412218217897691}}],"phase_balance_residual":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":843765121197327494192667036808306981},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13347902995543219300911276680186928873}},"phase_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-31343672035569964995081015423135469267},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-32694958394801181585625371647510708419}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":4059980124261430792951551829976189653},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":31135904929528938296851924325700443933}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":17597920413512572535710259658366080083},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":16520833074988625716149252951140596365}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":93207779349923422096249298573277839},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-22292790867252445906622032619061025}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-16535905210369193112113825802899788385},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-4403594948609035752586176201561918891}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":19165124371109828152203125425565639489},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-19011647789633314074537037017181089383}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":257929390920531037263974609562464813501},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":234463001309289422775847086610066498643}},"weighted_phase_storage_rate":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":16906721824610865672330243333584041459},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":124090259310480338372345822769340684829}}},"cumulative_boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":14457299279703110407612908639360372299},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":24800623702199708102674467395299088655}},"cumulative_boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":101266569768240003545193549776080890137},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":11579451346156127984159913971040451485}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":34468658168326192050369708583702312417},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":7456952470479686427573728109879202207}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4410909935150991938448305495616256777},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4343913208462967227227842494453280773}},"form_storage_change":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":14759835879817361437854421332608038565},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":29519671759634722819183841683984888121}},"phase_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5497336418916311505144466541208808523},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2727023361639195733562089985356002977}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":161797236208004478706477848035362528389},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":80898618104002239222921913585610479769}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":168523701079010861362028806391997357567},"running_phase_work_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":86352664827280630690046093556322485723},"time":{"denominator":2,"numerator":3}},{"channels":{"boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":26998596407867610167734348844215509125},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":23956615188138998935003271971540297577}},"boundary_phase_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":50666816019340466251219213095047594843},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":96900107972250449590401837013692366147}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":837285969561529759356761558304256975503},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":51652310938273586959968101590709443911}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-411297297914107426211232957443308555331},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-104159911741470498031725857549019045467}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":84544822777470994007581512964431350363},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":318161350343571810915857715405880521845}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-319651936983567340575650808036814642301},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-169628246461090274087414829906666993277}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":6439667764272596512893335693947011457},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12878131228839469017020335882980420589}},"form_rates":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":9647954787125518613136404015449485657},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":36883830198686840126994286278977575629}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-18472199839867864995011469701073108079},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-9657277674512113754514283662189192165}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":19404313315147475070626089299206232195},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":18471358117105583744258027868339451819}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":21657323908390673798642191069674765},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-44257754984751716934661772662575789}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-9262462237201309769198843053164403275},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-19462067662389321977536289967583628643}}],"form_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":64642467179349158234538647591213837623},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":58194206574900794857059997971134229909}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":75269351562905838395671634136817862157},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":34246184226937562786642039925726528589}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":255666073996807163491616498366163683793},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":240955314478639976942042353228899445451}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-30110552035528312249573543026594712181},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-31949519715112798849639589295453618093}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":115905941642499804560357104981476348623},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":27271770261227776404349864209189963007}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1185169979528803095165226819608466257},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1129689611107605731549985785309623329}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-109184026873483694275011626621194059059},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-29001322663166666226578492312504367893}}],"internal_sine_current":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":48657420255464523283061240282254977793},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":47135308698389479273423229217962532311}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-11772924711477810503589176804490646773},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-24305318086249684246671852853861691777}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":121920896317643828167328398368544784475},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":116058965925050195277856376649831229223}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":272153958748058916255592309259093273},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-69519918962236522795306009648079383}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-58197766637089031303818224890911286709},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-30570944395914887132029562728868214727}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":13409130491795389362685772132477251789},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13258873685639842455895663118877842103}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-60560673513095270216495002516527875323},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-15818161912278331562269600843730112507}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":31427524346641376301606056144659979213},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":15040100691693809093912712815559320961}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":2305875443265574774645117685975088321},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":8680874087881900697636865933075253379}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":94312830323064708340622853366167029},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-179795685767336363198664438691717449}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-17377177583593268383906513944323084507},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-18462815432183940986658256379133457395}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":4877870727827467391521222308751617431},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-19360021805448598650528444716493457713}},"total_storage_rate":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":65306232308022191654223776801367949293},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":237304435087648486689817105352127939909}},"weighted_phase_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":65969997436695225073908906011522060963},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":120916021937846896975697109409859480091}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":31445716972643809268450912482865948579},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":422602443376370925825484752228609243}},"cumulative_boundary_phase_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":53008291885026586128122675501870801077},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":97177803330448263697829397878340441543}},"cumulative_internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":18998454511418701612583408216932824853},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":33038389653194142221542603682553670883}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":294066446424182676354306861050318777},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4652616823412408318558425802687442663}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":64790009172068804296042537601989762867},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":32395004586034402087529651557022077811}},"phase_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5681992820163920975252126044878917181},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2818023652131309110907998262504957669}},"phase_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":83861341639193483060498115706286533871},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":167722683278386965847316105274909702749}},"phase_storage_upper_bound":{"denominator":85070591730234615865843651857942052864,"numerator":43594822676144868735392547315537094763},"running_phase_work_upper_bound":{"denominator":21267647932558653966460912964485513216,"numerator":11187173617932012643184256145308095839},"time":{"denominator":64,"numerator":99}},{"channels":{"boundary_form_input":{"hi":{"denominator":1329227995784915872903807060280344576,"numerator":217518325879618089821044541574491945},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":49534249087427895404453443345094661793}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":203424064267438652428366151466622071183},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":194761838402829451494489308939887377935}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":828787176570536984647665468432749595835},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":408988330037908347871785514367841168153}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-814322723587100554576900467629419364475},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-824931655930361491947587307471591088615}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":41690940215106013130409023259545529973},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":313759337102751489135485001653438983261}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-78893990634966715429762149131514482099},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-334922350066612396133495645375265768007}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":13076287529933952569914477340180081083},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13075017004943430062640454485895042067}},"form_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":38633572429285574815486527125445927955},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":73911858122934301480160014873719468613}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-18516467233172693531138864340213783313},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-77373806435663122302860004715395541299}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":19556478327689991624179149253695743785},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":18627266397794210219383742581789174385}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":181034795724568579528935458877660657},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-46295319339921308710126433936039155}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-18683229342613098027563114754188059383},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-4904119766254946014452336301561249111}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":135396556307895950118007983742952049075},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":122301353412702753871059075646148177679}},"internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":39845839496231976469756063744486640913},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":72786019690534102143640063057677306199}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":267197008226645829523851341451095284321},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":252460632389967387754883745637346223795}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-252391542086110519981253185172741554539},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-267130648349442811626887128085204982001}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":60623212652290619315995092678615908447},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":28600508494954757133176699440519208467}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1197546642382788216791718359230017813},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-568561889936497630130356567270957743}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-114499577351615804726797865420653548993},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-15168094372044267633128112094229771959}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":394698162233788357010710230474205297303},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":382843514373792970349138749834666534605}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-382478406622190646904793338418307225463},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-394308595569061394105235063229437336529}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":122876977288717765667931065939946507395},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":117038566543540604007229817466118523169}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1137475168584867118975132495160003591},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1163528281071122074888260368426557999}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-117390192096173141847762271412188754521},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-123253973039928259221306062781736991551}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":13287477744631836834046590521354173333},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13139931678127429472618865605483009263}},"phase_rates":[{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-1826235503046431559412678542334402833},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-3821884097558635716291563250885557413}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":3796774551529543346827870144193575331},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":7257360299565460751396240825373396803}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":9648483959723182818742586834771111463},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":18207649207655173961657043323797037113}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":190595467718322993625223268960831407},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-180978870474127479448275132251567509}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-18223173717442481465314657948882131011},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-19312617572761626671362989479980531541}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":19458105972635938608089003430238278789},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-19309289381141008739387255660082075703}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":263754193462893285507031755715220318517},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":29974933288934984335395787306201241675}},"weighted_phase_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":64178818577498667694511885986134134721},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":117498112898777120812107222803461755721}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":34055936883199226346303446981759851919},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":29368474302060921849914779299432303823}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":221568670552642531345070365357481113895},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":101742533918014578967231491056619051963}},"cumulative_internal_conversion":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":10433114118902287754801611852477818073},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":36450234326187928259525731638382294611}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5003903530086065041698359469380409689},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2482890600236731171763983802545700329}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":70822612158334915151138870407195008123},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":70822612158334915021981926786579723553}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":11731467144041449369956523760830124547},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-1454294715249143385912770897906579269}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":173484078504461456285213058464156956181},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":43371019626115363999560616633961546283}},"phase_storage_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":90038388582626918748995797345298075137},"running_phase_work_upper_bound":{"denominator":85070591730234615865843651857942052864,"numerator":46279609056613650771386158429774704821},"time":{"denominator":32,"numerator":51}},{"channels":{"boundary_form_input":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":7150331863677116032546663281905123167},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":50998658171646620086247352676748798439}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":203962348098658739896324229259342469533},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":48876739635289282627404196975273141903}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":820302764888523361215363915419493006139},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":809542522302267454449869493653857303521}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-806111699452848183769757724883771289029},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-408315570071331800008153086497247852649}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":328249515595847556400401109563963588579},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":154365418403474930524690840720657233911}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-310897999558702678346619736239981026795},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-82496885060223687184541426375273750791}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":13246143618075356406449472612995785911},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13244807607822581330653820958470915599}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":77248997046331413594966482090921238343},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":36977184191438337815924481615486505313}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-74143930924549043807714474651993166243},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-77390552899334160955734837563089920313}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":1230085195586962856187066728490428701},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":18755842029065885798525466317001584627}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":47204912767052907427696340105505299},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-12084378264894744962718847002538593}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-2351759620376976148689274471567969041},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-9871725040079798568144234673672986829}}],"form_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":70676025071444971519685891052156424007},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":128085168301043316130779868672792396603}},"internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":42063660499724484600530191688011163433},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":4819203022072997909167184800910516479}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":278735486063278390127956355196272669565},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":263992803986871941170926946294992325699}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-263926917619077879230694379886273911669},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-278674252976149582356388482411813609195}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":126600154065783232468841026833311493379},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":119739215233865109923857733640548763989}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":302102856646717845275269818482491461},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1142871781160059390365412899827168199}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-119836051935923604988484623686944403885},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-15836997058009302388343780294274515691}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":399805129257955660666592877571585909667},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":388272664430606063741849298052571367959}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-193946043271897204571937009247290529871},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-199700618548253335837970398197953057757}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":123661651639858126805483946815710609081},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":117846431060808136176002336655849270675}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1186388857298563622474933322636024995},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1214854207366192101915076468923284723}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-29553082985541717126665095322375716615},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-62025877728346204792006559884719927969}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":13154799120842075177337153156717888139},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-6505080495474116325498361479843468859}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-56320375763595953155630247318274179729},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-14756580028126141835278879820998330467}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":58643739388261027771288478673927531603},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":55962851185689038651455585123389186671}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":10074520157882456140100853994231860701},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":2382135998301751078529873498902645009}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":192324651830029573000629926625463975},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-90946846645931156110353970845789089}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-1192031251638708452135367422143348675},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-5041072731027968754606414783429132243}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":605652190394888404043787475258112839},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-19234895952489811327265117356703790115}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":265886486805440179525265339786100976899},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":120965053527792928414716209078939832377}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":124534436662550236485893557681788128885},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":113844938754542540698652549485087268151}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":36737311332078144858508445712474273107},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":31759036403856857166457623956154903749}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":231129405619767159777710563604012792155},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":13290591032352868651693829315381363627}},"cumulative_internal_conversion":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":2854745290466145090656634555041394929},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":20032318296371338345700560119532590985}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5306805344133458656471637534710156863},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2641378819401736966129200635168620859}},"form_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":38565239170366496257165190864965121291},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":77130478340732992376756197322799350253}},"phase_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":6048373274282367018716504354448573801},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-5997245304136086186396266518914204459}},"phase_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":89535139209376155507014062437168323385},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":179070278418752310713516910327119201267}},"phase_storage_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":92802330702735900281763951802779450439},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":191064769027024483086309443364947610185},"time":{"denominator":64,"numerator":105}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":58541335162838139132521055578727274833},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":3268509266129149634877870950097662657}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":204294874376296492135703084320096700727},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":49011972147854191775591123947972872183}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":811845950595297769267104654176141296941},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":801147160277944197144263314884898081947}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-797974139212963630290856394590841907435},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-202097792417309155052956332556514144769}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":322381940120321909833217139477079943911},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":151556067237607687500882634015141377351}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-305653129806030688963051002505434125389},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-10140236073856375813639991664874278735}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":13389493130535985666655166889349626549},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13388092677943013445654721061307746093}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":77133898982702251579977362615730072669},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":73899804776512702638097874424588456397}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-74127483828054826819450836937440348439},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-2416032900880189487495504341216848855}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":19779109627650033089451099977665073249},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":2357152373524289111720559556874399569}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":196604320758316000653453399826096467},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-201525398078925516293405147015711157}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-18917584126759832985045949899928009509},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-19843104948558900713347450625363909671}}],"form_storage_rate":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":18391128635161694679489605414054797109},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":4178652593948161881119116291867451245}},"internal_conversion":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":22140910130361513627236346705584727775},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":81443387692691177611215741221526147811}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":290266796368050522344039988224124535783},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":275536290667237904651700307900207839161}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-68868785048120364494777335197689421351},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-72553097709949168365074272232942494211}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":65980093544716133178400073651187173541},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":125091399610500214439930151835589773913}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":608881724439543644139150002898420217},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1146947538618959771074279033269086771}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-125186082632401167535673754999414019821},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-132051875980801736334594431512882567533}}],"internal_sine_current":[{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":3160843211250483979267199205023673061},"lo":{"denominator":1329227995784915872903807060280344576,"numerator":1536629362842270629874962419371073485}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-392981946063909054926578362337399946711},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-404170802011294251980109078131171320279}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":124275811001544989460451658071255531891},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":118483401280890414757760047820287192583}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":617650689758336835341027897547142449},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-158277677529127758321759063504108739}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-118862686632591150414677189082976331119},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-124677905461607829095146937229081505319}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":13011610419812511844836308621792299833},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12870053551456196382552598839174594619}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-54206090163230605018746190558848059467},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-28452111135161369376212440823635236375}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":56544146896087856756993625790495790885},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":6734399347214388841766564453744353161}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":21002116066614453955085443447632135437},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":9954457293147349999840696530480168315}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":96906536202870666139887524940858451},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-182542370238289970255304013704618833}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-4980995964314278717342335106218184163},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-10508354403451260461400089084559415651}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":19280850721593620613761829910329163093},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-19137893400644332930477674299669577423}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":267624887571076781874172260903783254337},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":243698316138490298337746465599154398137}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":120495858489783224438255417591344877465},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":109981433132149118141934744259395958297}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":39481436417836182630345370192727114115},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":34210418353453719392616027168728150741}},"cumulative_boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":120352863928078028923285822840758662501},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":110919600647684279692512302393173365783}},"cumulative_internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":24913672648450552627806483943979727661},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":10970573847709393910481714527206055037}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2806577734979953890920425051846726893},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1400728125121521303952536303810184811}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":83705869214251202816383735381245824675},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":83705869214251202670148192865445830193}},"phase_integral_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":3114866214377072008594224950465127151},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12352111609342740355163303887949252291}},"phase_storage_change":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":11529457553498483885236783543765486553},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":184471320855975741849481483684743852563}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":190952620825463244776627804906700067643},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":196823432465318482204644787572693104853},"time":{"denominator":16,"numerator":27}},{"channels":{"boundary_form_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":14923082642321831772056830437937849301},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":26708851742511843691621830603933121173}},"boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":102217148606248903417326329701531606483},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":196396848284624053927522561211163021643}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":803429388179069773939572615103566542235},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":792802610547557643493217292293454623877}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-24685061712005369795578851648524574143},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-400112238364556604339253252194741549933}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":39495175806966395790035133057695320641},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":296939474882592063843335327228518683959}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-74969044007547833344555759006776494263},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-318457603232151581811461117014864296825}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":13507052738142771121156088046975185663},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13505589186983601491142132649972756657}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":76926571311140558711534430369413805255},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":36876400687536304586687681630404287729}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-74021023259458231031965391867573467135},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-38572945402154494168983074912326376891}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":19849888100105364259913685332862385221},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":9465780131403424657189853342006877953}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":51095125347198277430402658144642871},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-209695534378530435579515377820432069}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-9496948509592647172392713592560806815},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-4978899201081883489061266642377090991}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":152706751724004668650776972894776861739},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":139175041179107308449268863215097650539}},"internal_conversion":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":11623537474600447856522959264164876249},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":42890997750419105073188611819967716865}},"internal_form_gradient":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":150888442992214128607050755738358085739},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":287076208611431112375627443723607795489}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-143510728769533808787739408469975106251},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-301731133367072875003578428200044681329}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":68659905972028910267918800568498992357},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":130451587389274538574449482945998836247}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1225602900643044855422772907782304029},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1149367334312585314044435243884862751}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-130542530625092545222906280906152041311},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-8587850497768071902464428181316955879}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":409054447435060417427409268386957929945},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":398164302062193865824602522677503316649}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-198877766309574118900258888109591364737},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-102156322046055232004116717569281093581}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":31180131314935235335257923286125292147},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":14868812660656613300171229371810862703}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1284160563400061935662299820738386027},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1317555900588354291331526686053335899}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-119342174677027185586383181116913934575},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-125133385224663487235376264704913328561}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12858457301092383533978022695246332399},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-6360066034912795983715622150408174165}},"phase_rates":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-6512430937458460933730488733463903177},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-54786773939604496425003247003201755685}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":54452531542520383990318543834744621625},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":25899328527907628416524768842659413661}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":21855126855346291842404631336879449995},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":2595251870898425052861134411712902181}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":48765189976276414346291289023958317},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-91463746342101478473910547180787733}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-20776489032708608088589242508415104749},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-5467195429015930063528000626042342425}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":2394900717908722743665957533604742725},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-19019416960843820752766926477405528725}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":268973757512917523260093882687867205789},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":245107210820941313170113054677409081445}},"weighted_phase_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":58133502894456427304658454896545172025},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":52966084820917002360422095731155715453}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":42279514413271526087606025899840460859},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":18357186602157102369352786893923440425}},"cumulative_boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":125144292768995946270972994545517956555},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":231045303558710311912877224843119998205}},"cumulative_internal_conversion":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":13546542962469068300452269403005320979},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":11975831607484841685634572616736548401}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5922356441688232865279116475268786707},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2962815093602997549016839983883583027}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":90540056075941804346522980730061861161},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":90540056075941804191381423544094578721}},"phase_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":6409638119609843172991898343855757415},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-6353425579999400535359613076474685729}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":189678407948053725057051943918810229119},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":11854900496753357795543029529446271753}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":196111495108661923016632884074891982721},"running_phase_work_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":101192629554026262899703849312044859753},"time":{"denominator":64,"numerator":111}},{"channels":{"boundary_form_input":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":7581071856873844117421382977029712061},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":3397225084580957970984410767262152229}},"boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":102196549759572649822189315911883068215},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":196565900412355843406407984326166056543}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":795065165120413066845203008675470828639},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":784520345810607894500854908317613994179}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-390983230657602224278339673902466145411},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-792143105570688241588126666244580677067}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":309024260175956472707993126774792123651},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":145124426677612436127453904231932130457}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-293601512068498650769151040342676566647},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-19495776732614030020931590626145494501}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":6799824352497753691635624354479818797},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-3399530924108064423262437035884287539}},"form_rates":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":9578965358231774021723320939458008313},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":36758992208942333461629775465136048719}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-73829015683859558199285422315080478283},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-76893617681784360060954691456147925877}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":19893894889086205997510451981192010879},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":18979055542995942412853715511445727609}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":212140419501887102109198466009896793},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-108924426388039223717969662916475249}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-9521594467925109306550619778614303119},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-9980552693541052320316737661584315783}}],"form_storage_rate":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":19758269740558398898206762037535746221},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":9027484908082493734953463878103640217}},"internal_conversion":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":24347326842690351128233526594239424285},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":45055453933088178133316137657565948255}},"internal_form_gradient":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":78313089535445631301762469823390452973},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":298598332178989566255936513407153749013}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-74637942517607524266251056140286217385},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-313217201554812344572895987078846375609}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":71336272714649748455595756152362444981},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":67906503480185845222513612484637203667}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1231930952314613559778817401985881351},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-575074818212991015780969667869134033}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-135898490089690996616498767250462573747},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-71375281155699236046511514575254326295}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":413212712585933047393332641830847551335},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":402641825906641212312696207154604203159}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-100555141953509447039257598436461868975},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-25798302845580214970465259177515604659}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":124997028069681518675385910738644956183},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":119248922931897393849396569957819612949}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1332917566873170849297120814015337727},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1368784710948584969981137201875418195}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-29912971230894739588246891907361876527},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-62709662041588786036332602539255793303}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12695908291541789286169098282515052609},"lo":{"denominator":83076749736557242056487941267521536,"numerator":-3066636508660846541809586905088233}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-50003086505642622993908246620658292515},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-52676767029203843924274406887598134505}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":52371667274797468656847528515388422067},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":24867920587177756528095353583434613223}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":22707040848576013428056160946543517645},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":21615311393917141527997056748023193845}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":196067900608776747680656921522633591},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-183051999932541280976089858339985099}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-10814458228249636415694265419339309357},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-5679864405251670732763774346785928779}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":19017157491952248423138515929648889573},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-9440333665661018440999992522476375947}},"total_storage_rate":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":67484664814400854841324268133002345445},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":3846265735043968995339839228047673141}},"weighted_phase_storage_rate":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":27968125333284057044910744057930853003},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":6357578032093382246405893034087052347}}},"cumulative_boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":22561208179799608815819522258113301441},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":39262292017749923216943881863293495021}},"cumulative_boundary_phase_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":64967378019487957115694059364443737689},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":240259330140539492072552599108409032105}},"cumulative_internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":29375647816440357019176431924220587985},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":13031818809041595860634169593085750313}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3116914523326395429526219420388569577},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6250315691910834315749981750796383605}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":97623396300569097518532999076413635427},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":97623396300569097354241926613871395247}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":13175849185819080464691232467086761145},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13058353148307586864034695082439163941}},"phase_storage_change":{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":3041935682710591539045171370735228395},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":194683883693477858156204864002992785563}},"phase_storage_upper_bound":{"denominator":85070591730234615865843651857942052864,"numerator":50268316584832111227315331332184879227},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":207742236841785445020239559085431949503},"time":{"denominator":32,"numerator":57}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":61404311840469161919340521283831781421},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":13775849426191166266622542400822307121}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":204183534723398999964207693512106453531},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":196566894312599752151274126208570695231}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":393382400000235855724954208630187884723},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":388155638141362654514741280768735954879}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-387059093778399589714229351234878662223},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-392079209587618425485151451485325558709}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":301606393128151756264177306226883620093},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":17692239230584992469623108955041543781}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-286862895433471445377839728889853859869},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-38118266447024108740492131759854385365}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":6834099997388638997706336050221573419},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-6833307731273981902659032432925871391}},"form_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":38127012547664497405582702595001363697},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":18299986684493347804847068960002478213}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-9194484377451469292311682687821910349},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-38280363611140880232533595076749037541}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":9955675118472537381800174893052124295},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":9499959525214278998291683464895568995}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":109938412509906949680003950190160839},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-225973922675593239178845894647624043}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-2383207265739401487718793772495971981},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-9989917442427487681986130203251373051}}],"form_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":81594941804735424990811583039022008701},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":74746377265231685940720195792323541853}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":101755058152542173767417935166667045067},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":2950571434685278341241260136697238815}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":324680467315849637564889688778450954889},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":38761136657692394428651610701649352905}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-77513157295602539047624760833751195987},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-10145561247252253098404394536932896675}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":148012133121933576865309207229845317395},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":141169115992853789308283992953973991783}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1236749665650310176660128948225128289},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1149314934500917570908786083975102877}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-141247290447592307813921067787414999931},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-18510045610156373577510797641930329405}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":417070862010260153106077071762394991625},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":406817417056184187304652017258850536807}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-406384894336472382856226879265186865013},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-416621723008844557537399646498379205893}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":62553351627440035780274328028514564491},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":14922501526906779522682758997159412675}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":690763418176895790348002233949641625},"lo":{"denominator":1329227995784915872903807060280344576,"numerator":-5546234495160247767841243092734101}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-119793063008459549721964406172754458647},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-125537004988394926189277531355388782655}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12524548258275051932505262587412747967},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12393050782993958921008384788286979085}},"phase_rates":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-11979879283278291868936274161363567799},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-50576863319549200638641520162182220993}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":50304186683897609185280521061071778583},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":47689211301911240831076167334552692011}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":11778431311965687573446606693706465313},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":5616940655543954139763436519365683477}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":196834822655495699885652736940421319},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-45729788248789737813960194379900053}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-22480204473070965419489605465703936831},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-23567722045702597714064879694483044547}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":9427988005219531540110161947750245909},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-585090437591520496207151214430728715}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":270526268027803480297984619707360415533},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":30858119070117438250614921991769364509}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":107336384418332630316361453629316398131},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":48686099015238067061739492174753916183}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":48000743477121209596608131451406217637},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":20922631892580383445967804281723838803}},"cumulative_boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":134720307634055578293049236545577470383},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":249473403311442605454643573774435783443}},"cumulative_internal_conversion":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":15880265995945282108425144889844673427},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":28276566194097150477199284288694429737}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":6547014541245988263542120001943096303},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6576396746301282094118520996171342299}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":104945410714601056109876297142779633383},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":52472705357300527968095095007306784523}},"phase_integral_residual":{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":422777108733482029519238202614209351},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-6703138036391977011711666258625948791}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":199481206807132901965558616698711788967},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":99740603403566450804138285998257091855}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":205831034123750722085966672945742771045},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":212887482879916855631699904513766081291},"time":{"denominator":64,"numerator":117}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":61955057993048492052037654769620770465},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":27827949334332057836636284754388004929}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":203817576394472680245775243011289654763},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":196411416971101221564685256438072220373}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":778539243822020484306969105493358007443},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":192046438478599587293471754053032185277}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-766387089070789768337765118976411764031},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-388140554653215185105292332303625972477}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":146871538130496396670536600061460691829},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":275455350946114781132349023438513688855}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-139846660846147446164316092821741534833},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-297532036095775559272284302937891582769}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":3428425589760926109795106991017729967},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-6856030261684983409110612279789514801}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":75798089216745055841346230341798009571},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":72803224896455731286259960851689837875}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-36602971026868136559147666887087304357},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-38075817782647116014484334581177477537}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":9951248134100939302741798569564572291},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":18994387510783995653027434615502551221}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":227582981622657306276586792109473787},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-234059496443744548725333500586437875}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-19061525770319223814189962450973979839},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-19972011914916727247659063272309138317}}],"form_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":84031128439026641446234693803990818275},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":154317364418194009588061517350020065069}},"internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":53037183474257742177122543569989162103},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":12336581981293182847502048766891838353}},"internal_form_gradient":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":168024555469139493059131420130339769317},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":321535576990737685592987550897537874947}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-40188904002131168476675326414266486083},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-168020703679701106838754429297782682871}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":153332547787422332445579031352732610463},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":146513601285437062526412771060207643259}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1240061913707759024326669019768978549},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1146885583160628686852867673673945299}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-73291248600412634784785863595897425673},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-153388876755146365960232797815760594801}}],"internal_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":210318542228708592099972128364869184039},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":102674719632734450415058721854225877857}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-410256427573119037071227069449092719197},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-420180220456551183367017147238886941901}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":62525536064281297075298614913939632303},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":7459078532914590042016825776448589101}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":714973023147801115485507159435930173},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-367659797265297105242399949989059193}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-59883549326247398013437531262193454185},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-62743925909310209013963860852123811917}}],"phase_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":6172486195617439065934980548884972497},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12217030488914516068769385663288065173}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-45851121880524646328428603842400904495},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-48489595058213539904850685413722319441}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":48252582626599774463991312511357909233},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":22830547494206263210139869814001239033}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":3050454114655315425065846469224551141},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":23318363874772379001312259196446951423}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":197361983306585212108825699887513967},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-182532509720845054253271039317298705}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-2916166125033156641177015661436793089},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-6103149487723766790921024074006454661}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":2334620456513570124602711507124655935},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-18547379914114461312761913218023477393}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":270744279291873898234779518003845477711},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":247225254473406710985050984562886947835}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":102682022413820615342310130395863841161},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":46453945027606350698494733606433441383}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":50904886820545357661547396518732191253},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":11113533508813599328530065064792888267}},"cumulative_boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":139497282080801031736309593803654571667},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":64670047120490743803872048792492604693}},"cumulative_internal_conversion":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":8561662491811598970350727252383147207},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":7647418828897405565276479608121662357}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":6861376500412505121335266102567357923},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6903325588192002650011667426932359717}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":112494861166846146957667363226712209847},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":14061857645855768346792693388858126149}},"phase_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":6939015488230707608950898949341286563},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13750294006491220651981393808624781855}},"phase_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":102032459761965799335292087524793907121},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":204064919523931598298425956933711062623}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":210378986398898511531580161706524924369},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":217815213530422818950407350742335844477},"time":{"denominator":8,"numerator":15}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":62297554659113492129807123556302088729},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":14002280355003492572201043017398255377}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":203306875399332945915928462687459145991},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":98055375681685076520066300479291943917}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":770398884232112686239149520879825530971},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":760153579163594632333774152685920927665}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-189695615967075151631150658359118302521},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-192130302368217462413242170142552678081}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":71367203231737267642699847770754560709},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":267421624637564299172406923032633362663}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-272124899748931385230317003742015741507},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-72430638954226154816124557612098355713}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":13737213505303816667640180623882638353},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13735516865586847537478345753972523921}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":75268446046940599818919860313244253321},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":36166139486840966069164269369218665267}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-18195866643132874362760044267480344893},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-37835331716969761132644447294669184255}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":19867595122070672927305618351280206045},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":18962718273495217302597602177223580351}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":3675822725077278398726451084954351},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-242094514267872900091300631424897853}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-19031034099861474905221799175728646201},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-623058863979448207459663162038866163}}],"form_storage_rate":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":43167319431596305176897833922695326041},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":79449266866935395484099632966356274525}},"internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":55168247970172073187935244065191492121},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":102922942801067433751146982997305644303}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":347346818337898126581031095887240094339},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":332925514195726034131697739480998140235}},{"hi":{"denominator":664613997892457936451903530140172288,"numerator":-650225416173987933696894361441146263},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-347356165470778230706527959057737563591}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":79313993399009215966916784560783706895},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":18980047180770124386453113673899470091}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":620935654159192644130450132968185459},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-571442827543030006457050363916144517}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-151897911488186996587690630570158199779},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-79335096195494431833252805366671420475}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":423919578517615835629023434267235876835},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":414294044085815583105259329378054787511}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-206921555956129168074281923805864701555},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-211728322596042989825173029540988862159}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":62415890879993637482700012573540511943},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":29786568210052751164529297372010475293}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1478136021632152584155203862289181523},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1521124694996677768897444950340630625}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-119575513836683306226077944529969160747},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-125273417589237551148069885968685852127}}],"phase_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":3039445181038992080853701633612141271},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-6016731884843021418179647025345778161}},"phase_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-21900078842387792067373222037398841489},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-46417366208240525181040801905036733621}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":46219210490156513415387381037521590445},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":43653686071977881933293023819066121835}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":25246428211620548156524626069229891673},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":377596041117119706426872690345647967}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":98824978701435108632431569420891567},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-22736987674470675308687140942285415}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-24175303458680156194054227237559574735},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-25253145440367916916760778753972639709}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":9240720545091536183165741012626931749},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-1147214218499761109319633416974171269}},"total_storage_rate":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":33825164234195899461908531881678846605},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":15453062660153141268538840723260905901}},"weighted_phase_storage_rate":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":24483009036795493746919229840662367169},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":44175234414289734664211092819730972683}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":53825084695191302605132105435433851663},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":47079561601817552171407955824933725951}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":288524573945945795312428334295783790803},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":133936439976060475569622205419952019257}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":73665323181696423624174747150176880043},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":16500965893744820119824212923243000233}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3588201162506746813845755489050287343},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-903822546884675018015008676422441499}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":120259827501810326278396318496006301569},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":60129913750905163042593391587115599857}},"phase_integral_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":3555764055218897425152416693717048941},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-14090097379666398004774014811426641329}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":208430612991300117215679330464595354235},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":104215306495650058414178733895692574271}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":214712366576670755845748961073908376791},"running_phase_work_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":111260355185483257416565741301405894935},"time":{"denominator":64,"numerator":123}},{"channels":{"boundary_form_input":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":7803713974645654688950928385018122809},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":56160245558579656126689345291469290993}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":202662724150872948430327760644254698275},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":12229740100779711035604364372660903087}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":762353552338960666455940893045183824057},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":188056002506523486073057725398842887337}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-751312990088225068919972826389760969865},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-47555506899271914134489006785661596385}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":69204302991811766303587638315119005329},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":259007971621610800332460277638528411175}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-264188746977516743926725158552250129705},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-140774547059045252273355574638046729481}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":1717479926089534315224475130095625883},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13738090735088672613329594284226159017}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":74669528429059470765266819074485924805},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":35895737469250601270202161104829346955}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-72292592088939559650673204827652978123},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-18780505238824827602118551379762384931}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":1237932952301006351523442353140050865},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":18905187580630925674708522747180901563}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":121440047570970437625238399411776137},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-125034054373495835098608104332983271}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-4743611164044154575816415328306346987},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-4969429018506052553893431939362913067}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":176998583717134997899506335065227248609},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":163222797667784929479251340288281477521}},"internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":57265588302854182290486753746181327033},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":13387312343729883406377648591624118819}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":358562737282987489293914569139653148159},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":86061817748944995246791671092963957059}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-21515852069376686153219754814089293803},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-358591464428421127940426071083419701865}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":40973217173215358682424514233850590655},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":157143584543288007012225837322343845873}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1242182134775643963119714021366588411},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-35541900119113127046576962196047989}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-78593784250546862093391628257696682051},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-40979659201584776335477248594026617709}}],"internal_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":213463256955997639457150615679667080175},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":208805369574951296679651081589757604989}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-417152881669211631567089010607516215547},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-426459273349869940496229448155484269383}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":124450594194738095468467629758179635811},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":118784796836094226022354845318974604671}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1526060645202222967438335386594557433},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1571224266673285093275780396006349081}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-29804987968895287146860666584685782709},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-31223843394149102746956824876212050849}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":11963573209199788144579724072518373971},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11842933257803183382343089305989575329}},"phase_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-20884379153637398775374332830475039091},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-693163348057686484849944350070711617}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":44206291014235440311786353684900824167},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":5208631005612367506829259316996407487}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":6521090047494959087489848495578898423},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":781568070476357695442057110047684725}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":197699426969986677099928813658914903},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-181013410906728889310711852712372501}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-6254294629886242874176908854774924621},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-26088461312613960517458762074661922491}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":18270734762046765336423206353913677521},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-1134271633563909916607522801927876927}},"total_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":135053410966550899016391190803978708953},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":246944089811015627276214822893553649915}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":93108238215966800133276046542730169297},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":41860646071615348898481741302636086197}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":56751477435683423113488703579815647717},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":24856036556187986776173259442735674483}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":298024389140517964770099948075983229785},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":277045185027705734415947684119399715829}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":79033972085089003213907880313881379453},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":71024105703877986756688469914831045489}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":7491604432807032281881605386933617189},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-944708283963929242477322978350462949}},"form_storage_change":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":32056945812265248147729148546809002911},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":64113891624530496193789000033446661789}},"phase_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":7281838450280259049903508868728691663},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-14425393593462729114345664314393387013}},"phase_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":106287444921588624650923410771487859851},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":212574889843177248899065813846758797283}},"phase_storage_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":109413718815716007382672637573899306925},"running_phase_work_upper_bound":{"denominator":42535295865117307932921825928971026432,"numerator":28375035429579997251676434770144023037},"time":{"denominator":32,"numerator":63}},{"channels":{"boundary_form_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":15587636236491364689066699960898981161},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":28053778424229458645082511949988147149}},"boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":100947992647205215087420382041382357733},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":195117636151984569603569778748999685291}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":377206108497152593846530013794042133425},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":744408606494168364776604076879352089455}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-185996686337645802506285159214612048043},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-376695288767723922116493162109314910943}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":16738804982930159953644550537389354409},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":250246727861589395590291651208713288283}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-255914903034845922001848573758558800131},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-68260489392349642100672198783764803533}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":6861360900656583405684413256871238577},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13720924125113621791905913069688423515}},"form_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":37002828076092042292391212553746581749},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":71185069495131804156695269425590285885}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-71737343030664702188368484193336488573},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-37254897478328270123665680768142288741}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":9860394892741900599169411053228425199},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":4705522246209678384943734035576190465}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":250460025491330447558460510556985647},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-128984804637818838624518520462349783}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-9446018348329877065438691753799281099},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-4947948105977237598934823537824354047}}],"form_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":90519701920143868347933088528613742127},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":83639123707650884759760278635209016911}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":118648626594449932555159670496510532693},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":55604562595257826297166163321754356401}},"internal_form_gradient":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":46210827309705097046880114892203627197},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":355489835901335103526927468442022005209}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-355514965552464402959565630796045356919},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-46217140880351782481517624415018506305}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":169121829008938726738216045826055986607},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":162417584864452545919741403859048212783}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1240999293417491701139553719137277877},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1130278136727402228639983885331311325}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-162445734894366280099028940416947411235},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-169128761919412299121689840565420370133}}],"internal_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":214832998674249428833292377927806122411},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":52582093281495688503600105819359631515}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-210096813262357811948334803743278194629},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-214598157899771736123789106049628786207}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":123909376626129088735670697493870893767},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":118262672959965343327057270705841500049}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":393421688050738039392414663559764159},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-810435429349772710015181132091977415}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-59351083697575068722828844418852252673},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-62177749680326485452873679288369162773}}],"phase_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5881265760060676885959651487232035355},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11645604516622473110708166883508291419}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-39759237785368222865827124079177110533},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-42326979240623358401618082452698548373}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":42215913588536506348827662271722871143},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":2481819862664021585738442242999964239}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":6729143767878724201784380335012207097},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":25849561476225026167951365893279319211}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":98755585960471606827693304508071425},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-89944676264431598562031270848039837}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-25854041692633981682623852279207881365},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-26917678478486779424971491828908184591}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":18045751917500240622460785635204727973},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-17927027237801814941786736100194895043}},"total_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":134635472458971863758097794142090353781},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":246319503002574073989320827826165745067}},"weighted_phase_storage_rate":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":22057885269413997705082352806738305827},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":79041255587272304469800270555747711245}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":59674159230025553992688709822484206685},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":52342114839647485300323004380782737761}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":307488263451193453684545608892362825823},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":286191324222330011116115017498259076077}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":84595626456703843802430989868405310673},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":76237033447183407972047797726245516401}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3903260579815029119364236606639344687},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-7884116240268446497736818998629352961}},"form_storage_change":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":8524104340403809469443704707519183971},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":136385669446460951297382880692260164397}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":14899626737471004685642059126967139107},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-7377952750456437065858263490566502309}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":216495324503097171999326086756820904511},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":54123831125774292895195321046246076201}},"phase_storage_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":111360721847397411156896161645725463365},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":231251230004010045712497811166117309421},"time":{"denominator":64,"numerator":129}},{"channels":{"boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":31030053526550480001411248530325694541},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":55850384964883412606184922229026809983}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":201016788772386974824551225943402352349},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":48612383789971831431181473422162719069}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":11665337740943110223821646026513391379},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":736733667644623205129404755146294277179}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-736817424643571583982662145189617672023},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-746036081883580942887092686373102389511}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":258511330020109780801574180141970851025},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":120584576039669946126413122183004092437}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-247332261095068358812068433764507148245},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-132115143878289383184331253696859426905}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":1710878355858901540532859581342528495},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13685183450107864116390151736709253353}},"form_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":36640511621917146474798169178690221863},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":70517197289609012771896155665132739637}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-17780403560016339515579011664311904293},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-73837938586178608814930323631689195621}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":19609495260869673385548390295251524745},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":584804122330392940986830542491000185}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":257987618447310181559555712916189005},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-132894273134380282175578859154534069}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-2348013217833466852665414177754180043},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-19680411723512157691114075054900985053}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":184782502706989195256360026191579162199},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":21381810709938079593371268473003772049}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":122679562076511540860537802460088040663},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":3601409090476080322684757103494128883}},"internal_form_gradient":[{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":11897149948338253654957393514338143685},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":183321402390494826448938832298541314867}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-366689081031750712371988162642222638575},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-11899485974071253822479764274564835115}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":87154857752241652661098198775531403571},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":83828479457364276887756731469310571765}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1238328247748310552495273426729039847},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-70107881156700707175767724022035277}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-41916726330660666802944598249726093539},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-87147671085796613144394047480380958665}}],"internal_sine_current":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":108036510697752075522160575662364442787},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":105859943697748342379433263143521631239}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-422973161329041304135107794561314705613},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-431675888499080358788020089274523082221}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":123210092504304064026149283842991644285},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":117581845408140110027701485966939486319}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":202623001707799071741725044664184977},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-208749836091562259957965305915527201}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-118024017210837605784828658990675825979},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-123655673780416471446539660116951075103}}],"phase_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":2887916317206322811718241370384643427},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11438472252386499455726016048488336793}},"phase_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-18887705937463562936488261509595395113},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-10078189964285205869224496261938166695}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":40249966888436141199670863432516470639},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":37776367247619177967556757063760726829}},{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":216736350402191457320850481882927353},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":26683433755033857370073210398942696711}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":197086061799468834447608227325275603},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-178528253372608998360944217351325747}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-13342508387509698435706225606294334721},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-27739965264502345140989216433292348649}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":17804220934419533036510266984002885261},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-17689184521217393037490592636921673739}},"total_storage_rate":{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":2094563602024923995057977210169379465},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":61346927826067635447470782591783016923}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":83321638352201076111061056710101409321},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":18583306406191476260728245645775472825}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":62583226748139661492821014372202240549},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":27480050817438197633118961305134184739}},"cumulative_boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":158455462712449546564723223804229905545},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":147653073091474864754730771882457292951}},"cumulative_internal_conversion":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":22586557732260080570067174839680484395},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":81639147082897528456074933381486709725}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":2030179349403574535191200482859253597},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8209491561791762134347715655719881889}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":144719966115388221863077657923192093591},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":9044997882211763852421374879700268515}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":15230506463400053961325013760279939795},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-15081356624692103917472133804714023151}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":220190421717309461190517858166472588117},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":110095210858654730377949690211129539107}},"phase_storage_upper_bound":{"denominator":42535295865117307932921825928971026432,"numerator":28299071209478407717723888019011784543},"running_phase_work_upper_bound":{"denominator":85070591730234615865843651857942052864,"numerator":58817944585500391168342878556743275341},"time":{"denominator":16,"numerator":33}},{"channels":{"boundary_form_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":15389854166049923576997140194898606721},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":55389036782148399274770331580913911763}},"boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":100017706587155216607373635392554341935},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":96839726179599142741376659730977153233}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":738871939412010096221768755078535825183},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":91148648189399283537248800700314753185}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-729815156213724549334032232792307399317},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-738831843439344263094330618794357111085}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":248918910971625491141749758617567058247},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":115902676117459286003507441064887835919}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-119234257598588726685499771287578457963},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-255142009259921083741384391745995967673}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":13633934987791136157010494781028240801},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13632049391658277292931622432726103393}},"form_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":36249843750937965429391202844768368307},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":17447965086087108593347997486844484613}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-70449162628002889573260370042218268167},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-36555131548953308598173114936773060755}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":19473370206130830229253884162797744821},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":18580440383345956847062234958989814951}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":265458478352502063536674193403289859},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-34189331908150226833967654943814687}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-9325481134396003064601927795394454051},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-9771943750121831108164481087890086677}}],"form_storage_rate":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":47055029271608871325795461817438518743},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":174542573344129134367231618372070790189}},"internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":63307603035793858676087340012601233349},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":14899643164561993733925127613476490301}},"internal_form_gradient":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":195810090212307712951726884790658323009},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":377696364034120998033156727361514458739}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-377766230122928237919231083970105853817},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-391721690839083531169022830289717451729}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":179451582888556818944497177251342382781},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":43214125194285538410889403177701071003}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1234174978721898455170989011782306451},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-138964295628554213231189772718733189}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-172845798227575026467827695602353151177},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-89706684774271032858952573936416877883}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":434374545958722029606493711246294875039},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":425967434979591004483965322306601373329}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-106374800023470503946857366688379061873},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-108476496772820019390775158412184442635}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":15294349195053743470667540961529254873},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":29186087504391389846870726472866771155}},{"hi":{"denominator":1329227995784915872903807060280344576,"numerator":6515331292385512832805019906645965},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-107408953953787860228858344672020103}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-29296863023008694538796604696103341653},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-7674866674168859703693881220704939545}}],"phase_balance_residual":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":1416703556359960201721631634640818897},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2806044186159568365133859001667101151}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-35817183863185868377516824610055944959},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-19160959381816831217800285475363985679}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":19155125713271493073779843569415139663},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":35872830827628451608921432631791498109}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":28560606462378799335174373347045476621},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":27510966544250221344787449560833341307}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":196425048503924885551730644097645949},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-11058427281283932792946134843533981}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-27509263180582927030074349346652918223},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-28554524620423400038525546557673028261}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":17549502683579050290009888740764247687},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-17438165381204783272693399322003963707}},"total_storage_rate":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":66654497956231433761883384945908116479},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":244156664457305344250042432242699147047}},"weighted_phase_storage_rate":{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":2449933585577820304510990391058699717},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":34807045556588104941405406935314178429}}},"cumulative_boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":32734412202137011081753989079372864655},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":57556462734039601482242781903123709091}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":326287585417444894686387725926511780647},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":304384870512287149141465605614693694017}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":96281318713645996531151887484903303207},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":87226513269608276106296856236540393587}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":2108446249253974995510074745906835531},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2133345529314060339818490007633254079}},"form_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":76608380500331888785289968561645722401},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":153216761000663777335385905613116016201}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":15556021973148806805444199224714200225},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-3850374594011664903835574782618946847}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":223659573771789959415757917354504591035},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":27957446721473744870593571319936949959}},"phase_storage_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":114919949689077152332068988015398136763},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":239061072147836618580090869689971387059},"time":{"denominator":64,"numerator":135}},{"channels":{"boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":30425191918597700975808442793105003871},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":54724726610401700244828624324100342371}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":198961596176978968222058826174764202687},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":96407881865839823246080582018798858259}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":731290915374280017728060098159949835311},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":721782268803758053939385828318404156191}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-180744730460730774879612080810180524347},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-182946424419656551654398534077148220615}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":239072747592253232954828162706401048775},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":111092113849655484683813016761325989005}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-114675061185718854804237828857896321641},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-245803792444166611814070976750251933795}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":13564631932435567815165608840055840147},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-3390676971236780568310138034890844267}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":71665562122767862620468641204747740869},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":69012919579636796279951892868105588041}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-17430900204659829599223618055375046429},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-18082607908970217065802726948309197445}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":19312754086187460469822433686904780865},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":9211275919238155214774647617999361741}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":68217154939834017675698013888085911},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-281137880937748874210495894722772015}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-18492930529661432295809544256547307295},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-19382546624750750369337173675446807923}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":191345886645226433018305128687502810949},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":177734969207871975546431594376303153009}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":130447293255623695868055260929656522335},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":123056528102389164958310895523346628431}},"internal_form_gradient":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":201206107819413112821369441736952477609},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":388641272288972452742795350000416259693}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-388737224761475278811275678693981026577},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-402543036372699888954597061603178900011}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":92271343581202942828231773185508520861},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":2781425202366239207444766563865630987}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":614272972396132765332433689198201383},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-550136873855620931404722173484310003}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-177977350994636511422377639509717165803},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-92239024054956608899033941578644665085}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":436359262848558162656003697197894910213},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":428247215763199513440945626599654652623}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-427779333969556019761664268912086586457},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-435894465530619707484602827231731424527}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":121345612715505572737694474323464294153},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":115752307032268632139160415680946493449}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":428621025615558447400235265808137381},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-883220701399833834831515043704255299}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-58097254695330759663725890068106026987},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-60892066084178600260011624248877162203}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":11110078377160198148596047425561789169},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11004362753744007895141521455981637157}},"phase_rates":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-8471553772786718833592716766211006659},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-36356256297133582430074084126183479337}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":36398573456593836160757427862371327545},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":33999303411076311041501659603927427235}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":29370880873358152675000337380936717511},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":28331364467005585220653953274439873123}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":97764579964595904739008747784279029},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-43778501425622276154565902258140231}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-14162987584598827855027981494430668115},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-29360593248637168086646847314876288759}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":4320986289090308763504322714826933853},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-17176305485456599258637708189235120321}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":264824435498442581791007079221005794301},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":60658918632179442728759500892934772527}},"weighted_phase_storage_rate":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":9184818606652018596587743816687872919},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":64900705320845795368606409195435937099}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":68321186146642556629990019670599323423},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":60121684293902181181219123668315912639}},"cumulative_boundary_phase_input":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":41951738779780097977724591675431731581},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":156711554718604816285392830089478043489}},"cumulative_internal_conversion":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":25599008896250839318741744460245238173},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":46497394012203884106858839732098633397}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":8745342957572921208062860245457409937},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8855406455763043548253312860849494999}},"form_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":80930907637941435301499831688985294685},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":40465453818970717589175921162682695279}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":15875942948090916136091301185225435653},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-3929026353383956160974113374433039391}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":226903016800297191431909983523200569939},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":113451508400148595482091300220762214145}},"phase_storage_upper_bound":{"denominator":42535295865117307932921825928971026432,"numerator":29132921567340998074960119068838100505},"running_phase_work_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":121309561106916507804039526969628292927},"time":{"denominator":32,"numerator":69}},{"channels":{"boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":29967867502117120612856533712447997207},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":1683109520448348364968365799890617007}},"boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":98902259076603702645639685932913841119},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":95933689885664653958147761626599293195}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":723845776027518233786369531230994455545},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":714519553424349148613280632498049172991}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-179078637843376175045851274188321954637},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-90613015152458071586882208927279629853}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":229000698907248606920824487418672369669},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":106166712972693380799698105447028377843}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-220002278210556171872677792807033895407},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-118120514858140213414772379731706961241}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":1685037592132038243182586839017425479},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-6739171099929144422494912608168293009}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":70782409276799916852634369134588332521},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":68184088274467532476411765378095305123}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-8618549077519149997353093914310637301},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-17875488712593840897671362396175772667}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":19127998294008820023437364388079450903},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":9120208071854115468543619040122607381}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":35026805677112376404863031675635845},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-72162095257314877277761138230195735}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-572198359986997076782961230803033811},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-19196728287350258589691468591778909549}}],"form_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":97077390292644055056213042938598689905},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":90312732261077253389529067893538875859}},"internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":67084035858889277199167446789259171661},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":63407487596942328243988842784279115877}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":413076881763243748476788713477397729065},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":399468840925015117763641994921888864105}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-399593418578391312040962670748237223309},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-206619796888041062435237792544363799293}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":47394619917461762498864273135542964343},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":183116300778819888141575671933672005063}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":305362011832916677395123137077391985},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-543718054040476173208242196276900105}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-5720522330982186735135614018997251655},"lo":{"denominator":2658455991569831745807614120560689152,"numerator":-1480349907267758643006637317078198035}}],"internal_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":219053896027446669332786394758141592435},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":107571616624742180912617237705119540463}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-429821012986337853801770922620512837095},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-437649018509464551339396356016462262745}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":120184757836672413923922983151122805171},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":114607914710988889191769062123495773241}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1760639286302936081955105034193852557},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1813631266624218230555780261620045075}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-57523653252200893303474313832267932605},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-60308300560498945767508602041221383783}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10881584537032489697475779634292546595},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2694897088097982308058481865500869485}},"phase_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-15992030417897373601027408878466757441},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-34417461764374873303230353029408665971}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":34516537577370887663505293983165529519},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":16078625876332127304132620089468929173}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":30172352143302544104560222783581068899},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":14571932214825734424632208499947604901}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":194399494462778095692071785219762053},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-173070831897696116358939117958711497}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-1820898812086772768449740827646887949},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-7539360167913365259177130682485785395}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":17008788750194897732579266336471838859},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-8452417014178160083433272334189976195}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":262735673175871353327862495186170169473},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":120417709564542663175062947311171862131}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":68580892590583243215436409308972789663},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":940780540733294055797933731801030821}}},"cumulative_boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":35565336862483018343722659853070661581},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":62646348574574703728671672368151838149}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":344885997026672380944825453959664525253},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":322416892863990693879362012831449770715}},"cumulative_internal_conversion":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":27171290986693556753097231494368500009},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":98939239986621111486591633475223433907}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":9055037434308141713620328954470360799},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-4587605838118153514296859176245914903}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":170640625995503956928883634797845632855},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":10665039124718997291952532958195218337}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":16190057627851932588900029222153758809},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-16024970494982870487142850527314027031}},"phase_storage_change":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":14370111659066774965992069754758095593},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":229921786545068398971090969957127064315}},"phase_storage_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":118031870583582668695329529657200438875},"running_phase_work_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":122973378520025634729116910242220545673},"time":{"denominator":64,"numerator":141}},{"channels":{"boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":29409468930066272971739346847987803465},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":3299761551757140780774275604712194827}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":196572907905487913050385539200669179939},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":47710694354287701356016379289827885177}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":716543276861270233722796421031248750833},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":353703609939238620694137724640344944869}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-44364211620763152582204593131737016519},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-359096536307771523096366708270781789791}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":109364664218638867603971109921077942177},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":202279312563807802055052168398875809497}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-210448904571335855148480941234890134073},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-113238911964318455140497937082943540555}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":13382114925405684698271293814598356223},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-3345031514957167982944205872196363357}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":69853835477645722775169454136784368675},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":67308927315686558657124588630197820669}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-34063425078509843603187518849147087505},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-70628188180058622826258124264474205255}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":2364933160625663539997253468245810679},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":563574834037742005037894238419406233}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":143746361821146475879693448440469471},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-296036530226911700656051624922755343}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-9051781029681872801022715972507807473},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-9493391551331426293756543047589721217}}],"form_storage_rate":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":49160755426501126566651730340272628829},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":91604556957490418425366221418867064287}},"internal_conversion":{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":4305321941083655088719705394704499221},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":130464721952484569075947217871097041861}},"internal_form_gradient":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":105901665571621254406094467868567446949},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":51271364212067652376925890236336434453}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-410326686433368801557760903433124705621},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-423803863627869641203698405936949884901}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":97277300472785928104686367922023920869},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":188167166552040093320423086024640440841}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1212888601014465091193860762054686479},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-536617141124200865886662888987173993}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-94039623896015540607947807046646339571},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-48607299986533681387911606688590653707}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":439627560647647869550291250694806779361},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":432092382164102961586072653285072074603}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-26976970707823828044021278558739386427},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-219588583719926002480106640104871058497}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":7429656643652475048058448019835075277},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":28328360933776915747515266645116067397}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1806370057110296403664814038244965057},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1860052377110157131053123066869125081}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-113748035139008103065297151419331357039},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-119297476621256877438120941280176511095}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10648700199940918382412843980760641717},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-10566236805417703451993574820267676937}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-30112174395334458107265949294897445671},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-16253558674803979043176624719236115953}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":32665638115154276300740563328726053861},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":7587009569215136052381389697379284409}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":7741081610439723814170357522103664721},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":3743466835544141567138226932865322759}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":193037216271265739004924673035441535},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-85405270557757757093689398692689167}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-14966870989553594106076011774161723977},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-30944368252829811927818418130036999619}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":16725234963154209317600783035912064729},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-8320391351526990810343521774803098577}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":260364197208419267234054709870618722669},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":238751063062566477373177189347038589715}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":63721175502414760967447788509528207353},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":55541949147585640522444746509304461141}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":73887811437159749778545883473140179737},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":65121169738392559314252379071685984269}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":354100352084742126869062276109695893063},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":331362648055419637883615083948292499185}},"cumulative_internal_conversion":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":28785786714599927411367121017382687217},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":3282961682129494551938333103529097117}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":2340635395360377524156142985253889345},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2373118286895391155087366625760755679}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":179538485147977895072903610325632649393},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":179538485147977894803664901039627905889}},"phase_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":8249086345452351141993156080964773875},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-16327904368673671187086630714732178771}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":232717673887924630522132912040691298067},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":58179418471981157504987246520508151637}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":238842525520151243470737385932493388061},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":249045578256598301207035616796764785319},"time":{"denominator":4,"numerator":9}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":57504127214147616142852849188100692391},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":51538272921321048861867020026124905081}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":195275042559080045818298267222910048169},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":189749999743971788482770286703195765745}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":709389713353537575841830235070645408577},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":700451011144208612488165568551545989619}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-351761150611175340299035295337966503661},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-355829007813467891884091663867012435153}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":52070971708398331078944493111990834833},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":192046953411595494213928109197761643573}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-100356324064567928519002047976134982747},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-216536987642556528901172568524537226545}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":13271232581036646482613885426591453967},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-414663054170256221566582573740032721}},"form_rates":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":17220822148196748483237597252879393119},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":66390842083519918998278271129154755189}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-67262132502433498477711748111567878785},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-4357020664812354905257499002812556155}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":18687527832048356652104516117388384897},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":1112803726356034062879486352221439885}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":294700565317656993442847077314911415},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-303292923980200928001310597016617597}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-17872934003827100870268346295313620313},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-9376536167886474731754481033332797317}}],"form_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":99404004621666609149764031442822796445},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":185482164118745274657554306885258180683}},"internal_conversion":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":35311813659511464401208025014209633841},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":66999251870487761477523578716464616921}},"internal_form_gradient":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":54249315615534142024237465200362510781},"lo":{"denominator":1329227995784915872903807060280344576,"numerator":1643515022313358667902295524694989565}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-420929403394883912225584842084644011139},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-434228819698839138850965155857550620473}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":99733437220993744946584649634823646739},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":193159403401911469120212960853676747817}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":150359413596254209631794153906371139},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1057702014908579267230199276886750613}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-193040511084270648996602581764720501993},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-199307087596259668526941210295590541077}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":440925813361022356050649684594222855669},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":433671991854083284768613789280283476465}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-216609007937074573070767334944034024081},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-55060781217360900618956278036964365215}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":117417200301835825515799612732559446165},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":111871232371438822006424220807168875001}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1851658262021420445139180473647986345},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1905645643723933737419572727299761267}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-56149478164518429603271227730907065295},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-58914514282302282374739782757492888953}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10412998010645746694029577219676191487},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-10388519936526005921400104843802091577}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-28271911267200149641513101513470055911},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-30626702171958032362866467748042102683}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":15423631911659307275697199340415346317},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":28572925817928564994384983282807213337}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":7936534762633187790569163863315176375},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":30742273856095674191409677046123623147}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":191443551313940740367187973410784135},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-21042312998869745661306615709665677}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-15361675778023742960356635130227364281},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-15860354092097053146690416426522728005}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":4108869923653014631714630005589585983},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-16408986772903870361745804579573837127}},"total_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":128861876179952447935747913375839507379},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":236370183000323791599405311831436903433}},"weighted_phase_storage_rate":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":14728935779142919392991940966508355467},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":25444009440789258470925502473089361375}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":76583317400322919285242110778832399693},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":33768513140789741739826197817705294597}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":363253869704699004016795007385769801571},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":5316518426459661179199139705273512511}},"cumulative_internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":60882055959779054610347494379847527607},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":27833988422750513325136123704399916395}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":4833777628316979351041774492656231931},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-9806894090665533304744321809366758891}},"form_storage_change":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":47135133807303873870570109859580679659},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":11783783451825968450074548608072543501}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":16800113054074386917018167575016278797},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-16624735585762358071126072126896769613}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":235293180427934593165068119952826024287},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":117646590213967296322562220220636683189}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":241401970002999565553106777600042660621},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":251917916013696950716250512568170135991},"time":{"denominator":64,"numerator":147}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":55996032603988252355771058475446531143},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":25044947987386390301663238823784208089}},"boundary_phase_input":{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":6059960956295265563435008176275708051},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":23574582332161484770069818866624301255}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":702390938755440240638071170471032275497},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":693656250904125578943296495884483580163}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-174350932657346576478456412272526570937},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-705303942544355363845535143882684673469}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":197688305486975987166909540081226745243},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":90830053859311425533903660012037944509}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-190814888557366215878750266703781104339},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-51610013004453960418330077743263793503}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":3287197835450343685994284005316936743},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13146755028317396602106409942429669493}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":67874056342784054483207132728465397763},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":16358270205711605242948434263068385207}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-66357245654227433384782086132850208735},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-68757424936359772167008554238493668561}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":18432568393096220486625398505028940753},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":17552193186928168270975952349314163315}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":301835400735559685709439439921526709},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-310408382262820950945434504430748309}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-17618833562938042716562369931814097867},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-18495967242603473179910816705452679309}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":200648241667384696711871843797071296113},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":187441981754033617655015217444725446805}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":144592704178362761901350568911708585155},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":137409554350810541364568230128235132963}},"internal_form_gradient":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":111058474995030210005387671538297807571},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":13474015062596982735314276205621882115}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-215697211696644240046777573208017884969},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-222253943747387925039226424569666656415}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":51077825051779682109978749886344305195},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":198088789042911168035452254053557052899}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":595708120458512478276335599881095569},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-520436951188444530881185425613859429}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-49484065087275702865465548823534368577},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-204114442334627178287894887831053646847}}],"internal_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":221004802420257148358547882782423286559},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":54379018790722705859059135539534736757}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-434587417821956197888888605576207477061},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-441583411161642709705266802950754568557}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":57907621450542506408598819236877698615},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":55141841170442353940686074718207121183}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1896487755088331165900519033945119409},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1950353386659141159130779525706141059}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-110702396172294873995144089140470063025},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-116213589620801072705608879632100976477}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10226741086208139988963023053784875879},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-5102301586709137633723149436182784177}},"phase_rates":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-6616133344526120373541017780123791309},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-28777596446441470770150905819785736311}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":7265675655469410917569131905361168375},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":13416541174088605615030920301338099927}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":16258576678747562476498768507515287353},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":15763404973633493641947865118096097347}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":94809892010954485094644589970538845},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-165660226698632799894106172216275419}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-1968908390730252322810651308732684201},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-32485822454001540700279775692543775269}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":16192382600457294196157820291579170659},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-16168208374183451332770370031321785655}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":254878937232521952960042848872141996877},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":14609160926953331190807559380309212695}},"weighted_phase_storage_rate":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":13557673891284314062042751268767675191},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":46304593077219681397905732640221956315}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":79208131428634868614418879144868955841},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":34942495077698478785216662137570179351}},"cumulative_boundary_phase_input":{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":5817872049049092224405429994534115057},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":174548823833989436128760561606244456837}},"cumulative_internal_conversion":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":16067736865989857960602599584678924393},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":117777026551196297427008630604860687437}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":4984902303105746019670660034910749367},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-1264775630468623194456388579343547723}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":197631821312804747036783274949822544873},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":197631821312804746743588567187551969201}},"phase_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":8547860801332198264172443094019553833},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-8457655122610600185983297725344877083}},"phase_storage_change":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":59412868585681101275261303180774156549},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":237651474342724404562972293594632922045}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":243744999250462155977181424800897545731},"running_phase_work_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":127283392293972802467469444522661338105},"time":{"denominator":32,"numerator":75}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":54299908339643411849087812920296847019},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":48455733592746959018706710617779108829}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":192511417639461949047833577156076206201},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":187389940183418401273109170531629839479}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":173888095564531476209382797306614426363},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":343513930974896154011531439621117427209}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-172868921994226468027744632817531694013},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-349567698684026265731632034692854532747}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":186965199961808628128901872183585944331},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":85570615504306561473097175238019854969}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-90387877582214784860062136251132734697},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-196207284154685858441146415111413865619}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":6507952111404342080485442887017834393},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13013851113421861169749442020797880215}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":66829266140614755079383462805850038185},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":32219367176350079652034068008007909319}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-16353760925968510675451388030144504079},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-67766358819060002738077591951965476513}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":18154978583002140819145398064771409539},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":17276787176283792279357330176916503421}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":38611869562098606020547869291794603},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-79343488318489390589297135957178777}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-17341640728881168823809824611725686135},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-18215848516703237539344203157337770323}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":202163240453442987994804778647693880297},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":94543490629101032568398464930723429475}},"internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":73900462015990257228729279480973946073},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":70345801318943672407563591127939551341}},"internal_form_gradient":[{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":14197458085568057930388423762440993701},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":110362533972405102509515087849494955637}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-220857528875347191369034166480118299959},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-454634922900567329167607059372314902573}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":13067753036142062767396886246279428421},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":202951279452468427778666928294388426137}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":589259909052057975845574769959997787},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-127848168014324902179667515053765459}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-101381220196718068236731364347036006823},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-104423718043915682111311354211908628809}}],"internal_sine_current":[{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":6920090542103885283701872748011974381},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":218089766169294030023757421052326876537}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-435746507038608282258927170404938916341},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-442475600924780545143311661492553182555}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":114071094684879119786774698817418081297},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":108553255341295019853474795944587001085}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1940844252122501240445152929456121865},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1994119360092430771680543964625495209}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-54480371115046627332676096485662649519},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-57226775878979423122928888417719212281}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10036006401993137631726625645168261323},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-1251880763679959110971649706318282749}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-24691213329403203846584245117004453947},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-26961085706868173513105343325278731615}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":27313146334998004342547512320230577497},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":25129585658377075387536525724557403769}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":33276759852898119882377580604104963851},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":32300699331684959802422497863003151189}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":187567254583031416751757211842928881},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-40695335809445906633997222730224215}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-4033830582748893551980909425070546259},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-33239101805447049030225511738355631099}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":15942589230708652150366134713135140645},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-15919575828768364415191262965275352743}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":251788263006874012442182015862544088953},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":230891750150336996481730127111097700477}},"weighted_phase_storage_rate":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":3101563909589439027961077325928138041},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":41804768892134931344933197249650841527}}},"cumulative_boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":40876719816027826772422435187753935273},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":18039088166889242818608800333837188607}},"cumulative_boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":190683891920495840611782359289687217907},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":357881551114076609817198115581159062399}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":135470063241917950300014166628772702589},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":124371945424847266715217717273105020375}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10269041550366613608258987896906405707},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-651635201950172034531906731256486747}},"form_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":103398669821385425798955953252680090255},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":206797339642770851292348529304176785183}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":17384858862104373400166169114179802491},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-17199491681881382147579753426540655429}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":239796346734263032917350118066566162301},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":119898173367131516180383623939864380005}},"phase_storage_upper_bound":{"denominator":85070591730234615865843651857942052864,"numerator":61468793650390959563190976273449413199},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":256995838416144414508347001306269415439},"time":{"denominator":64,"numerator":153}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":52421466521374051908315386464661959169},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":46640951794303614435310151620759995031}},"boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":95529997237377006917495556690762068057},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":93068305987175040379593575020421591855}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":344439533687690288990733726543690625755},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":42535649038526201183388972293749052393}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-342870894895725546982888085711398085761},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-346578249338435745603669390198612666215}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":88067941074793921634253967152775902425},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":160511486733686270150917758953734788771}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-170614150888270411011583424971081896677},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-23232213972939481338105143514621179623}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":3218414048189089779892183382866645893},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-3217897773734785776802414625894105577}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":65751886127047248212378959286137644883},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":63410736971108346113070446235430467995}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-16109557763877697042798810391865017659},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-33370933711554102113786558009960968571}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":4463789685201818998997660683403198379},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":4244760617242371717600296846139811903}},{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":2467790880046329827815000951463495},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-20261307316920158568616418077861225}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-17041744801109850300679397824074701303},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-4478276458570826666689084957129398541}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":203353475682231526645459743483505490343},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":95208276944839574194315101263183366693}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":150866678463244239587524474565281196525},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":35959716923792888272645214582819727935}},"internal_form_gradient":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":232121546025779885708617394915381362435},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":225789283668337655733801766617815176559}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-225942526884922369417785943786506115265},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-14518880971308297844903737166447390741}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":213781453948674450279910008626134749781},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":207743002550590346300610290997044105943}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1164194797698009387008525485183648623},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-250868125534865402129888668671770223}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-51878794602531423500668261685958480115},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-213502414921222463368683069856905846741}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":443561045099624988996817885000779984691},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":437120629547759761830970489914483075827}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-218350934497336334878058383311031969017},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-221584784683193093078409368624417000635}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":112187271057599442909905515522280902265},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":106682470171007289754001206573980855759}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":992357593516728379093691342520275617},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-254611096875845979218774110740034471}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-107076440543037515611689464373763167803},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-112551363383921800891507318565983986901}}],"phase_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":2460052226692869753243661853959810653},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-4910196511397443476301534422933299231}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-22953038624922665572532766471770674527},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-25178365052892295743329770550837990061}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":12799847694625734504792879484776433765},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":23463427958734985137404749676158614739}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":34024375137303925551629011733739840551},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":16531662874339337077423233832656158321}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":46321839193876821759413273228373129},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-159707608972287832873565793755571945}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-33027066410568062448969189977530538943},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-33979964696769386754415619122680819491}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":15686054331455151635599764713303541399},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-15664173349661343562869111115440735985}},"total_storage_rate":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":62115904525027211707524266593726680035},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":113908643823233361090218694365372679649}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":45110142417877320184637322891401229797},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":4675091719598446723975898275547328239}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":84210695875245062228047154116038899883},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":74342647282914953201090364692571879195}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":390323721081995775622079927019133379695},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":366606704800374269852785013239323586635}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":142541938794882524030679376374020258677},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":65557196174029216633169347503691859681}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":2641260796411723020923817761706829441},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-10730551853507308025797899500637930887}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":216022082816620278551124330746782916321},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":216022082816620278232928630989421227673}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":17667402621166441044046265381746629353},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-17477160107279156065073500599301129897}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":241732168626658186866151902247049957311},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":60433042156664546572666932853112132609}},"phase_storage_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":123898325574409078311500882587133280139},"running_phase_work_upper_bound":{"denominator":85070591730234615865843651857942052864,"numerator":64802332183484335588935308002937415083},"time":{"denominator":16,"numerator":39}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":50366813462236279526965839828024909695},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":22325569944954294256361495003765671269}},"boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":94785503564019327190078536253778668787},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":92421516338133178927476535789956593993}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":341187815195797286258338515120858923309},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":337143997558443972257648054441439525235}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-680205276954677673821827221553423826597},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-687370962039196895964348614600609254639}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":82610190043922945375986197733562263055},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":149790765572699526599213746749807704023}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-160347782621614243254057157116758300161},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-87704577135236929059931865212542578961}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12723101428795493214606665620414538319},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-6360514635317278300172075044863225887}},"form_rates":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":16161181815986270300537100739739995349},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":31175934209092018713989419364850451053}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-7928670695011787953235561396366494143},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-16421634141929579275800718863017932643}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":17533517583660282025904250748301616141},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":2082421082639422818184076448321585809}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":322780480211772373579725577387185293},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-330820789120379647754606344858328183}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-16719544001099953888909471932275158503},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-17588137489094367388571460881236969273}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":204220294175288532757326593426629325051},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":23928874823593632416847327102142095079}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":153785214397147336408156927078838302711},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":73423026428292225514998468899341722097}},"internal_form_gradient":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":237000944634988552957457938038251829793},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":57693495183164289850221709976643113977}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-230949286771725401153599794193508394705},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-237205172890629218739274751557775403017}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":218400008657151686705038796020632266149},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":212460251938902460957654601510666103113}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1148450263277368781564738107249227013},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-491486133836639375179807311067715369}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-106095388715659753635206194333317468749},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-218075892570920915354426596736858203997}}],"internal_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":222020910354665577538055306237206413771},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":218930874853896857676652202524168278319}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-437459903974746872302589414759551164447},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-443671867892229673211983760530455023211}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":110166340064829209955594898712161249109},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":104673900398408231167047015633762683651}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2028089570710979435366131182060106507},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2078608321510725797045350346580888499}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-13131499151306728264516044743473840107},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-55254763526066096779838089733177813217}}],"phase_balance_residual":{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":301246188979781073975960335834541419},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-1202646465861775351491058808248518451}},"phase_rates":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-5312753963027070031694963462289472741},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-5857635846846339627510234057967099695}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":11961681719944728708635002254764589493},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":5458880093251009329172263115660927679}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":34759440949098425367370382365927447121},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":4226762413328220855717790347125216679}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":45695384073945461044413026711117571},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-156444895322451988725932732460054281}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-33771211106706685333522158421714140413},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-34707856271839199111645391557090149067}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":7711908967792801101838703543482502605},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-15403039456965874034112631275559740865}},"total_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":122458995250880274285676734337204767867},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":56133695283327264968252570265005626601}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":40697696326472015814026875247780210683},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":8275945636140000134557916060721436443}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":86571640256287387830873677857977567525},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":19108917366313604571906063712293727719}},"cumulative_boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":199604931020561293773074894896462564947},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":375271221957074255377235938469632017321}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":149750620719748805424811732330840804117},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":8624862567231926838023112591668562863}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":2714402780088528451814806959313925033},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11031179314716832083530487565998311871}},"form_storage_change":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":14080692603832460093953330259570476051},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":225291081661319361172154922622820059771}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":17943247515917756192937179346423656161},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-8874106106084276293604161233616376051}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":243463848753243206145361385485214869365},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":15216490547077700346910729116187210749}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":249514135510755497179890295218134538189},"running_phase_work_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":130606030482705879068889994163114062043},"time":{"denominator":64,"numerator":159}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":48142389841500657544629306466368100345},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":42492250762799772134041487110132847765}},"boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":94025284237101468339245371760287561981},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":183515162840364227847568308676605063653}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":676046338740375628184766015415327507327},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":668184523659062836785850279313155827055}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-674869035639887386829044715983732936069},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-340891060919770146498096213673996369545}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":38559366112172569301386064826408313157},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":138997711401413551144273534955723739781}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-149993196916999377283963297727265765785},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-41219564746176142728638392051181205693}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":6282630588306476794916448618560007343},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12563186989531647525174877965828996393}},"form_rates":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":15877611588562062568843910076209260265},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":61264756767124682318388414365164757915}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-62390862438499869282622183574622501493},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-64602806823090325360096010547368255891}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":17190471938445042955585937743934295649},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":4079545943249302442134832275929918229}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":41200397412712295156670675796896989},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-168642661879294235571305810161800047}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-8187722584197363166709485322272650345},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-17241350108597470560830104918061720735}}],"form_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":102382925365983376620873816700279788163},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":96065727667344794482916399184539102039}},"internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":78276126241360289473189184934269550063},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":149708338792554027517873249053306713875}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":483590117632035358302627929820227484555},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":117838226842413091867564757955669951239}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-235875086562890697856562103312980944531},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-60506051140954237313380484483307823293}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":111468178522125539032763536518852358003},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":217099480750956859306175977498361302007}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":565647808455451675779884341565661645},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-480661117172220743135062423233190151}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-216785709834091716387688099173985365207},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-222564544091955114402023474349228409899}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":444334390629454633498571930966913844295},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":438409017949279868466876451196506144857}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-438026828346768310179515800104432547291},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-443988850965398835755319041961716651361}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":54005460353560439308814883994057067853},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":25632543130588104225823783958931476727}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":517739463347027484331822308793673237},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-529806547641818244988815114829956935}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-102889956480582693780299277618902717013},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-108330597678278794728611195078062981309}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":9435525674146263314820191638754181787},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-4708946365864405074648382193602962539}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-19586074790875853146894886855245955797},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-21718647614061496022192718221597953759}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":22285081896678784708048950443121500635},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":20246697302211678853607671140618388371}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":35481423218492240192880719413957814495},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":34552455504198565817192955189224335039}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":90025644764782724782948952959222103},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-152999185500063256621333015667359879}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-34502517311781002173554330446603910611},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-8855561837307186625197818860590259267}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":7578436580296332738073984030320905111},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-3784291507773476561491630384450633805}},"total_storage_rate":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":30145535845469583182219720480922465205},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":221055792284609687977153528449140689087}},"weighted_phase_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":18199218015894956108005065223410072657},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":28924336949920099011320730080062485009}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":88828314780107731153278176598588572229},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":39213746859880328803203724778731194057}},"cumulative_boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":204012366219175425101477021697726044415},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":383873495215216328557590702938847879679}},"cumulative_internal_conversion":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":39272251888719083140730804604607143609},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":36253844864152949862067527504017689505}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":11146570756821649239688879287984587445},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11327878401789957766112450213971910267}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":234589443933194106294366438861517733579},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":117294721966597052975044472401522618199}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":18212304582694229392273117260228065659},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-18012560738704825982256082949828505109}},"phase_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":122498396121517112693470300890323685451},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":244996792243034224772427850429552825701}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":251032844448312590871127470756346539563},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":263009352981739050754683933379381330809},"time":{"denominator":32,"numerator":81}},{"channels":{"boundary_form_input":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":5719364352707378148622628988045634197},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":40170544837507064405274825463309039707}},"boundary_phase_input":{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":5828262224407169032941379167802639353},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":182158577084563630803164124922594510495}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":669895109194057913268730245450084282419},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":165565868061072418615949086073526033019}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-669735617447016068154326547388508397491},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-169098238103311887594272058668618219997}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":35801170191008663062604817334576222857},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":128149753004953816362522135951347907083}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-139565820198054532796418235862370492505},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-38570135537524826969061583988910419985}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":6200561072483139021600994157897727275},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12399051046091367988450693780832490655}},"form_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":31175774932441748002395404579188144687},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":60151882120168916487759370533489187385}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-30662499438203684734089198645637233811},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-15873244561981839865885747534437837825}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":2103305817778151545811631802403921973},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":15955914025609426063456202795476485403}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":84086004470495524357840189148718509},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-343566517538039036951518757340091405}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-8004931764732829144305627595652681135},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-16873158442833487649672220158799693835}}],"form_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":102496521453342028838315804766743613411},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":96259920754348030099200733126172293619}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":159163977733128402997871128128812004317},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":152421375924210715228154795754382732565}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":493003202230257995625809954870338141195},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":30061773585564233004927763910325467231}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-481434782189726311721994920922707898829},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-123378438015091591009619281131498853061}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":227387289711863713285938090665256352483},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":221657295658839061963091485947871325859}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1112740573918497791717509276244961941},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-938560677239239252343979677068315525}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-110648305475165770120907130743872370715},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-113482599833121770745385488355700944573}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":444444832222332316552321601974243199953},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":438768379900011897174056874599310970885}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-219204338828258308565270941212427346369},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-222063339952288047405136726368654754759}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":105723681686152211679793758045449636549},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":100253964568329833948592829717918465995}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1056655895656909005912044582191793127},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-539673023758466147760089726540356959}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-100592939298288940707396378646139443351},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-106017181213724560127337080786840786193}}],"phase_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":4613822749717116728261747549885322025},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-4605524340780600172173191704228952523}},"phase_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-8979536213934016796975133089593690211},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-5010906692214768774539897215651235915}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":5171426081204094418503075622891383457},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":9348860319053291369683363475551620917}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":9047452788477996762359995996211731817},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":35277854276485949963101050525145079831}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":177098162718041471350326838361124995},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-37344142793575467286134883451356943}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-35220449522229318486084911304330698695},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-36122633436721653101262985135413768245}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":465192682358838241562785970035525839},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-14867497918734880563080744814861123949}},"total_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":118607643878776759469224050713520188525},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":217391808083953553680024420459188408923}},"weighted_phase_storage_rate":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":8055561212717365315454122973388287557},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":24871966575257493481622954206843821685}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":90973076412372997959011662469105685053},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":40155244004509400625202353500527499675}},"cumulative_boundary_phase_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":104191781443740400938091528036789011965},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":196206089258027624375744510647297248679}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":164549819011116726453448427549466637139},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":4755004107908099272643433314595545269}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":11431770532935908495824178962706421657},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2905126357118959574845284386015396221}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":243902389995013886470818752030818869615},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":60975597498753471528269738118627684327}},"phase_integral_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":4618625196876825977560184934340296591},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-9135067014728300727080982373106611823}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":246336860292445826208281333482489046583},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":123168430146222912786807140666942687803}},"phase_storage_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":126179232210135547185867741566386521985},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":264606994321902427027776246080098599251},"time":{"denominator":64,"numerator":165}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":43211334278422095578046868605014613673},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":37692537930976293802413502962361040549}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":184937801674903378537526255985088375605},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":90389238621896731546929120458197692237}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":663925525758541210607325710870069450145},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":328264016029054424643181534522651894907}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-664807258665723506362458076178410406043},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-335603044199621136268719881579260205019}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":33034596630100319602392145776745856153},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":117263140668437245050273805875832720901}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-129080002680673216932025809590158730771},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-17953804172826016520818730693481645257}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":3057908841808212210048869451494295795},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12229572541461663486779902450295051831}},"form_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":30585199218406576469345370793967496803},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":29507790497209078568538961766224336253}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-15058479795739784519509664368662799993},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-7794901960751603438665639075514166015}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":4110468475679299388898287597405592235},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":7786496838952525249539702731891099769}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":343001871359423042872105162163589421},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-349656612450498978449570969757637495}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-15623222530935341491593997598635734685},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-16483985217430969438823204552644081159}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":204905449649087893324409524699242044243},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":6018712239147719671936896391553374033}},"internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":80808514957883298705356859187494203607},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":77490638175439375340900271965451910257}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":502236906640742085237719254174384881763},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":490449706807730776021077990763758454967}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-490947684275184924472535420434078961293},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-502802075454143977562927001675198044963}},{"hi":{"denominator":1329227995784915872903807060280344576,"numerator":905272414131296295061124142744463567},"lo":{"denominator":1329227995784915872903807060280344576,"numerator":883322074510581966347926232045961565}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":546397579917839939424243861859071369},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-914726537080138224514957734853772009}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-112860136413116654517539107095623936089},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-231274838607987026763307034572831662817}}],"internal_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":222189518259178520892297370207268601067},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":219472803214877638134006844071138190241}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-438611311325644030804154377210056146581},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-444091328265789760436938268798267888425}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":103307340528052181265757994871137478457},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":97848005065813602906703469483936151589}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":67348259951894671144608170037548883},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1098478644953581022688234714978292625}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-98163602257170010119561309742354249671},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-103571933721927768295666929172453906991}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":9016712797901375886957753247146398951},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-9001114035357470556866286372174955287}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-16370796856923662212429486899390196051},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-18406356061957448767097532276151182587}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":19126010700133479154762935112550471215},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":17189283809754011702389238814023682217}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":18442058182877333608379886352372769073},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":35989779072139930721318146404273663633}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":21740468934343287328011096476728481},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-145583249953635887816486907213052935}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-8981124294086562866347504435547960159},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-36808533777241453538028975361286064247}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":14612594600246377998240056609038995431},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-7297466505965643657366507189192710209}},"total_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":116541804887508067447255900243897710227},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":53388550735348546700210027552929392215}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":28178160125928241570102275788553376211},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":5238852822166789324714856420502399951}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":92998607706674033689232609434965745069},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":82077325724533315022392839952415673125}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":425436085228472699621312655396457065467},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":400886169636858067334013626337550531005}},"cumulative_internal_conversion":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":21515702161052285713384454137286777341},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":79712439391003309081399633281909282597}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":11713081133738172742385892427448946543},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11908939354814213840222853354434254963}},"form_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":126607642820139052963788999471841592431},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":126607642820139052778042694589412854417}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":18729778538445276967553766667499880891},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-9260437779790511759644322374396028431}},"phase_storage_change":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":15468145680430316162155734994172262073},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":247490330886885057939224744083846443411}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":253497112150524626689960740036690109779},"running_phase_work_upper_bound":{"denominator":21267647932558653966460912964485513216,"numerator":16625700402904130091157086802039906267},"time":{"denominator":8,"numerator":21}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":40518773220020566429508352860171152619},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":35064953104796900535285772381490004107}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":183355754886416476656874496266356761449},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":179379706274788468617767325649375938287}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":658140857181244191081966402984888472529},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":325490550188225947313994321052661492203}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-330042949305170249594324078114061695461},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-41638990264791244562608694503345564871}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":121053792323459129870359470919355536973},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":26588246712133939082287739089457124061}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-118549065283562419445853233574110632397},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-33235330797585581264203357253320411107}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":6028857733216040721396949910022455345},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-6027833074128087986600522997689254935}},"form_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":29984605987322581645888395672437666371},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":57858051290547553513204492058983225153}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-14779910103568753309375654766965832633},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-61203554522381140813642108912016107261}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":16037194210171222751980124146265802355},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":15169864916169612233406841801569866249}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":349575783064117710717170868962167525},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-177774049502188625963118412268989349}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-15215953728801101675080090258647873119},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-8037130521148611276277584472344131945}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":204507274025880662563128967899989425915},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":192371600906590944762999648423023424695}},"internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":81954246917413277153346170779115390973},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":78692302727325840292524647849227255559}},"internal_form_gradient":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":255643657147206830013073648405690762813},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":124933143624550863480153959945563348371}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-500284497718495214224262790938141832181},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-511909392015687152897357826102245602231}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":236020768829841967091230901563481897495},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":230515843579954660996116903661229577795}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1071469709323483916166499706151401489},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-444929704400670699905688924861698099}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-230053638170478571363330442471333439213},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-117745291799137473032757502081526763033}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":444142715019883779183670429733921333103},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":438946299807681193388841050795114376391}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-438640418741507446809441378639562879511},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-443888588592942550962416453705698826125}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":50382331514866679978718439008950239933},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":11914384044146999612569591787200087619}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":549112355973565730548871916041781851},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-279246823957492013558205979233915423}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-95604656903527524293489881341949294831},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-100997560804731134178887218987621693865}}],"phase_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":4401592158590596789917816941529793883},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8788544957877782429280985195536975497}},"phase_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-7410985524726065309570737339785966431},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-16807640810469478610215343058890667433}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":17606711501203202042731540928507756929},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":15722015649751938173550308258555768101}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":9390968007904720692865288118261334005},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":18343867983373965429624365604667237425}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":170529700612068719943365879529569813},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-141625523567565117969419719920841297}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-36614173691105997632581711381500794095},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-37479490431260670189558982499844325257}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":3584252850859600325246621960832056907},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-14320322725959084680838985331139214539}},"total_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":114390835391511885227019792937097085011},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":209554205380477958405543863795388699529}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":24274396757143107890910617974204744107},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":8591302236943506821272107686182637417}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":94897925201362497740615813475286267849},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":83720995401320669734984360532798017067}},"cumulative_boundary_phase_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":108507721559693367991150911852235634665},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":25580912085530548550029466857960314257}},"cumulative_internal_conversion":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":22476103492115722555025229576104535829},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":83401141081346707845111726149841810201}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":11990394682498995160959234727067447459},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12193080891775197980194339820540040969}},"form_storage_change":{"hi":{"denominator":1329227995784915872903807060280344576,"numerator":1025444032212941721039715029529488613},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":32814209030814135025077913782947814189}},"phase_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":9489047593406317052003654517239958951},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-18764743457704426486430914143469081549}},"phase_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":124231930309187815232138471076504329691},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":248463860618375629787949280965789836709}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":254455296260390924376380556162933983917},"running_phase_work_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":133614302038040028137190097554629459129},"time":{"denominator":64,"numerator":171}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":37684492408850513497374084298494142441},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":32294676569829637952469776821098221337}},"boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":90881424778530218479461146901669193293},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":177966762708275681714947892964342813219}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":326272036996213568751466283091103087677},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":645625296921928524063939969549793669979}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-163893299245784622590044456268863526059},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-330724116372851670189794116354775019507}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":54982503199989579660655492084600914193},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":95433310195908976193031347144199835359}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-107985348881119357438664262132726504559},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-30556403196909563047777362976136304353}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":2970060066116197009959249131119056425},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2969552429901567578203845765227618591}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":58750075216535895433747295202289395759},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":28340678872825687621294290302302652461}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-57984058371832189586660449329870103207},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-60027906808637378633411826358543628363}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":15612855292263345274327110327470491149},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":3686744446801372766635189622981278697}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":356064945718445385475381458554850629},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-90308429784840678201323498550305193}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-14788496725452825822458217974329120993},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-488888261490737038282564852591751407}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":203803290151031572715708278523227355339},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":191842172309283035816927651094426819011}},"internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":83017944810019396316184474928421575467},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":79814186658368573361700752588826454151}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":520150810653107977387459948140705369231},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":127208245972088099723719546879105271689}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-509441157337730219366697881036299250575},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-260416004505139141399927757593691370613}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":120098789782056379583816228278628672207},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":234810506609125049341367739513783398163}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1048774866787612656410570469771744581},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-863999533790935871625337492897546075}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-234293794524336652630209061099538567469},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-29951211896918713347420138422727604725}}],"internal_sine_current":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":110935351923592922915163259965202432311},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":219387950535895438963578932931294612997}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-438501526537689906123392029219570491489},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-443524080333525505441007869556892041337}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":98098462975470099479001876553250219211},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":92657994157873271845108348494829746367}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2237222035339833054059037067896880497},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2269698396554281173408740658613501337}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-23229716335159655538811219652191949825},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-49148408663218729536463324897765983925}}],"phase_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":4293749183986791550341738249056688471},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8573779391091141232233828497977769357}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-13313256481065957886416984432882744053},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-7624110122396085989910350248155174785}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":8064225812040468351400130003737744751},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":14296484069303292394597025109097207649}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":19114316053168684127907292989014070389},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":37371252816754410854704816591502286373}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":166917704239792603966516933131261545},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-68754898315960249913531495508835949}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-18644507767152509489275750006155417385},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-38135067399899170979154579835375614851}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":7030111164568362615776514171699680005},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-14044472807395765636081766879698001089}},"total_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":112160830803621022449485349064420197283},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":102701434579257592410107305611067263969}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":20518371456210472183262419605613039227},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":13560696849232149003286960127707708927}}},"cumulative_boundary_form_input":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":12083048222878420695100652959597272597},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":2663587761422857312937699416290218631}},"cumulative_boundary_phase_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":110637754952940169986763282482743506383},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":417636785370439199380859652210068597481}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":187591760262865098844844131133375809333},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":87142431080957734721441448927443050239}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12263623919307987389406849640219058625},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12472851599137573959254071561786284973}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":271783294446754890846296128816392155295},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":16986455902922180652899705203022981571}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":19219422521972796337448089610193477161},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-4750427505074578582142766205461797167}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":249264447629546896873463610686886265309},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":124632223814773448087799583627120368193}},"phase_storage_upper_bound":{"denominator":10633823966279326983230456482242756608,"numerator":7976246250072843074672879918239791795},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":268266157649845210504170232076087925053},"time":{"denominator":32,"numerator":87}},{"channels":{"boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":17357924572263542741342339213433267399},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":29388717636644653747334886945307664189}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":180163343914969938107768629882406098197},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":22067976933360979529398050797661606919}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":647137865011710140176314218118522180637},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":160115744903811000569855718949826639297}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-651270550233764955528092656538256802537},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-656880982746112029499519588617919040397}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":98885081771600739758921713223271881671},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":21129270566204948631221759178005145319}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-97400265321950630725265318986357253585},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-55747382822508708083825231669554509331}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":731253167552173930971477434707045725},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2924511046937889572006029475695925109}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":57514943693386510812860692767349483521},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":55487437779655381441051010013383248791}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-56828953894355482747260115584488079977},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-58834067675709702295782380181689170159}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":15169312603870940908257661949811867359},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":14304790167259532948637252217980577723}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":181234341981788882383074867632732135},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-366706468959465860141453681612116623}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-7170649573243010361445745086090288239},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-7597460739847087874660139230700205447}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":202798794370602875412540981122767933411},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":95507484032780461887230726413715828527}},"internal_conversion":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":41999290777196349144950223075837205673},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":80855013026561719384831227611073768811}},"internal_form_gradient":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":264412033120571147463292512606177686671},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":129436811254892073613229994175220799223}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-16200434279220038910489491667477824333},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-529566511863897348294617286911671208817}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":244277493517537841512182238261484057979},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":119505802705368774083446837972573062597}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":512360794246246725776914553312473435},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-418593897536995184439015720200403799}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-238437968681446505622870448174187463841},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-243629566502019383088105245340943841365}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":443180491964720276120799970319746933749},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":438439698420438489962640301921201920335}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-219100003437575067924652547392777973733},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-221501629363712775815626233108863392239}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":23827900518164002661734326744976911113},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":44939823700606058373926795974344506419}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1138728954696336404339669213635885827},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1152042348906911496917520608765597173}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-22527260020767027368804594041393608215},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-47736253692480973168649765605214461939}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":8370075065243183109299678206991184461},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8357237277514581113156054567668612481}},"phase_rates":[{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":-185082134426001982701354099724658081},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-6864385587158130124514507794761039945}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":918238381765064949914248349307232521},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":12913199533873416944812171237765665087}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":9719492644853641738447466195006821111},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":19019939228724238899170699862949917645}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":163089506101559385654064554981649109},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-2081915248159847991738560392344465}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-18974290668221370475994621642514314345},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-19387424896066012558606610823250310791}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":13782988690416008194704880081102630991},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13768144409604181591041735389251027847}},"total_storage_rate":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":54928880448487124544306043351925787633},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":50277762162473210499852893230005401287}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":16916727423345622764683192284935217121},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":5048040292165959112475060046294974047}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":98291691211677072692806067978037549595},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":43306202252374576079206352073424146475}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":450996176557774895795854784456711811385},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":425912276720449566704383921259191700075}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":195466627283589414309522297960095285397},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":2841640931768056728675169147553504161}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12532701373972878824210409647442313575},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12748192983388825799065827450318091631}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":281010125511877661617833939237714872829},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":281010125511877661203262538487814743361}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":19453746264127105759358143088475352389},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-19231761223632007726317379875407296367}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":249899395700987258154219766387571767067},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":124949697850493628717163289568940124357}},"phase_storage_upper_bound":{"denominator":85070591730234615865843651857942052864,"numerator":63964511279282477747726313054136717361},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":269131156924619265160643959013287545081},"time":{"denominator":64,"numerator":177}},{"channels":{"boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":15810131061051219141368249452314766599},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":26354172656059924032837864509071616275}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":178561171552748453382617799634451928631},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":87557359445478493011907152464686161421}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":320962326631138280051717512598347105947},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":635496259676324555679785695022055826981}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-323589553446404892711358016992287022477},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-652523555678347497169619469991746077213}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":43913032749930166090916055248439871661},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":73616276310998448431126018228726082857}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-10850543712877046053546785267369936369},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-100759360264007300474105603556337085123}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5758975435373511948212738667604218151},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-5757986851031678259787430139881517981}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":56265649994450996909076941126037482551},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":54278107652771260150131477209392439591}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-6956999921266834887403767594359366019},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-57623721960671066863597583935878956883}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":14707029243912343081405543810643398583},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":432617742466351311755817492302226597}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":368786438002026857883774611159763825},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-371959601265828059870260857677483973}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-3468704162390920387363684251637417923},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-3681551631752434685623781020746623033}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":201499560678908951277974799265396803419},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":47473741201151791614177687530339092803}},"internal_conversion":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":21223834548071010586693638937061234247},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":81813718576051001674355728710558375421}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":537304020571644893938302278538727464077},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":526471957329184387032059927356833151271}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-263599616332397705932680759416176125121},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-538109748675798664922421357363245875745}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":62064488878307523148968076344166922349},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":243116432302418627439505463441376343579}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":999321145977184331824154936686817645},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-809465714721337977290348106444611771}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-15155220086249021816279981013593480745},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-123773859213577710756005604565376518145}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":442465192516205195565711969788495860985},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":437942836447107932170944004805787358073}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-437741086545223434332747640507333926125},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-442331424488427880113309557558501302489}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":92406990057610536812981799461060386231},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":86982958178872985604775420548668392841}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":579288382185357661703329861393268717},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1168545550768914190657501922228118861}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-43589022056174610656220225081214346319},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-11565935560124964582676732747108114253}}],"phase_balance_residual":{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":127364323345109749210886889276710379},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2034830227282328829024664745584823421}},"phase_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-5209260075590357126716043268683185513},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12249911500691453918076789866088664925}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":13297323664834794071645818275884004917},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":11572618333398634539359619314994165065}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":39511480781818419312165666210859448555},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":38693181947796061589636586467377133547}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":159046900118526403882485525037962231},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-16103808720164366288387184682329187}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-9648112761488448757811929032571118213},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-39398443038802451466569659720029337907}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":844126770772997906317786510846548589},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-843253461170411905677241574170575407}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":214974919879384876557736753611988716541},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":196689378296124301174518433352352255317}},"weighted_phase_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":6737679600237962639880977173295956561},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":6794413491517134717807683230995884105}}},"cumulative_boundary_form_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":24943472749662656121827335341048014741},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":43923878174000980548725989522855512481}},"cumulative_boundary_phase_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":114841557868577494887041248453644186385},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":108530194792115793856062554200689006927}},"cumulative_internal_conversion":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":12714097827444752704970775785093328015},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":189535055749660412042181675010039113999}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":6398789269438043676900890145414590737},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13019065601228207702969201699285114149}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":290180390636538460493435434346579320435},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":290180390636538460063872552226400193055}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":19681065558579629594994934614644852663},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-19454896236722806508700703861617264387}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":250376279487926761739712738855907632131},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":125188139743963380498641307471460183577}},"phase_storage_upper_bound":{"denominator":42535295865117307932921825928971026432,"numerator":32039657103082364874278091770154439881},"running_phase_work_upper_bound":{"denominator":85070591730234615865843651857942052864,"numerator":67457793931162391876495829701134407885},"time":{"denominator":16,"numerator":45}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":28405180241870078918205208194071356161},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":5799548213269427121778947187121346829}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":176959957363685384635530364415974318223},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":173683027836418023860341702345113291879}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":636906611245016257843909884805553262983},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":157681754009598340164573055055778687819}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-321649890933209019585184154061631670513},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-648377161203031668900710731907707102791}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":76799049464655275096014165936533772235},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":15685479410315838821764409773647125715}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-76207313451944343039301721439888462355},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-45014571864336172678722206928111548853}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":11334708557110587343831992512627205157},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-5666382980514763149044642798758778237}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":55003910264349515018548870569524335837},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":26527534429637803981108724240516712545}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-54466765404527927208522377410416698377},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-14099612745545594248113259493624196581}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":14226475991771042570565513338963548845},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":835274006785253411404738168737073299}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":46877218550365412282620542882949867},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-188493313935460445868791180837811065}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-6694756478935383834595748586589324187},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-7119370786008693124682938769021746747}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":199911800283550236789960413446436622821},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":23560951599226940722327832677782940939}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":171415198512974973158506738825709727825},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":41344724718340485239753158046331007587}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":545587866996611783653429901717794621179},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":535003993339410815783259619938103053627}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-535793947305000978878801876679053270045},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-273229407833259292458385705043160268959}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":126068263931690103402159035258629921361},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":247122402233618723712318961238408701807}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":15196642665640207976863701459163291},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-24402357899492796500033531310925411}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-123213971142633195786686902309784068239},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-125680897427026389203448832959030556183}}],"internal_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":220800295875461350305951350132962088507},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":109322581512684807494921596312396143043}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-437129856727046573985101162154439821381},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-441513734109732298186429671609511126611}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":22346896231109737572468270149084318827},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":41985450935217011639645670606729064077}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2356306006696818499701404395043075361},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2368676841241748539872197998343226357}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-84128791087184292883724138387561104543},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-89464651838026809065327741570491949117}}],"phase_balance_residual":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":495725510999845507249818386386374209},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-123756490275661626854075656851293995}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-9033544280424761463287019577220405887},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-10812203569121192533210982851115844545}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":11945450000695836350524775932964482429},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":5137572821503052450861735235802352991}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":10032193685871089872218823857742790113},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":9832687966056014196359604048643788581}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":154791731112821500120616923480990341},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-124280188249658836115193594088367485}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-39220225130664440789815652474237256619},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-20002736077736719901961943900429350521}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":826876068343442703770936253401468439},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13216881699058838217256020995614674677}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":210111237782990815607792471148022174219},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":192148255906496625336479551614430999707}},"weighted_phase_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5099718749720289408916028850792775699},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3660643112681099557856890192167472195}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":101105383822488284436600210498289153785},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":22233792909497494670696382910824069373}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":467661229475732731952955479646575541707},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":27641385693643454393293983381261450829}},"cumulative_internal_conversion":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":52865163167352936286584353985987097933},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":197287191634349253024635392143726177921}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":13058225046395130248863458292613942223},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-6642724086582834035767760705566147107}},"form_storage_change":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":74820147079683590489071095519909099409},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":299280588318734361511402105031105251303}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":19901392474405809279012101695525044731},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-9835563469047072634216764287226271253}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":250702910903289334425378419851759866263},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":7834465965727791676871454966512400665}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":256625229948587768888774607830085398559},"running_phase_work_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":135187018920691739464160043751424681893},"time":{"denominator":64,"numerator":183}},{"channels":{"boundary_form_input":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":3134756902135750596584538539868077681},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":9963977961980908214350273029113648401}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":175363033414087025287559766794410872503},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":86126006364669963977137606465555991201}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":632085675533747949352714151061475410759},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":626156909046061801252961757271817180353}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-159908317421682665727853595425228243323},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-322221385881707420037798926888575287315}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":16453555549543732142625052019666239877},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":51904135038012128460246428478998433147}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-32809048914120957181954514399827597839},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-79313085644172895636147895184769555113}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5575527757765591932211895426083259929},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11149152697285536568225328044651922417}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":53731330864043725722266913611928157803},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":12954978672599311924235422942621557987}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-53262727584779908681441599170514523857},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-13789934851636106322387080847722495631}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":13728131356190009940993496902336284297},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":3216780159300500930403508542973206547}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":95290560526463561750677053571983655},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-190890660838100663940085489939618785}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-6442929955513256496773754263786036517},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-429156145577080535111177571913296375}}],"form_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":99021062593642556545213204648273240069},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":186798799016602032458139128695337300751}},"internal_conversion":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":21608737062100195531711018552630575215},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":83481556873896056398651036193076331739}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":553673038500431091494521126557743693945},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":543340483264208920027243986906934813375}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-544195075459388292492727255210994779855},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-554611043577514053761524863513507898155}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":127955443328082851712207280462169056193},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":31378381083166078879720222943515865897}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":472262729533413028627242635188717285},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-751459807070335677499611879827722799}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-15641802829786050153129474613610555607},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-255069558424651687659372618785421690931}}],"internal_sine_current":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":110147910183017982535149687311276597373},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":6820110232265519788976172538514305147}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-436371283243255062617717238461589272045},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-440555210636409268199133306501788167717}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":86256393232244440706459999664483698507},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":80846503333374868238012376631657763289}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2394912999251131727647698602943514997},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2398802790911511557426288371631934573}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-40482122831668119956038166024691750719},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-5392935176751472188802543826544626245}}],"phase_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3855658806699888268598129945518818731},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-7700889103995844292551249716132481587}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-7690777527846776088182133585768514657},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2354039337556299015008994872179332427}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10636610933573967708636110222572381171},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":9021138371972418146685573859980264187}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":40729482602358529983248707004169936727},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":39952195644856819273255306828580181951}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":75162947843313509268228698593921639},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-29899635707531480757716555346451535}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-19915761913833969899122624692756098389},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-10148895263887577965033883414409886637}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":6477795189960754472616987354156109539},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-6471629526135964702195250862946232881}},"total_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":102567779516611626664104866848825749141},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":187497829578901100655845573387463028189}},"weighted_phase_storage_rate":{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":221669807685566882430728887534531817},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":349515281149534098853222346062863719}}},"cumulative_boundary_form_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":25570229415197297727579853112684920729},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":89869294571925688827880869739775682029}},"cumulative_boundary_phase_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":118970342916754515315827460928765887839},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":450336484194983079415560384706329087439}},"cumulative_internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":109781964533849659235364523950592428719},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":205113587591277008312008926786827084021}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":13314627854553598910243868825035894589},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13547336710732213791441590836985419993}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":308297510017756296050133665351638660639},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":308297510017756295589606869514939120361}},"phase_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":10057375754932127063830811381762011531},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-19880477438593038667901926557330210037}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":250887306637148015072492959568668253063},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":125443653318574007141699495185453128649}},"phase_storage_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":128394948083830881308196532304942574635},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":270767784075741052951300916928236467335},"time":{"denominator":32,"numerator":93}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":21646317802341531770488488270565321179},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":2068830154920490500256473843704398607}},"boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":86886727326427569759662995454629715429},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":170824674454750066195921982347874594303}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":78432945082586687022058001424575363451},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":621787393415517270023690534228967105659}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-636180056719807276203792333676467675261},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-80090142012972878787976523504694334759}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":13720230338233829553573605524684887533},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":41112212838070340435963002237570794797}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-55044927507780991258880341002936146181},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-17154858031642212677032447514260887761}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5483844161795583554459482756897077075},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-10965830426705051566258196757284516517}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":52449415136567228538871844418245407889},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":50574136899383038915203160612846894149}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-52045273284297219170858051893615966387},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-53908982154312278792660118284877845547}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":13212481656390476757615003315952222037},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":12352466633554953280916145851358091257}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":24201229928678244596101787508381427},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-193168888852794130470907126976953509}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-6182168741049367931348961287232825945},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-3302362478932390460669053600956513463}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":195897515672695778656277397787161025515},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":92417406937188372974897173997544299551}},"internal_conversion":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":21769290812342533218195507060225974305},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":168379186109740687545306641523731682509}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":561557194448387518721250490627046194719},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":137869700139018045451818453489316439533}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-69049986213557516163722206152347039829},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-35160249064427108313157451804792569475}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":259578818368706654490298672500796018403},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":127414009886397143392884398087512787911}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":915154379790499437833127454424443541},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-360631106555917379338336122244184557}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-254003964048136888679932692246870906983},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-4041701351956383679429979033245957567}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":439443170481427403467183430283336546807},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":435537797996168377383503593490472534601}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-435470217104282831618671739897082734371},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-439460754768903310761046489128527406135}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":20754117653703112312570683057117246439},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":38806418429689285797890531217388301787}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":304121624607092035993858071642872031},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1213715924244082686671290248394329899}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-77687423600532620503702939406398395277},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-82997421626436609727937934081400451405}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":7490797026190141147918933257136791279},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-7481094559172368557784530388745156941}},"phase_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-3195311296342356266551695145102567343},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-4031116723434108122715268623304140391}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":9371175295901921578216482066626389697},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":7810907800204981080851907187096430761}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":20656626032666471625803284782538320197},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":40557138985159454104455367692350683763}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":145651343235855708981075962777802841},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-57396223241074273446962389455140693}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-40425986443197055336883052178355732389},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-20584215957281749945644541281830704315}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":6341672480390865028290241906427416749},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12671784596877841923785312187953561527}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":200058660654895720254554256910364616657},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":91373993929159414683014583495935595255}},"weighted_phase_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2080572491099970799138429561601795571},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-130426626003619786485323812701088037}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":103295588807773950212061060338422432347},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":45322552940010436382738523715582415753}},"cumulative_boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":242013501176935322964139124769467543589},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":229171945405024744384247113814442854523}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":227727413122327768427552363048769597803},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":106503180970085551520347587804126003319}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":6783395223951511491531776703370513583},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-862796478875420020429440308370675485}},"form_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":158609129134047499394617888223078932655},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":158609129134047499156371189226630611195}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":20321179109612225062536360868823288027},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-20082983616365598297356921707866616993}},"phase_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":125468828398666972701739112724469699635},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":250937656797333944590226152222816463547}},"phase_storage_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":128409686406291159131381256850824937085},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":271020640413699542887583073930683080539},"time":{"denominator":64,"numerator":189}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":18117357447484281296480524392934991923},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":13073408475571309617132017884007420093}},"boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":86097007186064920582994021795562568777},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":169403759005668986560810852294845543833}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":623041772268594580319977670381544073633},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":308809865220570964901915958433095115285}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-316470216169327214751263151781146311381},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-318606395871915359658583021110733903449}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":11001921608906463147411873446746512101},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":30374643298251563253629797702345071211}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-44495363963984299522926236084889048913},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-14488939889339530893026577155176317385}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10785269325136850595606621751400435615},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-10783461412402487782130325411145896925}},"form_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":25579785111899708570759484090971855877},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":49319132416811289905652798613237830571}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-50815708463133725420080674523083660845},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-52647491302533854895358496401591019147}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":3170005280873425242790554760130111945},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":2955229803068270425133860188070536149}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":196595022833273210893860842243488039},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-195325260318725766022902151030245773}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-11825433763633263176815377766615559627},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-3167146921869860763899360658192342753}}],"form_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":96742645738484483463642850347973522949},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":182602321350897434661641089757343387289}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":175268425315815641147290890775554292291},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":84813306838130403357273530530269595095}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":569238208294374006597479972565140037531},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":279708274203101100825985661083487326199}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-280202943859889957232327973413619679687},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-570315402850349949324988182133792349889}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":131569108402818871224048096041155020573},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":32315384371769829163774607738463419751}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":442242240001050753813878684917611575},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-690326743675824789704034836490097875}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-257631148030627886512309785717631796099},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-65539441903985277605928539144203427249}}],"internal_sine_current":[{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":27384993968254518570296393748514906751},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":217223614473989077695181543972384889375}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-434431405220240483663543705651046712051},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-438235156160560556073738579810604890823}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":79670922417862414769964535699779893805},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":74273025911911118247765414175446834067}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2470485917861315113873385249951111039},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2454529611511291290785146193059997049}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-18575347918671479529188689173867028537},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-39799542010343525750943267348003205803}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":7270383246809007927716339482920143317},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-7261369143489892294881906866749648755}},"phase_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-2566719467989374224940748409790791767},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6750845922018773453830606254404134085}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":4074732813004157570021315275779244031},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":3322361001446455607221565579492666921}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":10469936980251022941238710641234994395},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":5143153160681751067024612703956063931}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":70385038540199551799434731895004953},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-109868913604539312783662726356913923}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-5125408837939280548109334911924137921},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-20861852293006714700165421541408469333}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12413840932391024090579131519305476831},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12403018916337545644268402562880443579}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":194891008413631320268522001698158440757},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":88954176451638288409100082710589842949}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1405716936662353341236301002211394859},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4693968447620857843440924336163701391}}},"cumulative_boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":52072419969062387948916792459670630047},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":45628960951156638951890055384738839661}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":492098596777564232232933939082269078001},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":466284692013440222513532236330206593913}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":235943120559006626606331623553873705255},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":110478804728122914177719784547732390589}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":13814732059428007958359752584414836467},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-7028848539572144389685388650401972413}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":326030263417987114217579432449357296967},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":326030263417987113724794431172411020523}},"phase_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":10260361598884218203883578502620246819},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-5069673167279093100127395149511826623}},"phase_storage_change":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":31357786831525254039370971222696672787},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":250862294652202031476984789388756990331}},"phase_storage_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":128360966551979616781456568293293734717},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":271140987321318403877494369986804296823},"time":{"denominator":1,"numerator":3}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":14498505169185208397537510824611051075},"lo":{"denominator":332306998946228968225951765070086144,"numerator":9280644023830477919392592905934421}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":170627259298991898972785347427162992555},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":10499485760185760764400810699138998043}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":618821619512305101874774400200628960905},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":306827499719216123877392989542038723877}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-629914499074138191713913560132890012383},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-633918076415214832340222530920080738583}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":33202311487841755711827203976361120023},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":4924794732290740017848615261198500205}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-33976358403620576106207685325413072581},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-23664513930455558721813515116290487349}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5302212880501758585430876608355154753},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-10602672798661117826676214641567555855}},"form_rates":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":12465778468354367989670972387207393071},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":48056210160890889214327162446552125963}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-49575264517616473460722328349585863329},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-6422062866253798960531179492685707799}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12131251662418419155783157942320564763},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":5636491913635523945644494151866461567}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":399072907816780580677552665567380985},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-49339233422290400333888555043726137}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-11269645512484062416298205213163767963},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12110904324837384434299779052907203493}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":190813085623624610790500222637746240211},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":180108333853518099495397534424404262811}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":176212501482994008924536238241360767591},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":170705280382218684230180454285359083601}},"internal_form_gradient":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":72089269530703858128394146914717207895},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":283575773602024274221930728334494615215}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-568210780320663379122333785309318655263},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-577863259340062373631002036182157697249}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":266587080360529485805944809398447145693},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":65527520446307592142583170974660287145}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":852528693485111412300505199170888895},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-658698107227185931977825068436644765}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-261148358636530215242450040617438226875},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-132767148942220612665914471652817426303}}],"internal_sine_current":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":109186616300419283060895158684611084701},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":216609965736651509928403342554505512383}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-433259502021323397604178155206765215865},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-436883104655442779434188274946356415539}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":76222902203005344072531834219959620811},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":70830246351582549467015647543540969891}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":626862257721957322526818092913964369},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1240030186025756115078159823314416751}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-70809271101162221979539680957841017079},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-76095056110475963681979643225020329763}}],"phase_balance_residual":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":881299641336432102416411367448896515},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-7042034402783076415441152536458582643}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-3919545197411288844750500399210720195},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2741182472591562944881047619773907699}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1742940161775108864089086743071315077},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":5522808065159625424809142787660878259}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":10607162900953649756160427672641396725},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":41716115150340371525743618669774896335}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":135684155695830788713758504820809745},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-104835059770481948788303077968585465}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-5195381519667355028385835943644191735},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-21130548034372313633391459754552450757}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":3036900447729912323959315050074949409},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-3034371525167217386940395805506113627}},"total_storage_rate":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":47410688358573557728927061630550153357},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":86494139183754118911280637514874794561}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1170332189330379874791976115545626783},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-7120055486009861672836259394654673689}}},"cumulative_boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":52412228683965166270734077869622451557},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":45851696407728570421955477614481265765}},"cumulative_boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":250048374778602238748641626121458671639},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":474159306333579543086832844354560842445}},"cumulative_internal_conversion":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":61050770391505492693667314930359372809},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":228959419474162329178729277890090988221}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":14058486861508437911548450100916409719},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-7153119891412197945680271866993087663}},"form_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":167360649575563953967094341609984964735},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":20920081196945494214048554482918513689}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":20713442686601350183338863564341460167},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-10233831314441613343177889352514893391}},"phase_storage_change":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":15666854215884932655968903012341550711},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":250669667454158921632198195647796568275}},"phase_storage_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":128252986009492314028847412980150669699},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":271140987321318403877494369986804296823},"time":{"denominator":64,"numerator":195}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10797019423807310715630094906738841643},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":5847623169338129767288475569961957823}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":169075504400130616399986341769685160961},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":166590993254930956024689369620501473879}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":307402113349202861183886286625969349653},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":304947054208977369858774132727810328297}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-313551090880494295011739579900504478551},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-630837138471859236156391391342966918767}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":22471897440342302888881678694568731215},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":2273221131048419043871586051426633087}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-23494304055105210704579547562403197711},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-18372816551558675227323173694516797895}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10425752342097783536610571450321151801},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-10424059180762775787145982885429965025}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":48561281231743044114050763009475417671},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":46786597657556938048859840895938209913}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-48325104901554536448602842298392907863},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-25048591954578821115229530794609402351}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":1445835401393665692721578661641627547},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":10709173748550923813343075173540570575}},{"hi":{"denominator":664613997892457936451903530140172288,"numerator":790758053853526640501843186349321},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-99630662937554544504098285423516415}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-1337184707711171628201653570703613621},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11536902580717823965116681304092853743}}],"form_storage_rate":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":46972205691818124332153020593779964381},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":177360187789623935237157043988675071231}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":176987227546579400308672931967366194613},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":42903861813959146006178258838709186975}},"internal_form_gradient":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":145995826719184698893586031743853308787},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":574681822955556883694327875852980338209}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-71976560066276282625669461605723701919},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-292602853254877055324074611153766078887}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":269923509595341027323779606787283497187},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":132793506499083239155941560251062653405}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":819300308875358557654648685923092051},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-626421644757952298821562137946396815}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-33069208228716013975385893780704153953},"lo":{"denominator":1329227995784915872903807060280344576,"numerator":-1049987024297766045728811528386031515}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":435207395659313256393483376176599297063},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":431860409938133240182234043831473083347}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-431959079572934309609479090820050890949},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-435409201700521995302313957689027774281}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":72675614005094240714626769301451624119},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":67287723148928499829556647745084624241}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2543861445379278218611764862570794687},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2503991670055217969159656443687307233}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-67214234467808507717824921612633337285},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-72488496785528484739734975351780113709}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":6831145863013066682554782314090679611},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6823398303186574241787125907534518469}},"phase_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1374610714919205849491262864190337167},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2128559628134385113497366365931231115}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1459574383892358230547885347609152381},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":2222677044787074968453411005642324619}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":42959660808811165815456967888338198885},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":42269485939669652695559899233313749079}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":130395694034229962327739078014254491},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-12462262652872921786699142666192391}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-10526255907470668322457474652898562151},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-42780320025430906927646391684165175951}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":11885117914368033935205457151882384699},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11875677193206533744973212180435036781}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":184323734338637119727183302342345816401},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":167996846630731393370643224495988965823}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-3565088428635377601428780032774041123},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-146302205607695966664278429573220397}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":105330567653421300231263316437998286317},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":45988750075759932838376301260652249151}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":508022163825960600141032612013371335199},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":481968259142404431650490158555521849033}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":252499357857267880164138303407407781609},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":118501946782139834527443850711174480389}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":3574525805782272597697140342076825837},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-14550428571760555799356735197370458569}},"form_storage_change":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":85819874234732156280607216327990190607},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":343279496938928624596044884648035609357}},"phase_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":10449703518099351075819005160284981395},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-10324980970172839168694517338206388729}},"phase_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":125184154160667626818994932734342015107},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":250368308321335252748755875914609596963}},"phase_storage_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":128089991581001068866428857957592600531},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":271140987321318403877494369986804296823},"time":{"denominator":32,"numerator":99}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":7020074760504488542737755405846864521},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1054545531695345351221557652261999757}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":167540847203858198712008896100247527457},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":165203488956444738098641047797596698039}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":610990544156417802288946318144742542091},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":151584450997329609356588659514810469065}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-624503235699889141563658547407108145691},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-313984973145091845410196717375326232367}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5911451954610903290741200591692744211},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1437811347773840770025147209497619099}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-13055087642833310373034000209810745895},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-13105729622666889544387125189244643245}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":1281732949286258287952452236194354533},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-5124091387169965102801102222469964783}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":47255231545736648392586838724566608399},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":2844465481571326399131844758901922163}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-23533165880410068889499286446743644867},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-48810638574402184988305475107298812487}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":2746708411813731014677197012609994189},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":2532502564018478850391923422811679631}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":410575586124802210741307683032166483},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-402071974875014100568681043344201109}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-2527360888195356667482451117328010781},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2736773388765169840509215905173521243}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":184720699471137033891182670597832725259},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":174365523719080663245696460020305178929}},"internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":88796815866458052454280454529699121987},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":172357744813456276885119937403753889481}},"internal_form_gradient":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":73880513960030772252878841944251086449},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":582005596653675302581460072317867861277}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-583209093542188596894393432419018728385},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-296170538616884780446651523463016400189}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":273145705131299493202526225902389366805},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":67237986044933720837468251889801187007}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":784812978459192772299886555316108919},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-593543324441474439884558948109833007}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-267845245017330785811443719662258152981},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-135971605752842315945082584966683630935}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":433547160894090905750489064873519101903},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":430373100641896996884362945536742660613}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-430534638630804196625128795371172259773},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-433817971441771669379126726877670071317}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":69032311744858446476354573135842962035},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":63648731602542145610196474264259842537}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2579722490226004141834589893731449275},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2526292724963368447549153276237249177}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-63519507194597658386319956913533384359},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-68782617381477606025113015265483051737}}],"phase_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3306461538996545270790705455882803475},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1651438836862769639433473540605550507}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1622711152743568545403613486196035149},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1537699223440185455876827024760164495}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2374636990617288710216916412139562953},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1706255500129260548023479308059019861}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":43472489155967594643446232563068935117},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":42805031370380316330751507899215270391}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":124906864924453705672685683679174645},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-47232677012028617204356356267441745}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-21314447364084021976466043654434519211},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-43281106351414494495838683419327239461}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":11630899752823328821760057145676088721},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11618051202331180739895126951717777101}},"total_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":89471739886329378811422110123898393137},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":162942870762031506514851524554376614877}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-5777219698478276268338450350035938985},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2855663239262289182711233866482141013}}},"cumulative_boundary_form_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":26414908414454987032926037180661839523},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":92076363795116304303429623551204060779}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":515875641038641453205658029018070438049},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":489712172687237778748863957671034194253}},"cumulative_internal_conversion":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":32603007418093540322715887002445884287},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":245083162852410432033877698488149924347}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":7266916455653558409177146340348168313},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-7395166721867209050740843430920646567}},"form_storage_change":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":43961669944854231644457701840006290219},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":175846679779416926305974778940186569627}},"phase_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":10539347906038065269559828132331729603},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-5206417257916358845328694740079538541}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":249966809154565586706256517916130579163},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":124983404577282792895232775784801179769}},"phase_storage_upper_bound":{"denominator":85070591730234615865843651857942052864,"numerator":63938132389198271835766311920933381469},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":271140987321318403877494369986804296823},"time":{"denominator":64,"numerator":201}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3174753031873602496252983748970511367},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1725652054356825116919357711646408201}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":166025181688355634772299588763239598895},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":163831126572441566860632693200557895993}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":607381358339591571443683042535650780231},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":37686667531113667519726867265275139141}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-311058626929933729018605592156691060481},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-625316296679371945790993102842015026987}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1261200240343914001520452338538485891},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-5943532789775862113771581106080324773}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2664139912512500174008942097001264309},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-7865964459643609332504603378679439143}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10109654296831476139008264652238467565},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-10075574191891592124998307276571917997}},"form_rates":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":5743256845626691449790799442256614031},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":44231844911232919989815122152536958393}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-45799992415247422533221362779006645045},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-5939739408138299919780183947508939547}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5196114392324958948961049045429984169},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":2384005656141363971444442443062820105}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":52024402129743297699218340203892889},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-101339301373927699777864332523500781}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-4753032481121922162086104527993513539},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-5170998366878072756626286248079905099}}],"form_storage_rate":{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":1416540369929743552897028542303135469},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":10695766794034044508438996833174264955}},"internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":89016544932281350881884636429194822955},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":43233291277133130937182686618552320167}},"internal_form_gradient":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":298947598268574131001870381603152236219},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":589121274589638907580828618399580594837}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-590398907645596452626503043345457939507},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-149816969331206087743229526955899495803}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":69062991460763471279378786819489711633},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":136101525741485974140072850460618779557}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":749080727426056016724288838353214711},"lo":{"denominator":166153499473114484112975882535043072,"numerator":-273491080858712119358063038160307}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-135510687129729744780872077707967746765},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-274972300216760123417343898956290962647}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":431770164093258560246454096036488823215},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":428762382663108989222883600454528757789}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-428990619206116160793115547147088837159},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-432113871612994451183998501920191813871}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":65296299208561135029817285973571410183},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":59916597243601790388301090094215964129}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2615031672611243799024644520009954741},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2546934437730026416929591545306180597}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-59728367699865193124826450044795181533},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-64980681924435887167610626421432896897}}],"phase_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1599002380802096017720204411179707571},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6389387229799697538142120101978082513}},"phase_rates":[{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-33763951667241595680940094670468979},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-968727530025652999053531294551458225}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3704850043058739252548562526542426839},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2424394148080049557438601405413253185}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":21983432951387727594884158449524138811},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":43322461168212656712467997670331022329}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":119219900544729507021378350942452811},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-89144232776108591339823122033137407}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-5391798924618942807515728367876967765},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-43763200792846016942721814619723780411}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":11405739064009682194850555912776932607},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2841259166415277912025475248592408817}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":173511213582094423938563891401688420399},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":78917449027284062810225335758920237497}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-7805953768912750832255762013112919633},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-6648685324988293257286638906473882143}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":105808450206189023248716007335880350813},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":45997736927534164063037014329235317697}},"cumulative_boundary_phase_input":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":65457258928785390448201196530168411781},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":497391756745320977195456115164810345627}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":269169360432149699226903780684804088949},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":126594702483436447042299726114564242189}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":7383447489967774511148863831008528675},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-15026036836461951804055314333205401379}},"form_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":179975886900938385616485604274808088561},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":359951773801876770671564473687479038383}},"phase_integral_residual":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":1328212390893475177495352000359840733},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-20994871895943349635526725157664182379}},"phase_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":124736897283733440404238983242881854203},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":249473794567466879865483394854554627491}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":255232217271249633868751670129488544673},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":271140987321318403877494369986804296823},"time":{"denominator":16,"numerator":51}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-702733482248460001573907641812721635},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5644510527100724389823549349080713479}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":164539118003381740784589547746056470815},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":20307875612044624522046641337953939875}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":75497162644632163129185346758110258481},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":599841188399559138129272564884581270073}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-619939821207123080509329653832753154497},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-622910489792488334747153232154360019869}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-9182043486535840948760404163333429357},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-695389234246953138258531693813931555}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1918378725023202646623243341672065891},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5312053116132214749036649003779090401}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10013022528902279165312628025517717187},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2489068777481566986507520109936699943}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":44638896222460220513542581097535157879},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":42943786634710230921328631503102028385}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-44525027590339744305230266291645537781},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-46221002504556044343692503842494357125}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":9783402344432881337586144468471469181},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":4463874041695432638865051270079531333}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":421726960923035597147813124066437749},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-408373979958447414997548538703335299}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-8883880197377217351774802636242954977},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-9722719935655393417273009695436663797}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":177696471076568405692674026055031525635},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":83826495102292293581944878989642851167}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":178311998796759315111493746060845223741},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":173327959074766850917184947378594521927}},"internal_form_gradient":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":302267677043446862104557079733357426599},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":298013719794611231895152026594720299421}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-597380386065707415502594369275821554879},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-302992389250743186742901809140388743371}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":279240687346622803922137747236059336367},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":137669304882222042679757409119685696367}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":356058981772947524666214893891209429},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-32885504218601084706692492496072427}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-68520107947705959250185726321547453879},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-138941222162606864492977617598321292015}}],"internal_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":214946864398525222746202099385323285773},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":213494054661351067068407475233557786785}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-427312013636175394681558029688535224333},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-430310632613473893318079262254133048689}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":61470929864767000027375061870248619159},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":56094695583762198276222901374483205107}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":662447161128279220243421643618393237},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1282944695354683856386711828276710253}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-55819065526904216747290185986086636951},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-61089651045532022354089897471659211851}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":6205809250294773170092257286171170253},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6199615965272881475980439553470515567}},"phase_rates":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":62258306069305316788180604934491787},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-843506510278133326376323934016594819}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2708828137177334820028221439935504213},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1480676018440386146760388787365696863}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":22221267851796745162389901929183293373},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":43821500768061675826521962194865622539}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":56668546981431661913794402067798455},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-83742248839355834053267288259614679}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-43621255524270669007992928337738961163},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-22113182306408082512560408698980170039}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5617396028602294070548043314719092813},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11171851353206685227701721310966613525}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":168053286426460859927645667983988991147},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":152664533167926595555313918793277135655}},"weighted_phase_storage_rate":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-1205398081263443220628544758880316811},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-14988457036657991608575839186008566679}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":105775509574208626686142230415170379487},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":91730887424110481670301049782732476949}},"cumulative_boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":265685421293345821342443603645971845659},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":63125901262479713923902950708317884135}},"cumulative_internal_conversion":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":69381933843936948030688762507851552203},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":261314153048502590221342496637500102593}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":234359093866143628278290022342561339},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-7629611234955077643461525069438017461}},"form_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":184022011240023132050727053925078252619},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":368044022480046263521974230307700553377}},"phase_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":10709211042320384224872748078360681691},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-1322424545591147857262225216825016531}},"phase_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":124448948404365343859107025895929113825},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":248897896808730686747349107185243324229}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":254641928348185955367007613190714268797},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":271140987321318403877494369986804296823},"time":{"denominator":64,"numerator":207}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-4614844239285903252117356810131588637},"lo":{"denominator":1329227995784915872903807060280344576,"numerator":-37608523971215294574972308280113665}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":163102726428724055063460658790572258151},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":161097100768759296158808182484716123151}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":37548682089412836562849375342989310053},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":149225286972440174889238494412925314735}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-617958939538592280291908989938020141629},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-620852584633325376880401817026024730103}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-19500095036272379164897217214096302407},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-4067526621632526690518349375711520511}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":8976626634579657958201482727480215949},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":5043515556030848918856364802443871887}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":9961982604608947393687418286883031681},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-4946747485647112596717841866245122707}},"form_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":21668477108485465675680988640410153067},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":41646345545587001296387901773535385143}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-5405239102983779643529438034927452351},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-2807609742640080426241315061725404865}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":9160897539370842556928207803380047001},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":8305731510421717515207415971659045563}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":427170781301415247844928617796137089},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-205559100922367669056579876307599701}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-4121529738836785118749582970442013741},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-9091491562284703158042441577224163967}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":173875064528777706047503888202443855105},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":163931089107238158269791756070078951913}},"internal_conversion":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":44609857079454571678836199153175196491},"lo":{"denominator":2658455991569831745807614120560689152,"numerator":1355788000474999016132885787775546263}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":610964470072968484234794103728682725267},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":150680684869187744796673724876835307061}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-604152098718105684469131001734613601977},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-612491161107196284651849767836892605619}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":282110470546918881516186991354671172117},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":278356978800563858093535691632666900031}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":337052075924344676871245104192414207},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-122946102652215078454921997390812239}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-277020820661976807670556174014481481681},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-4385514033611925863743711638378061185}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":427941266027251644427119451141721820121},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":425047772617694612087646038884398800463}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-106374670058270584868081292263069922945},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-107105272588510193024031518117549687819}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":57559616819952505292470764458972621627},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":52186450191660249925499762066174177863}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":335499147091184589903045279371564415},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1291565922672466320602718705579227199}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-51792670196326013069168250872458455137},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-57123526204494431173135448980144582803}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":6066997160256802543806186035168775159},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-757709354808171922437580549686016287}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1492164827834282827739859641478500489},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":206246349169897305854488137630093287}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1771976590295859825917311239095028509},"lo":{"denominator":664613997892457936451903530140172288,"numerator":1133104121208232332532382297851421}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":44899275885522689828159398302055354311},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":44301889120235657233226637019841339237}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":107287007925488526096926780445102285},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-19567479970983613019934593790065809}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-22044616473863531210916711139906161909},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-44670479132685723494545658505273771375}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":2782603876961834321789547136155235635},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-5528302776370593961300456176273755705}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":162599734139975518034773460109627967451},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":18428909579587120486092798703486644763}},"weighted_phase_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-5637665194401094006365214046407943827},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-16499812470541194381049366442185793809}}},"cumulative_boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":52779594375246049985599614657347730635},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":91279585136455898135401382083371112969}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":539016282888038082765986925672751765919},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":64069829587296662924833467402564267669}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":285892083578145524312536837372626558155},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":269448881051352584318139811364153380171}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":15231329643540672911158988512068827837},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-15491476497288469516979314072194474213}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":375959795831349155364700181959593320977},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":93989948957837288691689188153781886303}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":21581178537398721386305189674236985559},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-21319670179058998974833879123758695549}},"phase_storage_change":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":62061932914406625118109022880531142189},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":248247731657626499473013235184839690199}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":254009116003743229656954863044950217245},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":271140987321318403877494369986804296823},"time":{"denominator":32,"numerator":105}},{"channels":{"boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-4280369722959098469454963255785391803},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-854251668487404054377447739492370547}},"boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":80856829180194687556474820874746215327},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":19964966793433406722415717983459055173}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":597786597053696652538948600219313464027},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":594166256667343803769617212463939587327}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-616050314098328521953196242282212940537},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-619020952379268701023630162171444616885}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":-464280668666256469540341790912871295},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-42773856249450092774500349142691987623}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":440258211509746482750828760210548915},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":15315057860475117749239213026435361825}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":4984981867396343026794140689701002463},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2475943865430362739558262001897824685}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":42043265368893936302013756998247468873},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":40339878319473909562654621477315564089}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-41949276431842836294333205378554266633},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-43625080828397161024004640488414667687}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":8525754645879967569295154201311510117},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":1917048099957613524619646180647931169}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":216263328821474852890774439035987915},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-413586041244590423684949627264775043}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-7587928878899100434212021283591892923},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8453032659677590622230551159393334541}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":169877740094997528951957852390499971313},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":159970677127169650652031568922317876847}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":178435192034809298549174543441479959193},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":173575803056003307768408734842975895139}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":617182571323833249476548125526656272117},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":609205985223627698594515640526024838885}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-305356388831815435426567845979785873343},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-618786552251833705521936806691198475277}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":71215002343190484729951252467856542235},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":281256614354889393552530563645751571615}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":317608431760922489525185662705954591},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-457025166486226659037881925018039381}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-279841041064647330801258222669066216089},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-141671500496017995843540553825208141653}}],"internal_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":212981201821085245015471936001914485441},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":211484126187473159257930717632215031843}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-423539141521678502948633555006174388145},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-426471758188735475366376835437304517479}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":53568896323611110557014796467505499485},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":48180673819240882140169385783159985045}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1358822570132838391064483929405868611},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1299318868801290501691386317057617427}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-47676363243822499598279422635622318835},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-53111970608395419109445871664519797007}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5995050367422165268632196851116488341},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2995462168502374123999394086956251237}},"phase_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1221053416446244758369520780894974209},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1211634716219758972703453125585510271}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":881524716043241716365877648461670165},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-290323885071326843298286978357570905}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":45336878580878698349788382210345202725},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":11190845112967893553879895797463350611}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":50548951882415741927497599587514859},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-72737814363679395333336334299073149}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-2783630310338793229957884542367647321},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-11273859799593582981208045060159776157}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":11105625123408860541454669632014429213},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-1379413852490026053183253447874967145}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":157157332775077649450741249667808941845},"lo":{"denominator":2658455991569831745807614120560689152,"numerator":1110293813238679451160731934804077421}},"weighted_phase_storage_rate":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-3180101829979969875304150680672757367},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-17853069032618680903457881267395966959}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":105157904088964684489687826509465580789},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":45319448192545172547309148139375917529}},"cumulative_boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":273298305311840667362203220064879611803},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":520045499245910830919573633464311287041}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":294256233204777210182029394096445931243},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":277585246819602739369783970809917875255}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":15465059203133454242806150683784738039},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-1965616860739419572664765661117836321}},"form_storage_change":{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":11990287575244579334600263055389201511},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":47961150300978317261299886914621102683}},"phase_integral_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":5435652308722922267141950299895817365},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-5369872132013321644300027512922353559}},"phase_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":123765937638012654903056020283724312629},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":247531875276025308777422359268151934115}},"phase_storage_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":126694175730423655017968930969097535455},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":271140987321318403877494369986804296823},"time":{"denominator":64,"numerator":213}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-12546297293782789046532175288549475505},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-17749786127479707095407011769791985417}},"boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":80176174807251163394622538327164494319},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":158347785220293287091232732317402297713}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":148750114287877546755168834701066796271},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":295818790125544835320004885467001804267}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-614321856697938071019481864494271421057},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-308701298196989892608811601596500062183}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-39824607529753798971983588123117598427},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-26452485017547552567885558506142167045}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":4792079948806791255916932708156067055},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":25485214345355734362428132965618420545}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":1250726437783091165500834285769580849},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-9941832499129184892271268785481335829}},"form_rates":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":10187627846384831889620612762991854261},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":9757819546299215906546434445570316585}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-40647507410565925460470384579605387999},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-42330271765502048204695890412598074275}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":7878665710020606673926936321076359265},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":7013566048531190565171418800063198245}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":437794583546447708407880914414211757},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-415773933662529180885788863400640293}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-216251290599028445649654516504892603},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-7801033810365046431208905050406495909}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":165690769380017733545536726345804995521},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":9736815799170242621265757140707465841}},"internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":89138591289817927939527779162675132395},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":86717372002616355658468531914720167073}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":623187150209156307678206060071675496353},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":615476441548626096307651952197621082061}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-617061459719467727476042545597532960569},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-624869288017615690620657842321559687453}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":287488007193152651166086879756378017399},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":4438063693158675661210193076569316409}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":297564970927090378779439534430437321},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-210982294554104167620823585016729451}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-282539910195408068774400952629380565773},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-142945091366672391510306570138232523967}}],"internal_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":211944564563133266455054229395251961707},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":210383050227798588701163013539724337237}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-421430371593766103136949586843667941315},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-424438626754237779060139230777189244889}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":24751558314690550169289265021844257525},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":11016883786766191776910151470419422393}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2750744494901846180388297385351085833},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2612384671096663421744155339163698707}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-43479901816014034098885863448009476295},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-49015341018096844221323082772639527137}}],"phase_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2974853852850159912236615089585647457},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2973015954160338000324014376553465765}},"phase_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1673756670416622110892080288536280087},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2172569420982346245555550004479978681}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":36195725345683314614229498222804619},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1119117220965977379081240744207209677}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":45755137424428607137179474360855581555},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":45205745569464055555961882409369840039}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":47358936014042559306893214301690351},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-67157750166311896026187124073065841}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-2810476458021211872690447054411185917},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-11375208940864261869075326570800829189}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5556540316780952293180704984709005531},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11045425833046716330800803042678336715}},"total_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":75855539863187742291093565258514161679},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":68380313243836410705956049161550588209}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-13979689653642248963349595828776672163},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-9514213149525530264170007964109138519}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":104569796403318616253131630792814824125},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":89806875160364733824521092602042835741}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":554113127011861131292652303097930894949},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":263734025839056039375987583895844759873}},"cumulative_internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":151306488069098820463180061696473362453},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":142857500222424011356382697838461445459}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":15700903914141954247202638528072910253},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-15959993022161547031091640446093323589}},"form_storage_change":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":24451423719959669424030570425439914807},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":195611389759677355074200056869834112721}},"phase_integral_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":5475941615740164375591252310286839349},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-1352455285258625894412130168607056489}},"phase_storage_change":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":61689710500718773831995013409972538059},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":246758842002875094269292824723295100207}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":252720006084812737234949505489719325585},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":271140987321318403877494369986804296823},"time":{"denominator":8,"numerator":27}},{"channels":{"boundary_form_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-4142484577917313068256338946721041809},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-21874072676682637018563388997626707685}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":159033822906326420079581150031325535497},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":9812141429329234215840056846793455519}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":18513143931274506454935179376370383625},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":589314880942346152228278043332310704089}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-306401489155602198384546515103024015795},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-615993222441881297309854139589146981913}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-49828381019086881693525204054239733749},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-15732475750240204965920925578624851385}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":12116902565419093504040890299919113509},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":35576577010380202207946930560146775949}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10081577565428354268090377667152055767},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-10019687490504623561957747676544334227}},"form_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":19730818434750018945891075354297263627},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":37722276284511359218961613613915167427}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-19668474648779000292237323585832963463},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-41041313888117226455941121802291843745}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":7225926450029608308104219429199156873},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":1586582074568670521101492297072044041}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":110743641507556450914216207754594803},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-417678578549733145267589912559370761}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-6239960809312175373878713440531744957},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-7136055312838567261364735117664819349}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":161338759700310515834861927622815668289},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":37849732162149153843533644090271732643}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":177988554450770491209117679824515432035},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":173131254811564798585334938953290320207}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":628978514939294427471480931723846321155},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":621533226676201137071700603104409299467}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-155799268102646037521536219551633941223},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-39421262111950458748421445864613831701}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":72498581619208976105811720217060194285},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":286693900375181070750161072052848805109}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":553889651459278026909560773796187083},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-386924498398106018143315655478908375}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-71279041994542589246011535615123584283},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-288313499440611864680421578366811072339}}],"internal_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":210872773241317608989278136611663167973},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":26153373822329807611984884321900652921}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-419209623045203550601171947362814248937},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-422381847624125698404616063003511444501}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":22700917450793191655063811057150959845},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":19937578359128755331667060026569142805}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1391645642367684164554978020686354403},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-656087976966834522881281437400174991}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-9801707518611675415814549652401179577},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-22418578946424056656157392928509292539}}],"phase_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1483841531281992596298620127681258045},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5932266940228768741526325172150835131}},"phase_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2104221137200689294747980582380047473},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3088945012455270498408968426532409929}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-382176110603818176416851900706182431},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1903197672631288336680779686919949113}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":23077015263696667595747719737351039675},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":45628751399005454167789027902048726467}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":22038568989297784173425990989165283},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-61580946523410711323057249350907531}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-45377647489144974399576945588193959247},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-11471629649023944761533279477929705761}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":11159644051350632029502117306651976119},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-5547327395763849839850665988735028765}},"total_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":73139917121967871232189818928860278369},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":131369229803129468126854462266971310731}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-15058925456374773370482289765095111551},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-20029698845467147247280114094115619841}}},"cumulative_boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":51896540272479560026416783620152314393},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":44390764001822617607137966871389541909}},"cumulative_boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":280783918730297591116941334752824639713},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":534827157750109004413855210426784611385}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":310956189628077507701787514634720885783},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":293830528014140122646452970940358374677}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":15939447276151056322472723217540852977},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-8098883439550107113606477444437442701}},"form_storage_change":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":24909468955871025886450101743792394467},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":398551503293936413527408126986150629167}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":22066094957853988619405979858852070945},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-21800246366569575345393982390216463603}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":245937063079885485331473675650915796547},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":122968531539942742121017858087537220573}},"phase_storage_upper_bound":{"denominator":42535295865117307932921825928971026432,"numerator":31508016810470409620729778873509835593},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":271140987321318403877494369986804296823},"time":{"denominator":64,"numerator":219}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-20626149981386590040984478292124358295},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-26026126038547406232378113895345048189}},"boundary_phase_input":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":9858668256282075021845227983493680381},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":155667182490823259786368277493474540515}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":295023494600244064762363117671055085533},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":293599114277230973125041036220180159719}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-611493265328859632199215175702143484921},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-614791280350365382824326648834732373381}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":-466577658933761934750394535964177643},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-72845308778582773867277737096303135107}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":58522717657100686647800802047558192491},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":5698787777743704236155426167148618049}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":2538372629613691529109513128924322353},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-10093703459124014675755901324818624731}},"form_rates":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":9543504541121874293725500574000312237},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":36415326663920401158822090891812650447}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-38025297478489254665660113914606480885},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-39750669565639432453547631943802908885}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1640362238548982596144637201976070073},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":708501051382965469316291780592265873}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":224033312948660514987567760259970087},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-419296937457087189132933826319433811}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-1387064807268854220190721797554992291},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-403666608559080522488739616627875651}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":156803762380490314475366628765837512801},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":146826004382386094922782228508698978483}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":177545857822896699639522608125641961509},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":86338198950291477295653345072742635789}},"internal_form_gradient":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":317277505951245362084837565353886770833},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":627375838309807248952812524773928652871}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-314559543823620342376217947171691382813},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-318198331477357752316312081553640263989}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":73094099789631203805557117931932100139},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":289228995875463193801004255852373788035}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":511472604397397801628012141915275467},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-351596273549230851785125287158937435}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-287568693205294154376946137113615023343},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-290611677769883805333557075352282404213}}],"internal_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":209751792707096630474118111643306849505},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":208025838477458655783874110524994419079}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-52112837910508210083635356656842859519},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-210115768335007144510619589112993168555}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":5153349957851591661598493961910531011},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":17806573584682951498448848774176767131}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2815285640475579892974578418958145909},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2634520356775768229561460484342447361}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-17430370434275099434063502721219049013},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-20290496831179425955317087295844353389}}],"phase_balance_residual":{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":184916268492870883825920242369582501},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5914783685966234175315888923888649505}},"phase_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2512355386256912272951293236718874877},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1980356951893210781384714693629862053}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-760113784988610472951411928636552833},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2642332554625288526645684554978593771}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":46533149169488292302349126857774511231},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":46032224379085375398069572982634750775}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":81403393245931343184115904689715759},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-55958284908050301522597937437053401}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-11441994750524825014203923029050333585},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-46252285037306081861507498000849957207}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":11201351187912889350651582291367239513},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11139027222776503802855872268550584305}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":140842407640188742904641745889496731839},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":15746689362043763313210412146902992937}},"weighted_phase_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-7980677370150785785362441438170390481},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-20852489486035988417098931333475034987}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":102826229764581623644662419820361299491},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":21890388336397081386783302413483696171}},"cumulative_boundary_phase_input":{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":4445014364475052644533332738228668279},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":542124056929366344716341223434291230471}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":319278651713525790497390136890610352729},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":150962367082864974321460236020463998391}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":16180510892137449395210483232732000563},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-16438083074651691232721727722423371113}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":405666798403455723585264164927594782029},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":405666798403455722909330828988548281107}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":22229461084268205049075925530045510183},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-5490559546742007927571040583944417243}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":245074866300108759268027012073726387925},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":122537433150054379073530978058281936979}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":251357346457999022244688784591177453191},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":271140987321318403877494369986804296823},"time":{"denominator":32,"numerator":111}},{"channels":{"boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-12354303303772226324444992648476247591},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-7549866746533128963065411155843124703}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":156467475627452688987551604430697772239},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":38591854997639873059821078476120504949}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":293939732939506104767214278269800072531},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":36580459049377042814032048547780609373}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-305195711588504383768295486131204483915},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-613795401455727844147649731270363761929}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-69502205124309823927743100873066604813},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-5165506452274105302958365580594251663}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":34248823049330858635656016755442840577},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":55522949097654497463624741369208447713}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5110352072501329845937460229734706001},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2540758773142764062988893924390019291}},"form_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":18444186053025925167827525882173803169},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":35111236193677198229049750275315434321}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-36713502898818745500305516031316736245},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-19229509281362019487105559563689747243}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2942847702156508039583466349779343119},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":4979204537038867091584191915392910181}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":226535399568596559281044329536898233},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-420626231805265822936518573429515781}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-2422757968847026842453237907850315577},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2884720863068639263207121764369075145}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":152095015733577576108742767529728066783},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":71040196620088974559231624760420819703}},"internal_conversion":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":22119004367536682252413601314419276469},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":172073778574707432269129491693631153593}},"internal_form_gradient":[{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":39994770077564882213633398563808278059},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":633003783430526967952304712267085855559}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-79353361943180927614781502181496622075},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-641838261875503395936153846056268945359}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":294633184686055308710797535371175016901},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":36455025776637704762080097611839514479}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":467895717871761303179971082717910247},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-316030326644056676684030997519338203}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-144948214712536283421605276832094228285},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-292783774115926351106756928466677630751}}],"internal_sine_current":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":104291730389521812705130417252304333537},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":51695463536240338372580340265112266169}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-103628564770522841077156937299896048689},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-52248832455054560788229806108897013149}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":36980914886913958359392346166321899989},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":31285264788564544798464831678387519271}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":355840973531365683548199649671723009},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1321436279746580543488131893823168371}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-7611318636355948677602344739021818439},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-18125235742147290007777662678852378193}}],"phase_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2947463741066596963157355909249196855},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1473234088789650745266825371223349529}},"phase_rates":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":724539303185688308388575122338456727},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":4787838794647963501596022217831320849}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2231510829991234892003603880897865903},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3336613215652616379871134640482195993}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":1465385241927906905877968109527821047},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":46415980423154811738136967700579332113}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":18616979087705421403965607207625339},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-25148894326173967323260991686608213}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-5767306215961384608376553022424173307},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-23298992453825298516328978415956908163}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":11237375261549827868010313456244747553},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11177715082143633482843558360730417121}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":135405328265976804255032982737354268537},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":3768161060555143839244314399156714373}},"weighted_phase_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-8344843733800385926854892396186899123},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-10749619651206673131322594373913389735}}},"cumulative_boundary_form_input":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":6354250864365811089171606359972915705},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":43072976665306681933279222531107099401}},"cumulative_boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":288148125786421791648279035975479248893},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":137340007435355955228764418912140956287}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":327573278351352046342045237383517581405},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":154995346268209679765267958482033478553}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":16423901625569071481594060801041034901},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-8340372344301614793304754015173761265}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":412560547492601794878688422827322190809},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":412560547492601794182181431112736710155}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":22393705183978057919603440169984203521},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-22125102462374392426697749063373668809}},"phase_storage_change":{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":7630639267939057265394246201094701477},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":244180456574049831339324405923517871871}},"phase_storage_upper_bound":{"denominator":42535295865117307932921825928971026432,"numerator":31325829417247635061982099517502353543},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":271140987321318403877494369986804296823},"time":{"denominator":64,"numerator":225}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-28811052589873343680487335844930896179},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-34387857268364239342206068437479098703}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":155220935444307473792787729195300526817},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":76547811209841200896045940050600698281}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":585917784355553422805474998013125130591},"lo":{"denominator":2658455991569831745807614120560689152,"numerator":4559233169290747473921847571386123621}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-609496021243159435274092343672595210375},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-306502040412715565879164012014195791801}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-79166316099371011492559188602827149309},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-11541927886682886572773695929670871609}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":78388931916223143145055359692274716699},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":32685544363114627536959270858205529247}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10283145333536919254109658385913869421},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-5113804060095218868628052889533186305}},"form_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":17802726915414912748911741011279263687},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":2113172516308070910636924696776279061}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-4425298284424180212089079056678853991},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-9291794651799867900765985581281110591}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5199252146072873043456375473379154385},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":2140252302426125974248134210432276619}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":114496784830834368096135637808187059},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-105415985067395522516624613280891491}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-4132317641820793268379432080097851097},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1267241939766133705739905227382021119}}],"form_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":73611216787893227385196314371954630315},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":34293029932939729086864086628958971553}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":176210780441822697765199788139833155001},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":21415893188826721857311129849434311239}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":645062259536040607913437229167025637981},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":638416708122570431794966002275705277323}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-640320027767479605352614392011182922583},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-80883087060374533471222172483711236605}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":296763735964002561945649773595908870989},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":73481616978605717922728569260840486555}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":423176386247206926058694557557845611},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-280277493753015364020557299394884331}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-146049205460195358031931035794224229095},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-73707233814666018930187893967710855045}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":414739812647367633289713908334170060735},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":410994331237525162307801043032061274543}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-412048561843195620653393353190890369525},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-415663494527342005660700949389236490549}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":4083483086565876129185116823205692255},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":420237556883159860782839955929117287}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2877618064673604225517244652316285573},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2649392674069288948815622535018546335}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-12982058745843702678898480331231573565},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-3981157968290164915738500250756013965}}],"phase_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2934075999909283001213210121310423669},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2933345246828466547005482219677747817}},"phase_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3261637256746898266601261359538760763},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":5570308816350229048551992302134509235}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1449155993687652411406736724683312087},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1993080123278042810236085050918981925}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":23615707754544540479377120162981497641},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":46779850274121772482221705311253113263}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":67350613671008138329726672675146295},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-2787971785512513170981913508479853}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-11622226491816960875489960252675270169},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-46923482412936775227461329158501118039}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5633831201073281174912664642088025835},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11210663682638447924556320874063203155}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":129975427553464724799711140947898349529},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":115199219171795682187744072476306427483}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-17247006022321729970681487796010911101},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-21972900559963234159712274039529458729}}},"cumulative_boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":50158747869851332220861428945917757761},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":42267011260579395073696267802103683025}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":583572232921795496130594996756988209981},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":556536387042346433499061982528307640611}},"cumulative_internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":167916579342281242649894488726286130273},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":79505413120557345056756897664401205955}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":2083678166816465333299393252230776491},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-8462777043172628709103063059572837697}},"form_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":209612550168959946520407636139829200899},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":209612550168959946161652854612631050337}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":22558669053035129862221677429683957327},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-5572170757186759757128348262972196207}},"phase_storage_change":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":15203868588176192378843417656588708587},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":243261897410819076875054013047494601333}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":249820126267136697373076769397435822873},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":271140987321318403877494369986804296823},"time":{"denominator":16,"numerator":57}},{"channels":{"boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-16463657202055109239336369098318224121},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-38585147564141316509340337439181781729}},"boundary_phase_input":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":19252456839831134507758328980549607921},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":75925073536863929483765242061255324861}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":73039574866636426038963191433426509477},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":582064020683012877253406373999387248815}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-76100686677557679013605279048680679485},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-612415677535364184114402846549094591623}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-22177898760002890057508255938464961181},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-101904585871798308891917722251085128313}},{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":689009131212140471974755168413849371},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":75131350437995888800891137740151560845}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5170374062887066762892464611654791901},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-10287355401582550583584148165254381641}},"form_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":17163000704304395246277671481167264191},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":32514636627905823986054329392619754009}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-8523190770702147982634648687526314483},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-35875962700746401423676607640486119397}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":562839020938127098618969650311796765},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3572502635458388282524174607844113817}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":462815720964015517688650768506026661},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-211203897889466235252296641675727317}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-3409258099665391078197041949766732991},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2178917934636460871244970862909911929}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":142196120032948130427812355624792269175},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":16513924765305519491141656820151078785}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":175326067928136924991390140923099460163},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":85220259735657656705683881920332233551}},"internal_form_gradient":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":324996389187090376321186635629408236675},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":321807197651855397069993492089656101019}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-645598155797676274311831065206049106697},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-652075811370266580251209741833474165467}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":298767199746907901256972657959740926017},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":148043405417771596743748499200146851729}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":377332494334444833026104911628578041},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-244388985243816011011300935586108281}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-294173762346662793252262342809263676899},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-37093299781853452816692695740677353195}}],"internal_sine_current":[{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":6441039634331349567510738825483856633},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":204173908282454970813021032518733392247}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-409509890919740332895782066837328259199},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-413254333021374886460039315798497944311}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":28291374933326270551900848446209366373},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":22446696068972495628765132776693650391}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2907956937892829621254893240925814487},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2654066456076303846689385894910246593}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-10710500200100291744992223897968353171},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-6845272576228950764038752001397320953}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5858897035817270078086663792242953951},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5858157650198873670865820210409613775}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":7207465043093980538236764444748979001},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":3145845802280242044676035948547564461}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-440096286623861228761783587877932117},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-573890415905787967544063252621273869}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":47550276673444053588274377443967754409},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":47123679528791656232010769065771404739}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":1876697864453796456259015093088289},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-19447857519382793096094112235178029}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-11704802101352964941381747696840239561},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-47228656126971999644985610710374916933}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":2828524176192448005962303983279386173},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11259964594959812674427591293229002355}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":124579096214356334482039362616446412685},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":109832375719579044908966302354531412771}},"weighted_phase_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-8808511909295897972886496504172928245},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-22279022402865111020166952206677217509}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":98774027877009997950535073288868182011},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":82725343729089665936017207286745720031}},"cumulative_boundary_phase_input":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":73848988029591521446375546265586789119},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":140913590671606856722041243492887581829}},"cumulative_internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":172025784059346951829380195154171273871},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":326011051832447285543185454587635970715}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":16916887192229881041812318824518348027},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-17172313241937069827216466111337142499}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":425653282753766832521014980698900038773},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":212826641376883415891039498742936793627}},"phase_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":11362149373427129741969884543350717957},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-1403359943106069033431927161335950605}},"phase_storage_change":{"hi":{"denominator":1329227995784915872903807060280344576,"numerator":946590208260108526224001377929332873},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":242327093314587781492908080955683132557}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":249005799131596801665895941969333670935},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":271140987321318403877494369986804296823},"time":{"denominator":64,"numerator":231}},{"channels":{"boundary_form_input":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-2315667645881298635109136431212135895},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-42787450269971512149326279553084741955}},"boundary_phase_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":38211688758675448203520338768996364843},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":150619933473668001385146005090803249207}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":291469535490835272899458399275395075797},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":72581208002325208563520136080600803647}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-76039703646453418699591128607550560859},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-612028929140972106122732682050003672227}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-49066732878572757880425116822815150557},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-111359278464140097774565564662823980343}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":97910942127274507993805589953491227533},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":42399720165224387744587550156376398871}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":2599702108257761821781120515189698833},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-10347531543151141204405218135109467229}},"form_rates":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":8262761142356115496669413641547261207},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":15611310243624177951146152533161956719}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-8196200812072932685417461821215170777},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-8646589973663091763583754514957917877}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3796786440050251240805277759630338283},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":713879620145295308390043562435663171}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":58474420405821351412392607319215497},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-105775666542193165550977343916740593}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1338261867966617076387005489609846573},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1818386007357696426761542397374403329}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":137027873421701785367771458955821075319},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":126904837109194530756933381394580135687}},"internal_conversion":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":43575762746611612530771195607270944309},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":84708257629321125114986628224073510971}},"internal_form_gradient":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":163677344863591230095597449681346725567},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":648596605806508078255744762817899572417}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-650660928912620416770174544176260315335},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-328436519128920723206274863462071295559}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":150321849105723411987074824231538363957},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":149060033414302825360363827609222649401}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":330925034826941104708052944693518625},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-104483620395339718405294994869966319}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-9253794077933205177714550639937120579},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-298536330430637306131319436601371322407}}],"internal_sine_current":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":102408055548865919560461298243754154721},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":101406385977456228598217622992950826049}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-406900433229934782130369999911830557389},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-410768202808806370096754060943897041463}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":11927956387311213219146283099521620925},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":2242718970195931906391505547217704349}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2939244953117591260897267854343512517},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2658432455500141890577823228702337875}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-16817094611933112229843415162109480987},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-22850512488421659237492264131408894525}}],"phase_balance_residual":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":732858969479104842752738698214657277},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5863000265544674645852556730803620943}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":7857979863720575286969974168038051539},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":435405050775048069621363685388100749}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-1024745620863800081263160840446673367},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5151888913280068190594385784977998747}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":47848930679779774811076685613449226653},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":1482727570958086460956003176897917771}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":52668355085565293573918504068014571},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-16629084658055487727009110928729031}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-47129186235442474937415814109286027897},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-11878383170137835558784385550611853315}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5687572230529843068017432832769649127},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-5661998040445807978573124442488166439}},"total_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":59603813832378087685927295601628902753},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":52236038309854699347594461645807476087}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-17820245756945609995916867752563269813},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-22432760489485132061744458102965183513}}},"cumulative_boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":48518638571299511987101610482729540045},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":80719681997684751304017537932694872751}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":597956595878983818109164433643881131361},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":285357336034002807226546846480090864811}},"cumulative_internal_conversion":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":44027752954210447626034998685588231225},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":10436014093287379406959857843238839449}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":17166272269484494745979813084955096833},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-4355223880979304667640001920888178039}},"form_storage_change":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":26989900328272836692044550125080801997},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":215919202626182693155961601383306108867}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":22891124664832019251373926596677541823},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-22620371794633625645563820262796878287}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":241383773099154052696187630072153421645},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":120691886549577025720442581198720695353}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":248174416602768699362298530936772206007},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":271140987321318403877494369986804296823},"time":{"denominator":32,"numerator":117}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-41176046406655362335374234692308800363},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-23492570573618234345131028439894781603}},"boundary_phase_input":{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":4740641985383888415540997237577000523},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":149412070802181110143270815973088096075}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":581772231009246556321247995735610339747},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":579377343218148510679242310659893008963}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-608031618996429192463980087218188759491},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-76480117619065694406536599050430853075}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-107432150227095241699049701766684446173},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-7542979433202620873751632229408883187}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":107531256301005197015881802630299353641},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":23593451291704048145986266836468445409}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5224228415056681621681022112202775513},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-1299917357056751756781614618882725369}},"form_rates":[{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":993153046572627513250450335756670729},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":14968426490775033357002483828732061291}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-31480492826739163592191542852015757803},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-16649440846935245633031416006553143277}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":770464374750898434729081994913180045},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1065356429190517571005540512475721585}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":118112583557519080956755374052180205},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-26453453142604147726440283290269759}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-120961714818848561537352679695475753},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2906150517839951994084855685139009641}}],"form_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":65862817577606253986032995654584717469},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":121569201465878757345963288603055077507}},"internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":86572293364494066867795220123212840411},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":84131159736167806709483001982276723559}},"internal_form_gradient":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":329604696323884702025744835967812167441},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":40835232073238359518810148478916703441}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-81938578012648634261584703700659842301},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-330726771592854939324282782482090188915}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":151195376597633912606462261947742513571},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":75006514913193671201513546840858441463}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":282841095507664090845142748643642015},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-172913801987436523524887485496119751}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-297941259981938594184998702653650069907},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-300196418692308347012509116897248719051}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":406960052467372526002446699450823683477},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":402835863126548096809265056628601073409}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-202113955644307508659855719081769367681},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-102052092868368437470768244615082926407}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":19363881756560607251188096935303273387},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":13387663725598339027310740304744422491}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2968492998406500406405069096878389367},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2659391169756384626630647645730491993}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-1520049738562073073433475908532035507},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-4564970558536083269933197719623406273}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5868429513099240295412489751909642431},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2934761793868539609321534512501174567}},"phase_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":4235221761293562927907414696122959517},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":7596092179631881400894957639138994901}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-4633285084320306181611024190760498531},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2834121101401504827167463790836237025}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":48126983116308218389781763002377900661},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":23875315225061475121678699720081135057}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":22507779229785805941260614316632265},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-13760043157556859255215693383626565}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-23709412138576515056229069138418395045},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-11944435983341280049886549603466447407}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":11434619086560083222150097694442959753},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-5693297593769286478135774847095959191}},"total_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":56930774370752362337579428393870746311},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":99137901938090494005666127215963297991}},"weighted_phase_storage_rate":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-4466021603426945824226783630356985579},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-5607824881947065835074290346772944879}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":95107149967287053864732553714257105073},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":78517253506408041834161504016454736975}},"cumulative_boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":302533779428529825366237964750123316073},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":577718362886857853991059512458920234125}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":360338176136604899777135791371257053589},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":341839747210461872901729482419481305201}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":4354317684830561820176029030069385685},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-17671054647699792408346163644986199717}},"form_storage_change":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":109443567864048040504148775639053396229},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":437774271456192161233522181440527958945}},"phase_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":11529643687734735104358559636603441229},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-11394168760437677349584708211958496049}},"phase_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":120219737062861212211320420180435031497},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":240439474125722423131577030656848334847}},"phase_storage_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":123664178963939639767799180703947430649},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":271140987321318403877494369986804296823},"time":{"denominator":64,"numerator":237}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-45297135964220031614565796569465089829},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-51173764048407202145212838675703810915}},"boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":75290358857700846315927988498176646803},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":74117141845984273101662229000574616125}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":290404295897755961753611377826019898565},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":578308486194174544012114688723315029103}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-607944966958570305208102388727218616407},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-611850127565145363325178012680945575807}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-116604658357851167383293063268375247957},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-64945266832909552602079367541308368139}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":117054281526559724605786849983270849189},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":51925075530908884756919786108344988225}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":1311641861146986190145997380559395077},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-5223092773777581198984530509629143249}},"form_rates":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":3814546838356852738970852545991563723},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":3582199287428128125760444576768268641}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-30180134507302792179422729338376868285},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-32014482856969345503854011356185496653}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2358646537154811170962838103110284019},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1398419872052441607811315220738980923}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":119254447830496161679494096471474097},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-211554270110479368048515383882294579}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-593105178831429160467485891797033715},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-270836078407423749570739598434007593}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":126301079378827989364757671401314545643},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":116112831133226825557050936963879724813}},"internal_conversion":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":42964038161250504892396448638150775285},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":83490854269029650994401265516271597971}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":663494646847716877018045982205465081867},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":657915739913272516351563289387198320593}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-660141160935209491277972820474718766605},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-665819095089505602648714743520316457657}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":304008730673649948276432080070427962665},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":301803787633656254692530923679767821775}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":233689231431041291291744286867564589},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-136879732766249075520203614536345373}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-149816197534261554079178194283969918013},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-75431765868430546617324965863053836457}}],"internal_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":202107357068798316771834724886376917475},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":199990998413855146649869150315834584105}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-100373837021010630670617156685480836405},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-202789771758805791561487398721627485201}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":14819813267081120155672829444940508255},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":8786531193347858341759720500538497049}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":374648897212193997864021481790606305},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-332308670407316379524179652523378441}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-1863294872622878400186565570345621167},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-6806853074014653440684674258739515343}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5868750486753801701406787412171235251},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2935408278347812604193927769579018081}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":9038532367354389062510240729920475293},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":8181322513773687805499925917429106631}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-640479722321781243070014817461787727},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-383789732048836093240516903043233783}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":48384492229804093501815710555032912523},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":48033564645753026498098972519650981123}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":37192796329596135534111882931399813},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-21785086078846212940730241167033085}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-47687976785619095925182808524275770353},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-48021353616444946393833795115186925665}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":11487441268986973641791502936586490669},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-5721278998654035012786826519178208731}},"total_storage_rate":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":27136990228137079424975780565507978001},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":93841023753873590991716527388531786315}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-17753118466279671664854549139282633639},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-11135903689676617282667204787673969249}}},"cumulative_boundary_form_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":23245961679741059970699945500015857247},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":38059241658319477116802326101765560419}},"cumulative_boundary_phase_input":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":38257876874998069067162136151371918299},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":292333422467459439797170173213862052193}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":368393933291839369444460125490910323955},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":174833507399091701341227300530815883755}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":17669688137789447773790670144756356709},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-17922593758191805443197489687863179447}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":443455186252611804689849923409919245057},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":55431898281576475485507802225388821687}},"phase_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":11614307913958381223418089856175353751},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-11478743865394715561584132800120433487}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":239501527470996272596716400649164487933},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":59875381867749067817242827940019514575}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":246477387192365824659300626376619848459},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":271140987321318403877494369986804296823},"time":{"denominator":4,"numerator":15}},{"channels":{"boundary_form_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-12352012568524319144812787032833592799},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-55347460889133451144987201061923866061}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":149487588422015547620107332706582512349},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":147086839260992751982403774662801453793}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":580047311229460522662430153897920085849},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":288721145021676571249339742381605864733}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-608055558570279046944676478987767711803},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-153013572503261950649329231909158150803}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-125648660445166892237724553413105226029},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-69482765047828845412444209343363205367}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":63238226510442464476922913548669654395},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":113224976938459600292912537173828735417}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10532799918212960811515278679144105659},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-5244013813265819493128401445568953773}},"form_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":14629095317733560076304758031885975949},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":27385556615765889311021377928640745321}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-14442284185882165852308157778929779713},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-15367000207087895352544359374122562201}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":813884416046737138602864313560827667},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":659253598387631729870795739741159577}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":240748972243859030414627506053574011},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-52832656092015230608678452332372645}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-429610885642689931896174773412460539},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-709502465568407095646580287365824829}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":120765019481700417552273706193336517959},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":110546649841094950100481773812818616537}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":170442727741723865665989724835290895279},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":165579680452620907885745628576116278361}},"internal_form_gradient":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":333782815743656855701387656861449370501},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":662253006562384564352941348279296786089}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-332279382880051208860634826533628594613},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-83746262012142166871144344999796312835}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":305497159972306249856201967873578412267},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":151726329561041301966393583631254089741}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":183489481484858521733697946073819943},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-100917164580772958193341181777093067}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-150597151073627751703177847010563472383},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-75781966364123989752866511703956052261}}],"internal_sine_current":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":50175076339788307367574006621164368665},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":198534160265665062338990146991805178737}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-199353548208712844855307079367000769697},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-100721526672065145146799162668829245377}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":639223325580912056182870927097086901},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":2071106261547219803392964747543805561}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3025340810242402281258223915813467401},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2655658947972977340438683383277666495}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-674831201118639734362049733273503925},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2228967733533552957461185867922393159}}],"phase_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2931901065289741278719756581171056971},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-366677728492682560762517898043344859}},"phase_rates":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":1195297939897083063398788188998974965},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":8722295175027474568877699014377599091}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-5570897899728184077389621318009112399},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6569336464432099343079479943757305283}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":48621383110128046866503062005658469905},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":24147995346829685435099363387027686095}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":7300814495921010225175103033067039},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-4015366396462088945299108402288023}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-47936562017849578778571518677118592215},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-48244298176296320313229933082180583877}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":11533554759689485588710695582311602683},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2872955998327900544553248250164202093}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":103272933131548786426127269183189190415},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":88587714154606668862643191574591332781}},"weighted_phase_storage_rate":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-2186510793768953890768304626268415943},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-5489733921622070309459645559556820939}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":90667844362365930043147384431407130339},"lo":{"denominator":2658455991569831745807614120560689152,"numerator":574406805370787685243620134013698747}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":619133260707251083869286709642571748051},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":147890385131319478710878880841260730633}},"cumulative_internal_conversion":{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":11761982379835396113986043557580143271},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":178714281159700003869799463700568609029}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":17923330266135845605461063515749648663},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-4543829211025482365848065881064625807}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":448875963672996677056243368070640306337},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":448875963672996676227308514749713211783}},"phase_integral_residual":{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":731216864493542828970024217707228225},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-2890956794189058471507060443914897841}},"phase_storage_change":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":59644261008584652430750726122277410265},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":238577044034338608357631298690115347265}},"phase_storage_upper_bound":{"denominator":42535295865117307932921825928971026432,"numerator":30703592627854193603219154733512027167},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":271140987321318403877494369986804296823},"time":{"denominator":64,"numerator":243}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-53502027533108735730812288919105915613},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-29750273029339107607587490397996735255}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":148421409309424551190840344528005015507},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":145969934315700056449054278284986498333}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":289743724532225265288468854295736152979},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":576777853475787720723521807720736686751}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-608361136941354431026537468468213355931},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-612451090887067185292329925223298451489}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-134561816949852438421627851156836953513},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-73955162770214312654652049790066805955}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":67897049061526566250336246792501574585},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":122494660336535286155586082576919145065}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":1321600735791328144565743770749748671},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-658016379282596260669342246932879385}},"form_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":14003532967373593289425070125355681055},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":6530362488964914052870188171205475467}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-27594646474715053639500880641229594593},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-29458288151903155779801062680055343837}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":222463763786783958120287199626075627},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-43097478505432381430625442314905059}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":242970486872279132798306875119015333},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-52742371545562651184809169972534579}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":333809985365188392290431732238874445},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-331874545019402473739564178914001051}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":115128700136189383577644349971103079811},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":104879583896447221928765268250054984055}},"internal_conversion":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":42227468374519374457571758280021742457},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":164056440308536973636293380601098560953}},"internal_form_gradient":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":335712463368923414197917792393232241755},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":666358382788343296809314576786546279443}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-668757276946987883854879962366332290781},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-673907594569563148598252420755055828577}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":153428337500611499855412655167026516979},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":76240780561420971803823077810780697365}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":138744888188537375170089169213374363},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-83167202967185723982527741018828937}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-151295693707203850375984286918192072955},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-304402425527359630577354387620608866529}}],"internal_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":199261097358736294539854619713170643431},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":197049595693877499878502179659808341029}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-395867514053170028573404996870100285213},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-400132485272585890157628636146700980955}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5591124208019964520106798377574832021},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-541578887443641566032158587487878349}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3053257186388349693070475599879566965},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2651120751687087581303289654094714725}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1048694997718192247480204227570531267},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2085229265092819833241099960084785599}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5859878248457558729199276330594703251},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2933025569621693885344639443230125503}},"phase_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5021183186279155307059008079428348489},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":1152161542763830380911653243201451237}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-5974271892058899492056325335261213885},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6954695155795258246289696141031624009}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":48837756647187868631426046808221604743},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":6067048545767317447707817845760318925}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":690060461998063977652094814420291},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13236471455354552812481373736937905}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-6019864380504714017394999964150398135},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-48447150711841830047739242089137942203}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":361851592038989365366611686800133867},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11540880018224403747405102318397912291}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":98048639202269500925610871466597311567},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":83378501758091411712622953290501187603}},"weighted_phase_storage_rate":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-4270015233479970663008369626126442061},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-5375270534588952554035578739888449113}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":88159936821751458055765558388324040545},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":70734982990960282372972049928941245685}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":626090514268630359706357350792321983153},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":598403881196326354989564942659651664641}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":384301086474955058358348098520068661383},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":182559353979431339189400089808406856551}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":18178243521726393263243576605430220255},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-9214544412578581625806799002043162113}},"form_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":227015967235774677007507903075592589521},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":227015967235774676581250029452153188851}},"phase_integral_residual":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":1473131679541872910593061170391129643},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-11649452357863209765410161007827638611}},"phase_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":118836450797020631600352911432920538773},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":237672901594041261796736849159852992829}},"phase_storage_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":122394852285411874636082242706760315015},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":271140987321318403877494369986804296823},"time":{"denominator":32,"numerator":123}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-57571549414142780384441732269721278495},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-31813867974056440649255156935230028639}},"boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":73691194700446767695697701146109708809},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":144883675255871335523480448140293045683}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":72390995815862687786910055408684489995},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":576314175785534078168844251435125781089}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-608859300522823250472582427408390201009},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-613038046701778797964508279804658008375}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-8958858427496049725510942452566536231},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-156722557083463396970818320127695928871}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":18125425929231025675030519645494285079},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":131655412106951511378422038356073082035}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":663871062980284660975162044494845209},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-10572203743275131520155809834545675247}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":26763733918137204387269490065822833241},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":3108247282929837261373095034270951193}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-26311227712302119900556039971024706493},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-7047055829604911161494360837648655179}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":72791221839631392330923186856926347},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-837346672607714216936414088344340817}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":122599735059599125275199276341957079},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-421060152652675686860809430230548827}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1103512232601417728220897436713720109},"lo":{"denominator":332306998946228968225951765070086144,"numerator":96118024773827471709150372512251}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":109404065250391325697946910216070424859},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":12390123223547455008683731763695700407}},"internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":83632369472898775987033698106916278499},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":162409864190819652420854631374612958793}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":675079102358504564219258517022603440635},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":335113232966012612051495298426182613623}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-336353325997713949814763160720632912299},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-338817838791839940672798672399776489877}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":77023449673337003107326987472671106587},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":306273672227014748281155024305706039321}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":135840877794611281007423436562150983},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-93080649222048065003135353438174389}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-75952831966629839741107610809930335355},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-76390535498459493077290566668485741093}}],"internal_sine_current":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":98895996104873059439495642186336414885},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":97769720248422722957248121646596036229}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-392980886497537770789080139939601089985},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-397323157991638487502879371247625093849}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":457360735554421793670875442582610867},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2630602155172252740804309237486903295}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3081267415962332990922045575695840981},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2645598964586085659308488231900673941}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":6933571846174170131423708212690800553},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":618421617678373136214057888818996641}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5869163296251904207092109537294114481},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5883311259478532408221333760932960831}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10479284178797559425098833839542072841},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":4832925496193175681043089548724203905}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-6331035653255658370545353915981258763},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1824350062864562146790250753710963937}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":49034650998005660476585895579149421713},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":12186242218459084317329286483650676485}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":21619747174954467211969169824416111},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-462945169684116613833753068384613}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-48353074597269044169064695122514423507},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-48631725320066924470883377011702131495}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":2909056387239639807370484352498009905},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11600640247775764375164378756259037873}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":92892164856717013454452071679825028025},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":39105099869487495315894645633119550625}},"weighted_phase_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-8255950196837156121747419268122698417},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-10455393024702324718840281421663251003}}},"cumulative_boundary_form_input":{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":1335332350671304925394450815440325869},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":16938108217098122765526094741565857625}},"cumulative_boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":316499531885898622088914505137384884177},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":605195303473945323842228088666227901157}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":392141621113039318607132507717592062493},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":372731670342807349586027740462498695545}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":4608712540368907522146867143586870281},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-4670984545831840993047231272118393987}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":458918953372675470736719588003109607169},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":458918953372675469860188434817299342161}},"phase_integral_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":5935512615680644623422827711189162967},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-5867915151340328076644462277355976539}},"phase_storage_change":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":59198933205907145932196722948348122633},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":236795732823628582285223420702847166653}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":243967717661262334627920402106972032423},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":271140987321318403877494369986804296823},"time":{"denominator":64,"numerator":249}},{"channels":{"boundary_form_input":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-3850787166341904715572606275457434079},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-33863105477640354427250515079752412987}},"boundary_phase_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":36592687185950671961829705350171962543},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":143827864713288233318962883158662738069}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":18092741413053729010309329711730620903},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":144012538964764226154792591866636312883}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-304773748794333290275572380767413169705},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-613812525116479882129477608068709225645}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-37996461232550916123932398190234166799},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-165399818952825258935295852450859135451}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":154100413783161545680028850307204803487},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":35175783504454564273174443366760839251}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10676026678271364603792439482190356801},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-1328431527095384320377013032051993453}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":25528966900122847441147091390136250427},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":11809891410473229065377694778133375749}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-25035112437415822886916761409833849157},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-6731184071906386935123476386700281663}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-604404821522878754921682287020035429},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1593759891888398741252695802975571381}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":30935942912828193514306920119365617},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-210048477983724338569391760106657579}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1879027923357083041087668617138991831},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":433425882720693678977688028108635055}}],"form_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":51803353619271867813118817867051344707},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":93285616263114356210459966702083812203}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":165525663141347906222637771365818705091},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":160656891515553079876946226411417158587}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":678556675602155294822367049192269847831},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":336938665572004962017959585441252381033}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-84554849831272750619017579856802557045},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-340591606258456171786231880378990448051}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":309264419373568478874327932398208820219},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":307446509113273098781799651881101280697}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":42793237510219850260689641461875729},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-69706333408572056641041463744333605}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-152446282354464450975086183648469323661},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-306662119640207281327397713083103546735}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":392590689531692467639259502596843774013},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":388011027521840645650406553967759001303}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-390050789728701580261709331665482519159},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-394462795180959086112100952908577368915}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-3797587494181052089800318613497673463},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-10013888735885313178845296495657931521}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1555010095789028514420180350698927645},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1319773510662771615382111423362328403}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":2951570159954348570735213264639544535},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":2723295138062005135886426102690670559}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5899819298911931603952650378903303285},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5915126343483124487179708502135683481}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10876279544174046657648843649215167495},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":5035110976690997355105557044845682609}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-1661213500052305395192241503416043799},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-3800392710917397193341572182421046411}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":49220961065748344621543322400906438991},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":24465815830862430382993053177176770829}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":13621510561314002230695679189325731},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-22188215053571936599792429203231143}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-48525158785391595588295413470911690551},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-6100849024972148602472674947980872649}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5853537175694234931026772453346056791},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11673806934451372704504267804150084601}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":87808728109395994326515397905850025677},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":73084347147880839693652853189218820307}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-15797979129147741299722237828252663737},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-2525158639404189564600889189108123987}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":82573180068207086688565397481587780057},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":32288883364931853917274821588768320891}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":639860192619162995170672080027927011331},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":611937234632380709779054473814290217003}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":399900636572790001711318653250364814295},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":380262462132598900205259594825533874853}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":4673294271892656252762213624469688003},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-18940410690963856250006775175428471913}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":463533405950033233050858092500949268647},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":463533405950033232149877275556524122439}},"phase_integral_residual":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":1494707263749958032234820112468895885},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-23645816206974059866101283330545915431}},"phase_storage_change":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":58987978569897509145873235590856934217},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":235951914279590035099311201871847221047}},"phase_storage_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":121585292334985120247802173300219340949},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":271140987321318403877494369986804296823},"time":{"denominator":16,"numerator":63}},{"channels":{"boundary_form_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-16404942365532083069596692275664202199},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-8973466799768656446678117610027353121}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":145386522112171208202231611990919081227},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":71401456394012503878120095078559963537}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":289502742259670378859257555462748510367},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":575984595619668390567451710930742961353}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-76302878816291846624928924952931773801},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-614771739922419453017388835348215262235}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-20061477244454068475375510190008081653},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-173939557344487790497203946857372843153}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":81540449624894762847716804965050062139},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":149633801963957018568643568470735365481}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5362747204053034453028561691300044975},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-10678459251993225275452610007324509305}},"form_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":12151736606039673739554004446223971971},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":22383721618829515146899313386164945299}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-23767303359317906542587002880453651363},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-25668713022917568433364094136506555853}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1359551575280936250693600907001483489},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2354618806836048707006418352245326975}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":499508229585602792148158383637482203},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-52355058114420536310006769073656937}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":664863367766535647495564123819501503},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1640965445008463067500438434237221673}}],"form_storage_rate":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":12217833127986515573437485485643613609},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":87386443412736649392298360749241009431}},"internal_conversion":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":40921168031714551736534434964805581883},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":79402452506967653627433850691383821945}},"internal_form_gradient":[{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":42613978378324819128737932063260091673},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":338657895082178545307068696075784101959}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-679957228081928042647160352777535608633},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-684527226126305524694465692275972818905}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":310320537059994876188976299731228963519},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":154243433824335090996370330755390444337}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":206993469058836075678924131657540353},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-194284830207887893157269025188523599}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-305842853793139784892158980704127055213},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-153816124781848425402198947877286528441}}],"internal_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":194773328327493493499065298557356128253},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":192450581768814653609802234738639382339}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-387082456137608973005478003143825921631},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-391555722743664479556151986502744338419}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-8542314482158040125164628910098211051},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-14794506291120990089820784064834979785}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3138502768947547085509949423580421533},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2631652255208483991984655678782307533}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":8354919487265269312979466507770712039},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":1288811246708323354924513658646611453}}],"phase_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2963994380681075571275593259347331185},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5943700203303939758479592688873726085}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":11229872881258698543507092816990885527},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":10431047400186274161908102595081573241}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-3458197552814668937404438564083268329},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1965674838824567658644184316482801939}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":49389047416029882049257146844212835435},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":24548604932610575561860009411986388527}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":32944033788453053612150649843370407},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-3865173886919368186573708842513411}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-24338200995255013998689014690227663349},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-48961193172541916026046418970541954987}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5886858028272660178669135712420034339},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2935598085593566335665541054935887937}},"total_storage_rate":{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":2587152951450658641879797521929411587},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":68024360307668610581182678668518720683}},"weighted_phase_storage_rate":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-1869221322183881005918295397925967261},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-4840520776267009702778920520180572187}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":79497253374669821113016017679900742145},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":61212716679950461667045349073776384361}},"cumulative_boundary_phase_input":{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":20208599557599094392348490213750041977},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":38664445073082461376101764545494075849}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":407573355578736480161918859806265860899},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":6057913157111361214575492473872673565}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":9476528180115055377219224189508232821},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-19198393858098612046483058727658082259}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":467872215095307690154315315780643958163},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":467872215095307689228451818758508520785}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":24089790781389711341833245529361007253},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-23821187416071291150628424270286572191}},"phase_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":117573778185986306598771309225500179969},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":235147556371972611671691744241863662913}},"phase_storage_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":121201340709892899525742286734318574539},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":271140987321318403877494369986804296823},"time":{"denominator":64,"numerator":255}},{"channels":{"boundary_form_input":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-8698428631397740038273719163194057945},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-37903163283266164969320625661832937171}},"boundary_phase_input":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":18053721906610421947938078145548084119},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":141808910982180761101295925666030664975}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":579239900794546875217767107976568832831},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":18003630999596346038260948113918317171}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-305741522080988269277386468931022511587},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-615912748622938832482458111642896470669}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-42214253843861183521745492491215588039},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-182339126284001226223033747785743262149}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":171940424121894885639404968904006738789},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":39610767238973683059463863511357069365}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":2692171776495682657802526489227928345},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-10723178580021252303567403972868773179}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":23088019653788079209784783870270677315},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":21158561405497062234767999076179347821}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-5627191977049972259588355678477240851},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-12210546422798577694128844681215982233}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1059618063280446386993868298530690653},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1559620102692801156793062878404782959}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":251979184712030969265513175621244167},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-417282739107459230428063118653852655}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1722074273750720357506551097480497563},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":605033948822793695605137083545713253}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":91822473714091353528089828672628393081},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":10179415472224088911508832034506775415}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":161745931408995883901827813554475440059},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":156860113174640952835520974039382554043}},"internal_form_gradient":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":171220298884760953874433657167521722649},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":680542893105230381346281548093085443489}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-341631890844449073602380683999712097407},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-687661157396039463198193614307212862005}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":311246774500306167408872922216860428961},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":309396435120912080779101255444685527957}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":242392284002871048666124350520157357},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-62501093274708741466258861340927379}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-76665555540751895728751723460688082779},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-308472524928451287796829567180485350909}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":386456474166276907524198227305343015395},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":381753869500115529170202904264143568315}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-384080563827170292569467708487287500891},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-388606446584981578842809524173244559679}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-6657776646425790034032040130328566439},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-9799382114021326042619230029318296015}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":49475997221803877070593146516060605},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1310932387649820233862587846255179289}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":21640223549404966365555025439867001691},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":15206161670352892840830830285954679935}}],"phase_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2975268931677374961729308499042591815},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2983321616851235161973857952280176737}},"phase_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5770162650234035332023144836379850109},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":10748581317497029467804518156540480601}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":-111658852445761622634632913413494787},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2020687212769207287320195557643811859}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":49536462683132208406195311801624058659},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":49241972024504049615541132480076792029}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":38577930166391473913037714553509267},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-39789431773270048168263392545540219}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-48806808516787636440707305934536485057},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-3068432946900058127584775208287828719}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5916703367491274744180941719952005497},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11804003579368791561208280362336240637}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":77835991150630980651016557782268801627},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":63038342622332663716106591496495968755}},"weighted_phase_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-6993241281730186438536635445179795727},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-18396981155460047575964064779558234565}}},"cumulative_boundary_form_input":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":4764708914868479287416460812106435651},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":57659295122144258701171540417979546501}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":653445331558149928785628466144581874809},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":156319603467902276298562869810875100251}},"cumulative_internal_conversion":{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":6486799939273955659684641227603623393},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":98764814965047103099249140996486791345}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":19214292047982766289164156434998333669},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-9728845860556697191163064407788739035}},"form_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":235966423515157718693666130419462522775},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":235966423515157718218077141372378694749}},"phase_integral_residual":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":3033159571348154846527889508603270979},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-11998788684550168105286490323890004835}},"phase_storage_change":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":58597123582215295436664389186423667921},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":234388494328861180178058921510854699759}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":241669773315310380390569803707437745765},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":271140987321318403877494369986804296823},"time":{"denominator":32,"numerator":129}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-73509910153420661557255218979419816373},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-79776384472646491115376469499444714641}},"boundary_phase_input":{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":4484392347612152050213961928399709273},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":17605735186335532508476552333444184299}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":579669524335455006185207597216242903365},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":576443536830427236073194620433006110837}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-612724524095183085851529051135350580603},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-617232447936214889469173872090401549223}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-88539324744381719231463799481823918665},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-190595730579679273535472323382598390397}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":22584286981660114740302122321947633277},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":167126288967176178860805167102863485199}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5402784809242825007829715259581968893},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2690395461628230000189383228318034943}},"form_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":10941697232619592058727855681672641403},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":9972542357979790890992968911798211019}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-21260481423519789258156798287574580337},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-5795713415582691657503083041781007397}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2882827404698531852525484779076412497},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-971749337645796779923080045645393007}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":254162918309645235162256888840527459},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-415423492339428149768047062557246373}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1058118340461830155233296146050985499},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1601860077209545236056069557694527425}}],"form_storage_rate":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":21464447937082803250412225701318591819},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":37722011167030766508718583863828975155}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":159715514333995114575449919620349906455},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":154828606602492054101365941785555144131}},"internal_form_gradient":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":343865303926359642860344297108292055193},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":341779917788575975481472914511599274561}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-686359600744370764631708844299571960371},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-86323283957526304774333137249280153079}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":312043195883626828033171867299203577097},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":310175291866810360084671185217760926199}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":277318740459960269520372961989084055},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-153273869297283646165916833030788045}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-307350791326240426922641842055323248009},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-309183038451352188029650230703538237757}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":383324783351572326866893768074022039937},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":378573725436333343767304053897707799087}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-381049612609017036493175952801045313311},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-385619537231652887777852949200215667775}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-18113338792336474917453094032555054439},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-24422724642230261351691594861754764045}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":798476356976524220509165447188623881},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1305091391662163224413012759397821709}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":13296707220094037141249893380037733599},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":10064783701280572595132672946903320621}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5967448636683039741048610080672881171},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2991963679329965253111536591595397335}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":11807924970277737099552810561924094513},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":5511552191157190501354885382147116859}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-7334618714191200776440526346732130131},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8261388001831632327768660198244352373}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":49663217083071776709011725812093706785},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":12341482731393557261099344198561966291}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":44136648356221069247351575976958619},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-24394293945483782444038546810156315}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-24458198851388396859462859607384624795},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-3075500555606515305707185842184416319}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":11886110523665629282624062765042056633},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-5929300736834895016448314130834086059}},"total_storage_rate":{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":569965683919557798711406343227740753},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":58132043496498414016694934467702708245}},"weighted_phase_storage_rate":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-3225546051656953691647222718030887723},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-17311978837563119000742233259955242065}}},"cumulative_boundary_form_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":18197391399863518772041758651010666631},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":26959888549994477215069134205096537751}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":660171920079568156860949409037181438719},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":157970141141621232471232546592135492529}},"cumulative_internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":211320930423969591607770626774417899509},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":402316850794680227432998092507145062761}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":19476688917561480794232803793847618943},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-9859054817581298311630586527352759271}},"form_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":237856658406115331328684582355592878603},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":59464164601528832710055889387271618375}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":24441576446384741831758938370065288667},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-12087394559978721269628396038122028293}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":233680280164930488501147871189771459765},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":58420070041232621722173631113448079843}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":240977598365677058129321891610082065237},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":271140987321318403877494369986804296823},"time":{"denominator":64,"numerator":261}},{"channels":{"boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-38690785112998428368584060717567689601},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-5230770597274841320759632724385805913}},"boundary_phase_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":35649721391489312612911568460550169681},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":139913826154946297784144859054070765777}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":36268299770841817237967987698221777367},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":576965114221855259741717802312405779945}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-614144292561423446083629423587001422729},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-309363784768327642134341176880716986857}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-11572109821323694433651434355539540283},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-198706399524982176163188366427300887699}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":189277539362899391484626156437576385295},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":43919633631249189307312789455836053203}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":2709032242457747098708631203501274493},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-10793654286578673785845212057801010029}},"form_rates":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":2586301031143390910843182272318345079},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":9372047900896627089668757835941651193}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-20023451170596008027417665556677905811},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-10977502946813116402538896720133944601}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-456211780503251063332544794245222457},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1164316002966186746219329667728707125}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":512611036889724962904930998584729405},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-413262604400554499442711845227600819}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5023786950055401472168548077362784427},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3991074174489705832227272628913602799}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":79860388047004507426914893107242437861},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":34712202228645550536067945463146809085}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":157599628969866631595149224419230007401},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":152716588633570980164234491883410234497}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":690373352299016740795082752334812256349},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":686367962244041245691586762963501330179}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-689245983812641068032949957723815805249},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-693303996695525200633333287699644738199}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":312709971850967708355696412172394848249},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":310823622690216464342190637431054020111}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":155861411635297926927655547495131343},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-181945364793811236626588936347961937}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-307908779708907918921388835389255259657},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-309763980960850944977486617311340990595}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":380156260807061925397845043017158403397},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":375365340532273093722474261815219502497}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-377994120654074485168132519939971129393},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-382599590199807116834155801562727759773}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-11465852624881062453022251977504177915},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-7315613202751208390663859182211129111}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1610415067641806438171713201839944853},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1298302761988166974360225424067661371}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":31565384350988645565099271845258999879},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":25076658613017616857946709953370288703}}],"phase_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2989358983266997703594561900505761795},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5995547945682880259794709584294980001}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12032987784881835490601427746482051869},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":11254924662640313188921445940605542491}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-7482236140683478027728863836810919399},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-4199552735544745564108962013414414515}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":49769337774208957979714353839016111661},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":3091819748804884325753822710490394635}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":24806114099038315103827093347744317},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-28957504179593164507383600776305735}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-49005204312066177125719618588670777315},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-24650234380871591209445766886826475387}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5965903300034666185554458039598424329},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-5953080947982951307362594553138108563}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":68153303198618169023099651543094719827},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":13327788360998622774938240825197270599}},"weighted_phase_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-5853542424193169201907620782073859017},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-8056625506648304986191463812752267887}}},"cumulative_boundary_form_input":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":8645288061888809053576534863971336953},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":49996699152032823439568543866903721067}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":666856242840472402975870328123534595535},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":638439025167498037593561976636701537261}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":430029343455901681571563873443487205615},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":409475440886878867128196584314179917503}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":9870026619808138442378609820993513209},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-19979454672484187550747119520653234933}},"form_storage_change":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":119803048319631991863130586955767666247},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":239606096639263983224714516417302333153}},"phase_integral_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":6154623487843341087850092956084513737},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-24352626290623817131719160254288260101}},"phase_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":116514087831484860186699237508776193297},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":233028175662969718715954583555066417931}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":240331613106633938385499770245510969435},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":271140987321318403877494369986804296823},"time":{"denominator":8,"numerator":33}},{"channels":{"boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-40598391871519369401266672019951014911},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-10943575518162294674911073009937886535}},"boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":70862386201603404837205236389536886053},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":69506365661564750684886345167127614743}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":4539906604823996200008958863025023789},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":577679297234539192522693542883662303381}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-76967375496250138373503642755727805685},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-620394675697405759530074282110341263471}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-193079174638686955205998364642830570763},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-51666990452181145130156773122314983681}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":98872437721318676733119481214962948819},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":184094575125723333599655668998065109957}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":2715091530690861980836613101142579861},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-10819395013871373141603586452471883375}},"form_rates":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":2438737035959722920911350448143619973},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":2194552865696478495022014763308616079}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-18798718230409616924246263586803949411},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-20738594386877842798403069439304543735}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-552400772190716617383099183666511135},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5429415327470507354045145387918335327}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":516814508816495352680322742569057211},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-410800161010410809538579733116065579}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5817447977890690108481792216852207157},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":4781552558368362714860703597712632121}}],"form_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":36921064467707089198484327268206729273},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":63388422650619275324879249933799361043}},"internal_conversion":{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":1214098448496323338039188909579478705},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":75265183478974543936455393105673115691}},"internal_form_gradient":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":346405523844415886310601857043176562709},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":688968770389054473880872919005445363097}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-691924390714986238337980216404994543969},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-347907963547792767742000879139576837631}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":156623690549562429292159920848418747013},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":155670859128269012455171516827585448945}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":345555278298818498940689373145414951},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-422008481117216436212959460186846365}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-154168251863138504948797017847222254293},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-19388477668367621771243201748635795075}}],"internal_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":188477807593844432960378441576001007619},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":186066674833800110375156656560819933745}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-46864827588914433163461072759689597585},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-94887805610126298366327860376490965881}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-13883345662013474242683073210050537635},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-8528505653034583713299121269588360761}},{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":25369072877601862937945420944997467},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-645283383961905406540744964510856815}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":36552103659964379928748555512830751697},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":30043380780247058681849869272546279577}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5984357782335836898501346724857161755},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-3000757734982424429757119189139382947}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12215858127748820371038582061208728981},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":5722189181567620066876642235742337537}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-7589538482001674854385401591480626933},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-132756647323192367676341370892588929}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":49854869112516467482698057431542237847},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":6193946681406527558747999424895267681}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":54996830652752513492230976459648153},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-33582367898253884646859973278584191}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-1533539959490924739130997502675317691},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-49372352959160518582878687919708274695}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":11970489455518985425742404914600438341},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11946676034255922605012430615923606411}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":63434616633350129396226511169352575547},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":48581312625912148266864698123248135873}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-10407512302064049000742143367060882999},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-7403555012353563529007275905275612585}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":65356205257155531547243528409900287977},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":2868303645795122683529805718011063351}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":673499591546872722179358319035053678603},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":644955246948269732970270071496119751143}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":437313934146879621599799006900964077845},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":416531551838032730622239277417836772099}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":20769187434139310514121985316880384,"numerator":1220959057916155762982786826924687},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-20241536028382164597304743949200873023}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":482428603375652989579426148278347857523},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":482428603375652988549737791361663492799}},"phase_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":12397916787088788848794262982931815483},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-24530893333272304192659037335275222173}},"phase_storage_change":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":29054643296945961133507448820127413033},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":232437146375567687364460004281941684331}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":239736986567228336354736326002079014711},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":271140987321318403877494369986804296823},"time":{"denominator":64,"numerator":267}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-84949939254180002335836284931155569327},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-22834917174920971264894886281553938693}},"boundary_phase_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":35219552048827808142913516299436170185},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":69071286187363786159242934237819466549}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":582113483778355241467522080612614955207},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":578584344325736198729460971556573426493}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-19297035636370425469625117125148210595},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-622230154867874800253264997493294184525}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-200851513891519086080237916648356105393},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-26809627706279312113857185172549188271}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":206070701004841859891855152286864720493},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":48092214372111261951764543922236355455}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5439148029561237406183448105759510073},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-10838817097952685862411054825012020639}},"form_rates":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":4585680163106921017887845817906156555},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":16382920456091760848642104239782419919}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-17587359126605167788404791077239427473},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-4883675014880880069824585825616196397}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-1297683571443958646368568508795959317},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1550707162294522809050425052399723131}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":520936919921174285586258893934962779},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-204018215885156724781125549826616037}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":6612815528561751494398586899461866059},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":2787254926813069026164643776869461901}}],"form_storage_rate":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":16953740934269450228206690825132598369},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":28674051091813999118052782613496872533}},"internal_conversion":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":19142107316970085804294113122895166879},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":74138168188819605580019706107613564051}},"internal_form_gradient":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":86880684320960942976181848490535123819},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":691363913752694094370453754761704804013}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-86799555843344102822250225409369762321},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-21816369651699513806877073638166891043}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":19603488248911373995594388809309471061},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":311729976497757345856371025000726965385}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":378767739423938874061285228029060219},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-120218857721846798184707236059897681}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-308634378888762534872488347501086802949},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-38817301827419715047069467215258543941}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":373727583237068860606643576714498997519},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":368882409297845958972461459110417878221}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-185913827844703226122683685280926599031},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-94119767019920652952246758524988427397}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-4076793174732506080769021380859428153},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-4871690228933548078210639776400511303}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":204571450076006943470672355588472153},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1281884256446609645156408717799548341}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":20774772684074104037560863502901172341},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":17512839203515788933373495417675372555}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5984395049402734133127184263235836271},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-3000927755784679770858290714207960585}},"phase_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":6178454852025192400862522767076564085},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":11591830643553997694558844781239067965}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-3828540692378646723483659729441004147},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2138477129808945204319662092602376509}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":49919872906530058803129361932044166877},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":49613366669538440867089672202645474825}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":60282758013062832929491963757469695},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-1195839091205824332245022482386253}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-24560343504121732227985059419193198259},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-24711861853295638281861693538292325045}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12002168950403733671180587706820649487},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11980150451400570129814143485493734879}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":58805072625447420930086911056243827813},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":21974059244865330053001818390547688267}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-9009891111630379982739852244286565663},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-3349995923474334532525482111474592133}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":61374176854615843937751202553752370665},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":41611311362424280824309100310385650111}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":680103257556027936206154603341197960513},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":651430680028335087922699096580915326131}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":444492224390743403776409299322049765425},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":26467625319108410540335382804089096483}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":20268919345292134759101747487977616425},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-2563020678988533067760774546431803701}},"form_storage_change":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":60670279476681373028597121582973601283},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":242681117906725491586037152752173853241}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":24973401014425388871456301286576801727},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-24709395798276296293992614291856644555}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":231911856652017073017746098545442362433},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":115955928326008535633397932091957886115}},"phase_storage_upper_bound":{"denominator":21267647932558653966460912964485513216,"numerator":14949912175173174635562086827305992635},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":271140987321318403877494369986804296823},"time":{"denominator":32,"numerator":135}},{"channels":{"boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-44317720261361335626095458570471725195},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-95059986800662977459100987624188117973}},"boundary_phase_input":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":17507353974220557907084933408100798633},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":137303356461600180925655647079540598129}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":291653601450429281762020034155895261421},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":579678395325203330317504553331864707293}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-619439335705010829087108778565821362533},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-312113628676487655605053584170014970605}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-104233569906341731440127047572516438203},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-222129936186851630544013548936285450727}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":214249011189278294070248598462092500623},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":50123875648815636271572092676487920583}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10889930075008936284610292037087724893},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-10851938588612857735003416208984098913}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":17189772049363983819463752657299834807},"lo":{"denominator":332306998946228968225951765070086144,"numerator":14867647351014387066239311275558309}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-1024405865666489826821157035607927383},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-18344439609851667977568368532154513323}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-5963652094734667381788066740939337287},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6976884166817508429181238244176732469}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":16405596193812706207527135816663317},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-404971863261715012190508989758792675}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3704624964411240480481304652020945251},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":3184650633085222999912623926585393681}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":61790905542759554549857376324285664759},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":51315539626703627979465928703156934559}},"internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":75401459369019578483330131026542241931},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":145960962268413595724348071911386057839}},"internal_form_gradient":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":348539289822340328054195552033703745105},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":346777603305034811362687140829822158773}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-696663947109638779301308932563396117013},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-10941088189405425302532203186070349147}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":313935764097741753024765434948690546289},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":311988904013109847825754615761656233461}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":411312860494982642111060914158719913},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-270232643931914519860284526178021597}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-308802920930860552763208442663750023735},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-310732789775786481860097549163552778069}}],"internal_sine_current":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":46309615571772328940831968607190875533},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":91404298467789808794969885472025779889}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-184362888199570436025176041950006561685},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-186693886366428692018245626774184249673}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-37470731218767625426084445768352766841},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-43837056086841659960014777241145973277}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3298540830735530981611133137104998817},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2544513261067148330393772339964258261}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":46553690289998809276583668450161567731},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":40019500132602482838606240464947930727}}],"phase_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2989250431584595132598450753310239751},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5996224417943078904864085619738886993}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12456546436229624622272126880284102953},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":11697676504223034680576710077722714385}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-960721436332254338451049007943562383},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8572117958982789298454547593190132693}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":3122776791842922973937480205126543407},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":49654576263509294173897426309346090133}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":65462474905043647612421775279336255},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-5376107633319533854884055746755641}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-12286877826840541580332606627368291607},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-49454659473551174351462229856617090889}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":3006618617138141326873750850502444593},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12006206536930375397555311687024559883}},"total_storage_rate":{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":1695932629046555274189051964292570579},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":39417184734111416606933238436838378791}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-7521061413269785775807713466923406231},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-1487294361574026421566586283289819471}}},"cumulative_boundary_form_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":14304847645028304680701188328192661607},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":37155374481143203755913741515501832081}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":686668515296360645421311453369235760001},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":164466693715618149100897301259442197917}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":451561111206588989259221499105788100607},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":430323925212066455944944940736271765189}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":5133511073197495039216868988879654909},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-5191789450175642302107652588727125997}},"form_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":244006671992999819928863079103646108453},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":488013343985999638773595642063650243047}},"phase_integral_residual":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":3143875254635515938512050838337892257},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-6221981097831614155857103042606476685}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":231456665692967734652464112638683829117},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":28932083211620966606617262557817261009}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":238721015556312968831151512786585955193},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":271140987321318403877494369986804296823},"time":{"denominator":64,"numerator":273}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-92247711928216172131260800061042299031},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-98704001505571612779148009064342391209}},"boundary_phase_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":34816392845904130146312372246679026029},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":136495167224651640354998585591544579389}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":584687168924335766424654766682326350123},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":580959467049820804493748462506459563881}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-621538732090626167344141426839740806737},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-39148302734726769109315128869514928947}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-107961074504200226558664972407084732643},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-229622794150363143346030157970230907783}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":111136640412067900534789454690514783699},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":208468319827925392580166416690410355875}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10895244002063734251140153944154872451},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-10858727805432543987702536723309894633}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":16051971412486292763167087446668027049},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":3520496688484167269522211397345894791}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-15209298366805112841090466602364332943},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-17168963286089368507194357025592902147}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-6737336517820992736680943607961473481},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-3875482677822504186474323887210089963}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":264470971875293338346724046872625589},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-200803536012619274637137648047011491}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":8206113599483040737510123386354344213},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":1791320874435208834331131231404462553}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":55782007094091733700482864123937267151},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":22651455273081422552854032910468943617}},"internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":74204675139905780612335701302645040449},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":143590764597599612228490719244124785909}},"internal_form_gradient":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":174728120096922169667453164492255449113},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":695544628053950165341066380050268335381}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-698728861522641093877736390363236729001},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-702135496094293237986491177909473740533}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":157043924916830998024966634937568299169},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":312119117450499820909698693851409319449}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":443144451961699705765617994610025225},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-600750998879696533962838517562723989}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-77210686737798417382791996340366134539},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-155399682305377331373459113794354171583}}],"internal_sine_current":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":91802103850925348787622126355425070805},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":181171196276355900134927912808862164775}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-365617540870366349838303949953703332257},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-370281986615919099563647154528329168437}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-42331933818297339748362976430635722715},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-48700751639046714677793159394079110319}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":830860062331174374951603367704416083},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1261685827104196392571707268358010933}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":51560532397318431388185894051194130799},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":45020803994781572304914016282026947693}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5965569412215060073093696519317760289},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5983506049102379859347819100700957865}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12515203416870622014438441515120301327},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":11762341732723928467147984048568497561}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-7677211926710058748328254577841025107},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8551582258929700739375078617000576577}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":24994316933066121441992233067122735793},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":24837650187863447708197326186440194687}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":17632157508363365765345519716156961},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-95612491039097380475695154936171989}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-49153849815361860187058221911213622743},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-49465255187621887504131023389185276935}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12042227732066845328053167102307337751},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12023648172322974850869672462845557509}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":49833393451146872903903743629509525931},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":4374276410384671700389877057853530947}},"weighted_phase_storage_rate":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-1487153410736215199144780123606935305},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-5154349631542735751294524679054819829}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":52895279083478085654151903309909288661},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":32528624410569534406891178590610782493}},"cumulative_boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":346598294477483834911872511582744038691},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":332132492913064071022614881868686221913}},"cumulative_internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":229258899750477578095813985551455536575},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":13657960696955591805254857600026253579}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":10399690692775889658071624060905675265},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-21030330485732991466554480297973742143}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":490382748098700251491189869913262247551},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":122595687024675062594806348528711654917}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":25328438307281389778058730185256152611},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-12533111009967179136643096969273841949}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":231075624632454375631660522819717523287},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":57768906158113593445575846506525069739}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":238308523122800240930926277002862613865},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":271140987321318403877494369986804296823},"time":{"denominator":16,"numerator":69}},{"channels":{"boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-47890888573989131629491716649689484671},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-102264822410786721694754970321442507845}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":138499762207566551458338064887805307351},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":33929653587175806005894239535449660633}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":146562561130542468123587270752313770447},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":291212899240684765403210921988583558303}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-155949486099295662171164310818354117049},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-628677081859040238779229089949211589687}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-6975430138196532913337443215220082939},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-236947939018064948770898102502596194941}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":115067224694473287314124628344156522527},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":216281779146849895818120671216297714861}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10889852616484507716605091637235283009},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-5427409406080013432704533399327823001}},"form_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":7465031483437825884317640537315317509},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":3239249166280296320541224162968729811}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-7022712546886654728676574676567318669},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-16009293893741742746897416855782887357}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-7511354683219486102880311978816249163},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-133188671855941758679176912765898895}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":532443953728392930314328107345635199},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-198771445396506582509894383188425769}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":4501179581959065999607634407398779599},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":7961998212217640218084281101117269523}}],"form_storage_rate":{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":778110209918256745726180494484610221},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":9831343841935572623329218590578711815}},"internal_conversion":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":36490492831970145154427343615087365651},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":35293505807267661426156357582805569745}},"internal_form_gradient":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":175137168267782763118743120475169821665},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":697334720781835849868891369428984128491}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-350296879655836918499526406613248023883},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-175960716733649330473914838549339360515}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":314112305838132299557006644256412537921},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":156061098596025906659790108063390127925}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":236768385255764325013998630289525273},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-661071160005545822014776449756960759}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-308755366507162517349449178732335292875},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-38842296217527915225537823295936189501}}],"internal_sine_current":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":45490786603174724209080708024957109653},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":44883094453157680869226937397934558451}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-362509462262378459999320579614402832037},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-367165819404066880770598054076831977755}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-47195233382619252262203907535935604039},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-53558342789633060040045489969320017125}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1672722013481423031141956873734457593},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1248917825202179611947057198430293317}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":56563490828683913494620040027617875967},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":50026710182796012112697028435130881605}}],"phase_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1486164537978115354460305923898152001},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-745346280423797618656624443667013063}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12533226255456389724775549753417883297},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":5893214499166712357559056461318112999}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-953824558944341062204435241494854691},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8493030060824935143620453763365902123}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":49992526160131969176587792993803468621},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":49675790531818340513809780413068511493}},{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":588794670020955028618301822454737},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-105212742850375881202485007552807385}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-24569971392882368808054281357649835655},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-49455547552473574412587807570192307283}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12046562669587034221362371203700707389},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-6014820478370236450789059109432283441}},"total_storage_rate":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":11375088651875884137546089756014210519},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":30688344102847815297776513369561771127}},"weighted_phase_storage_rate":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-1074674706816223794072798155739553017},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8637031264894475195540360992753076133}}},"cumulative_boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":24202754139833302281943527437000449737},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":27734960860063906827449539356793164937}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":699688765308447351923354619957103951165},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":335313397936861802835667466825134627597}},"cumulative_internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":232679883453474779204041549015369977105},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":443672274641441624285559760247616158855}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":21064600939771623308779800846489065763},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-2661679843167376211297326265613630465}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":492471836441277154421789100450898389555},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":123117959110319288320397885694957952491}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":25505445676895357583508081121962795627},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-6311004005834081172877432731662275017}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":230772474643669404846759916741492096611},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":115386237321834701473142564391419346121}},"phase_storage_upper_bound":{"denominator":42535295865117307932921825928971026432,"numerator":29745157367578464250206941215590510905},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":271140987321318403877494369986804296823},"time":{"denominator":64,"numerator":279}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-99230830110113144498229047718774101625},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-3304374484385737995307989096486376569}},"boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":68881089899399328497353403538517478045},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":134971996666921452294939349049813398121}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":73499504697738263481672375593995210621},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":584074442731269629266250509363612415453}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-626212008197855742787543602129631908911},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-631137107500629575209806055472828491429}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-28791836854283039565485865712550572777},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-244107808649479668732816454834700084605}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":29728900052690693570215281227953147035},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":223926491308424693796263925502018437779}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5441485201513003792583525735004431449},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-10849372059856757269990740550475326967}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":13825446703159049663625454573913104237},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":11849304028016053443628993455248816241}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-6449537220448036758819923067643704707},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-14867036544636917178397882127899629093}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-258897503251466196486361257588898059},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-1162047882608909812083761800819854807}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":536252384195434981242616679277310113},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-49197480159708535652865940964641377}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":2449544562947785458901029944267481343},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":8758442258939671415702815180069746239}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":43856829335945503639712480548703164015},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":33388836946663293705303821856843033551}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":143469039116633195473523610126092462143},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":138713842433263111904401080166258351325}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":701991249147419274277888369833905381211},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":698927001499452807854679924401940709583}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-351130058136396080957110291093692724851},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-22042373002294125295240134609389700913}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":314010964055524910376823978763664625529},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":155998626705046382998932641983859365847}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":251908782135285910667269950377119907},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-361338478327841124327721646089931161}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-38567499380913531422468240431454959239},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-310551561326592225338285840436308272679}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":360636460219989408417757030504613801673},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":355784868103181205915133140269667729523}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-359402112926406471123418288165528814109},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-364045009676271663366948380923334713057}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-3253401976990183244927927738580929141},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-1825340545561862760957261631859763637}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3369373101316779767037873219668565629},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2472935075917919094016453465236881675}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":15390942407195167281686487843748695827},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":13757728928787632656797085805490707837}}],"phase_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2960869047549945204683168862522036853},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5940015572813113329032459972424450323}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12511361743160223699802664626922904793},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":11770140832950826609942687452645297159}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-7546385609105272830456532049608486951},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-4198715779034408846593352294799702553}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":49976397114488258923096880884330797691},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":49655905111310962158192576867851694047}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":80185055770180179036810254868395277},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-115017609910359220495177881836380003}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-49105665353328013494775258953145350167},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-24712908035016515004808164401102711417}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":6024755907377907212705429617609412893},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-1504273868662473378737583820383208309}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":41281524981333650870494557197468173699},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":26497158739385725466577088795195187993}},"weighted_phase_storage_rate":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-643826088652963192304480837808747579},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-3445839103638784119363366530823922779}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":43754063118255050915532568262183363461},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":22778399133485299834487555712063600083}},"cumulative_boundary_phase_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":176536591871629009742495375384709991183},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":338476804108742774373830107818489629115}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":472084878115541739445904517255400538373},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":450174486005500832656078560880409519073}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":21329680607730690606769645978999465035},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-2694546935884996054115505842438940747}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":494282565746716823097335762571472584191},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":247141282873358410964256519389036187929}},"phase_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":12840957979667385491670070339149446043},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-25421235419736627981717691681262358213}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":230550646061278580285095839059877611943},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":115275323030639289166092624488584043723}},"phase_storage_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":118845273482974522535258150388366451675},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":271140987321318403877494369986804296823},"time":{"denominator":32,"numerator":141}},{"channels":{"boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-51294969870947952064481002928849440529},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-109122477463926079935930673575194350073}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":137052412956366283857614198422133988383},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":16782015056985775968711711139986022923}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":294960586989607076036880892012852085633},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":585903371501499372174526027274157510929}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-314388412377395701049305782000603608535},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-633747734137118655360494629506143752799}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-29660187050581886922338636714925323233},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-251094085594562243648866364018027896875}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":61338255000672097401274959647956241025},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":231396288615025218748487911707912937909}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":2717517484429816047482606540479564303},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-10837884425551014706006107837139455233}},"form_rates":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":3184734571073084529567099397070281517},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":10760503922418651008210386677635778675}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-5886024348005335490414381561698266929},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13743279610401952937490299637246191727}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-9057011237467270486232086633959801171},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-10066904710969015544611561489903913837}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":539985660660265536025388922809557037},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-389319578277833560944069809528747889}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10592535362926022471008721443799081723},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":9554164774276239966674039183321763651}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":37966096761457054839093527147941364519},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":6877146135563595409875122623158662615}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":140936408709701300474468604187472986751},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":34054626071915967646273443640304364345}},"internal_form_gradient":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":351621021903764211812163594133603314607},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":700324382615259890573977169825499134679}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-351865445992678112781224255552186512335},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-706676546208251960642459371707363749071}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":313784283933891431665090612312364361337},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":311746119610394206774372766431123103967}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":266627128724821819583675142410725069},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-392446149997877895687215408961756785}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-308198378872504074612823107970375948189},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-310239374858415579667829665520978443835}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":357343161190054818584146206989477714199},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":352509445809346009009240563142830305981}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-22268872819122104804080993256375738811},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-180461823697916366044925771773926145379}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-56906879934214758552097671445013207173},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-63252227768737480152743463931807454297}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3392829969148242457061353365537182197},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2446167054032636725376223007880606415}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":33277431279058486512664115132211614493},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":1875955866628288790924638758509279633}}],"phase_balance_residual":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":368373117872188796991035092165449705},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2956193927258658628803267065005493843}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12450019808896405953383155529125409675},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":5857072129210835727988745324657597651}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-3712721834909126308193684322245038521},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8265417156533342271375024513086439163}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":49940319852629618705949603577142597307},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":49615935925711486522949286278505864305}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":21217512749477234450128497548998023},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-124919489339091354668638850973448863}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-49051295450467783772186022456317357131},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-24688065025228158086844042349984785643}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12046135401636855052412158010309923121},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-3008091964507725518559453085223728387}},"total_storage_rate":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":2323736149599811429135948347187734777},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":22430105356439477654414380223540193777}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-786318367860071972918353592937608087},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5078479185814903985086110269094456683}}},"cumulative_boundary_form_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":9736289923213420102371868559400932103},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":17663283002363764837490805388226364923}},"cumulative_boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":356285349671922854262903583544938747719},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":341623431931927607367963553657237008413}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":478691272273808987905645233076688334627},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":456559728393985076589754831562966587387}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":21594449180795802891230228763665879127},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-10909485694759012597244001307852255329}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":495817460577144644318475865714858831437},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":495817460577144643120644704698587552381}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":25857666919172977673144984645644768343},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-12798856220320714719660837011144404587}},"phase_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":115206629254609602251713429441715225271},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":230413258509219202496730661504622098877}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":237495941292459478969220887455483918767},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":271140987321318403877494369986804296823},"time":{"denominator":64,"numerator":285}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-105853570009935537721182359290265185435},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-112406868392173854472133253439716742407}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":136370452402537072114121263989962425011},"lo":{"denominator":1329227995784915872903807060280344576,"numerator":521761599785656145496033128897745983}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":592023065540042145440597242478206871593},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":587910059011846669822962220932410131499}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-157871935336042965096860325723730221957},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-636504277367080111292787078825871560979}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-244049007104447266947911973779975790487},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-128950799686219269624622569493200589127}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":252692064439919835480152633458613153231},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":119341691807989425228243471896941148513}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5425625621442384331968940780416749721},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-10827857271576958868860098646584967923}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":11671593203917478701494915643712548825},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":4845819835416000532535881234271905303}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-10665654947457147245578386631147050347},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-3159834691226633959605159142007391199}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-4913813644204797293738792966212717343},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-10835049701931369742425811271744839679}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":543645462499346121301624227254120275},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-384763323073768749556338177799462255}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5692405087222470904488741296860562531},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":5174268598105883631313291312073963137}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":32138928714832090405293513789095237987},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":10844651724329448260127998015376961653}},"internal_conversion":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":17296341341271424138787306745950509583},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":16711818233015147026686110708497310119}},"internal_form_gradient":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":176075976390435313541246753839106792227},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":701529548268790957118643687571627022145}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-176252200655008826135849268005306105757},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-707807594896931396575487962441860503963}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":39179167912209264854469599979111553775},"lo":{"denominator":332306998946228968225951765070086144,"numerator":304072134345668081920446945601733439}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":280903359601862272223580046641374815},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-847686700038469639178427606502482251}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-76932887946954596432678108678575336535},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-309802833412550614061596438366515657037}}],"internal_sine_current":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":44256397687474299116235550417277698535},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":87310787836453547180404277435074844915}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-353213494125884853452654968276615539239},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-357806345046168041748019303655348598681}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-61748803382972325071126182335638722887},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-68078625089735740291274465110283636403}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":853956295572685604944120183574409973},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1208769629139348086984515418170954875}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":71532872013101123204329045876416385317},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":65021776862039209461436910524993413811}}],"phase_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2930733261445296389877152637302555239},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-734999926693963294473590089629290079}},"phase_rates":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":3087442670649211806183024078770527873},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":2904749671147939430527509842394922685}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-3634277939390463571054370863510317427},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-4048893982990410014259292451221221327}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":49884465915643818739383676271653012911},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":24778026617659369860415675054625257633}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":44707158211756601178814997983655015},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-134913528504379187157525433008565973}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-48976997612370877553544764019310491679},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-49306652321482423864186279978581980257}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":188070826558205383545040914622078347},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12031671819078448327839251063993692843}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":33200634052679263321733846093919243449},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":18485210573523086065099653635703546733}},"weighted_phase_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":530852668923586458220166152412002731},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3204092875135810455156342395050376573}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":33983273598637952078807051145872547845},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":6197105523240307704554779566619821311}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":718963064300214633781156601339406984111},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":344754001530641544240939752430623484311}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":485177400276785771957690473106419775721},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":462826660231365756724762123078653078681}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":10929370200671800027789002205360942529},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-11040531098116876537130859118302180335}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":497079611679189972189449686622614606361},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":31067475729949373185139737875980497681}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":26032519234319032500015469391971816137},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-25773282050032530094053753114867533051}},"phase_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":115181561009408174512102250573399504519},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":230363122018816346962340725145886372379}},"phase_storage_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":118690252635704257100807326068097904681},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":271140987321318403877494369986804296823},"time":{"denominator":2,"numerator":9}},{"channels":{"boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-54508103016292225892253528354704306645},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-115587746768552922353971866374024242993}},"boundary_phase_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":33929074578664560208261292737266962491},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":132916537832017506954267586507212088499}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":297149485401943627685329206560391188743},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":147522957430986062513814961561833958381}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-634339903307172609786459303335490786823},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-79925231097075405945743889835589071315}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-62657927864098190162770582251847629979},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-264524825840855710114443149648325240019}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":64960022374936397905256889933020835137},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":245779589306439758916218495733631700207}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10828655010028982140403744159253189021},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-10819092846432097130991075694236700819}},"form_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5312251323253348031487836543560987001},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":2160947369177653612587754216887204243}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-2395309691268142342509773937988941017},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2889142235737586503140433159552067067}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-10595975413303684884295777887016432587},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2900059124461349861737681566131418481}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":547233677296650839539582535576388561},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-379912431180855068665293258900043219}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12174388970146162655232596702243136297},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":2785234225418730871625072913275574927}}],"form_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":13194685610285342666657472272680804953},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":15943328887407117401584053232849875091}},"internal_conversion":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":8486164235401479144817636602280949325},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":65574231489547312773441533380066331939}},"internal_form_gradient":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":352589938958361969264581521073886273127},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":702545370721318799345349976072184174515}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-706096763264662917862394954267966758727},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-354376092911408152853943024259644789039}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":312959339449407449648056711447358231307},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":310869677202256416449646505247192048079}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":589436715370718635791256987263118677},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-911028704699930810522239313060324335}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-307140654430398219511940867440873806197},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-309243069782499948715263382360579651495}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":350765289843325017520141857201205680059},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":345990622398488198771633725915346389413}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-350141137449670771974478450479457191103},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-354697685582070067113972326637583556421}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-66576477032105859088027394776736793133},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-72886435523070596566774911418148074331}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3438370600784171803464894443140736931},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2387060205610424362190136930638140763}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":76493941901111586461656177828184919971},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":70000571048818744548546564854686029377}}],"phase_balance_residual":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":728044343350711663086927613516586195},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2921488186362358925180434958514510297}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12211221173786106108188523865479039193},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":1435662468230113446156606046439480909}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-7076550213243975045057697004148532697},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-7895388392743540479858748071671693873}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":24904512930073798806611601903256073543},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":24738222892060496399146807691987736301}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":93811766891100433221895423917165657},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-72497360825800304483051096711153823}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-48882953377077519660880577405517678555},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-24608781586398398733571926032747422493}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12022844969505634674900046191023353259},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12031904431827774211152826734903196091}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":29351636032970219275195766324211198765},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":14668187850246014837385287504756040583}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2962264812399533941880821778849588859},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-318785259290275641049691432023458627}}},"cumulative_boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":14436569470430277950704141431309509549},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":6976035416704697173767127896957256231}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":725324765783714238820205593727644539579},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":347869232886079454560180398989386267635}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":491542023453336881316303700558130487715},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":117243561108377704324318066708258574325}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":22122393403315363386277486952114884901},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-22342489140666560617356756592555019501}},"form_storage_change":{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":15564771039172839933041152552565826201},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":31129542078345679787522201676762155457}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":26206296798920879096458003665934066473},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-6486945558115129185216251504572995599}},"phase_storage_change":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":57600684779435726725128775271644028507},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":230402739117742904782068320876318259883}},"phase_storage_upper_bound":{"denominator":1329227995784915872903807060280344576,"numerator":927136720562088628387589525276760939},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":271140987321318403877494369986804296823},"time":{"denominator":64,"numerator":291}},{"channels":{"boundary_form_input":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-14009044961022644741193559975525659213},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-7416233447351341202068594321793139159}},"boundary_phase_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":33772490521736052606311196892269967281},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":132292830646568230702043222575585717373}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":149186497167212297246849782921760632585},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":148111463050677885271268585053079522395}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-637328250862655900126484096198801500377},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-642435352684533462955112144088598086463}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-257023728354091320459742668681729416071},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-135478937491202124958755093874851888155}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":66697112496247235635792208388042409245},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":252676318657587739239803006270275279161}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5404394104493269412078604365423914237},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-10804082159507933466290356963847394885}},"form_rates":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":2399698469170759250100027248459549619},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":3809033398152882667045337863460813395}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-4260091654412484313286247566147084045},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2624090868213889405029324946484502597}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-11361471668395639635156483371222889161},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-6180946616774225278151848486355865715}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":550752411135831775336380109205796081},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-374768385535417674513300179499184235}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":6480332786662005691272994761482890189},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":11930748125023510031657726221404091165}}],"form_storage_rate":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":5183936174973978018197060567346845911},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":10290233779129379213104444063521867557}},"internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":66583337813409235304471640415787268073},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":64293345824265416240864271343614890857}},"internal_form_gradient":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":176468301053737201568340001038852731977},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":351687457572780494195662241047231623637}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-353498946396037079846403369012339456431},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-354756816820172338854656770263259964133}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":4880681096495247401059314255709030793},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":310246857501232792958327975750467495287}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":616108065676912147983992635634632779},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-974885853817680978695363276465594191}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-306426935237783986828204849012852621137},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-38570165947386853528721509520104652193}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":347490229333021682787887928808006345503},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":342756463027895822522727995561671930127}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-173544642927858818280888751675831657445},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-10987569180774423315710889403756649665}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-17846557963700156472023922460775679091},"lo":{"denominator":2658455991569831745807614120560689152,"numerator":-606813015109018537983772441234431637}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1730239728771194538595629794132423769},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-294342401698943874328919915615537635}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":20358565875394429934508457193410862419},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":37481550661404059141667436593161899153}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5782774778871346717631463251025275867},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2900729197348994231720789000047502651}},"phase_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":6017507918190667280685801993696457757},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":5656840241783652754270741299603299361}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-3425149132227949920247515404307910143},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-7659106992033159370597338335339422207}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":24857104709196493696952570723489247909},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":49377320950048066734330312147806283991}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":98056644131266666893697244623232785},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-155157902585446811429355483232478605}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-6096170179949175996532731603563840387},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-49109060531210512181677618701545705859}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12011579009570247414573933837528349909},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12025556575918283802517196819597645755}},"total_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":12822337249258509441759823632211920369},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":10992045822844768693179110945276949665}},"weighted_phase_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2454464899310553405365702497518228547},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":175453010928847370018666720438770527}}},"cumulative_boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":11809873540238532061730348935898448447},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1413860331191191272215682155612401861}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":731657107756539748683888943144945158445},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":701939692208716794934519074037003115771}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":497784211373343997126097916847110544097},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":475001745604535700069853292271498193317}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":22385253150315363664700873216913178727},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-11301549683889403764926696732898190279}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":498800859086042255006769847644023773905},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":498800859086042253719705221253111060433}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":26378827030505490403089675586501345613},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-13060527143062881289502616006346274219}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":230534307865878288211510832776393917287},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":115267153932939143017515209430377208345}},"phase_storage_upper_bound":{"denominator":2658455991569831745807614120560689152,"numerator":1854671010515572541626151517732501931},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":271140987321318403877494369986804296823},"time":{"denominator":32,"numerator":147}},{"channels":{"boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-57508288235066643702879370296407852643},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-121617495098820120064980837600191582183}},"boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":67245733833748988986376486846940063353},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":131699865675558442736938816767386503553}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":299680525924430749451531897645022877377},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":297484566389629561101494348108215073395}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-640447516372845171976636402144098694019},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-645599483350986785236629831300482410023}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-131609400369901705843180495681362021457},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-277194480546208738550716242514305131483}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":273528102428172980491562202380023004057},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":129682293626812870165018326858124717649}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5393347860853175944402478037535234699},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-10782993566954932157186072532816986271}},"form_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":4297815194716207020215496500277644447},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":6615620472090563319603611401904449419}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-935488508581493948538907697544445721},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-4730076420186546176778283791004911145}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-12123541956281985110757852316575124769},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13119458671319471678292264768196399127}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":277101999166238212487219629155073283},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-369332789898209801176603680839516753}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":13743042282279504049311648953034223431},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":12717362879354811779585643877626744247}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":15184790360055928085774672818453129133},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":2370907357360178060996982216914015475}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":130541384751808575684938777559460722507},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":63007794868584848130975277171787120959}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":706387332380670683610689166303105129619},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":704021444371376827980823206844359089293}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-353857759312312703160468341590887827265},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-177523867164966215516453634306177622733}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":311647534602724216554570825124310225075},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":154751413678449127544621146255808553625}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":320893401450309876251608363148770127},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1039224631176947006441632274593347061}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-38198968918602583720610613719373877491},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-9617467570315084932179717033550580595}}],"internal_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":172115354296522774053405458503194774083},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":10610788580261956220163512402919305201}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-344062274254028027791914046668011400519},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-348524427249083909020733688273935259057}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-38087230345343114692245543007338405087},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-41215994980892162056998878262580696693}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1741083209751397958940860770761829111},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1160293179474038511453517099732033583}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":21587520335991597713897946175236069077},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":39952773794816616704263395769486840587}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5736880017138521186944335605204799923},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5755598382932779536029521128464628249}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":11821838144642728425679863069249979481},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":5552406271965451776185586466877456711}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-6590716039380078706249535950754815617},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1847469313784610062841946873929215571}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":49600245634426055164324539106125881751},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":24629452437383924343454422681411322785}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":51071771046388792559457220775737221},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-82698868517331460072769276166404845}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-24318218897637091706026597174631544119},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-48981360122932679873333669606526512445}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":2999445181051498413190267116097197183},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12012796935248832270227370445395133931}},"total_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":11040075650472158162359523815791855051},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":7462094262115858296766862655669287489}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":6895360940888388238944374813130580969},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2720279547395502174772898221841256539}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":18228345058439566276315756906508660709},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2143479875783000927915147303448289277}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":737961395303453716401361738786845789385},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":708113123412258596937813081072974358125}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":503903338783585024111329422045210265465},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":240454363186732764791066112253176617953}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":5661792717349736033815772980995297121},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-22862746350726119843592442926372467693}},"form_storage_change":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":124817234372824617965391255455859461459},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":499268937491298470544052736025346458481}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":26549941180861370145981428478111936907},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-26292943120453246082765190859716050607}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":230759725809534942972465087505876029567},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":28844965726191867592058040427597062859}},"phase_storage_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":118767669470839913735932967336624139493},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":271140987321318403877494369986804296823},"time":{"denominator":64,"numerator":297}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-117843443596179620193143240212597643839},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-124455735206584326910723156285468200283}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":133920852458632998349947939941615284371},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":65568836717630401614590536657245544617}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":301070460087969742750268684286993817291},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":597658509046533681867482318446890724389}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-643692222128666714178941306923594506117},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-162222180679233933077575759539810669465}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-269210287268570202011583658219690346113},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-141613995836330357177409520726388283713}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":280049611070927416224519410186524619533},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":132917509602453956016002596220420859523}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10758733546100921293283773557669937943},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-10756010225544752519000298895473583085}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":7616211812346287073248495578760938295},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":2818817309543666730369458482570195721}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-1618466805642359107456786062618687431},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8449403070807586060707359555708112431}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-6440811483639513579388292932622030135},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13872383151190621043249245117840846889}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":278795505250015273173059306478441919},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-363607362536690997558522520044241423}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":1815116350675525898525668262225700999},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":13500181877631893757156574887077624483}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":9744417230263120938068438050603119887},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-43141996928591551898019722315092339}},"internal_conversion":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":31977295467716726970443805887757437375},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":123441418890746526555507820778401382227}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":706725919531016058837376317212545581673},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":176122105887001339406606635095417475229}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-708253181350135280722929878709067576795},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-88812680165533103817401723496036447249}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":310812733883516213042595218475532689827},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":308639126225712652567947817958550894363}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":333220666752449041069236075536494311},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-552005207319483996952643226172264621}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-304636569426074604428678153565385218603},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-306837442006641496471757259484283152769}}],"internal_sine_current":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":42623924062765362897985770371605413475},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":168180723090752745894728133000376200771}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-341064372191147117379135088777916757337},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-345468767048312367867578980373804272259}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-40468812080317345249526249731852088695},"lo":{"denominator":166153499473114484112975882535043072,"numerator":-42559938472229766656166357349170151}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3503447644589210456994026072288508371},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2284612437872858089480941408301673343}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":91237699083087153605934022737445166217},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":84824144417788836910805732091497965647}}],"phase_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2843418345647735897372725226993449669},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1426390535201253245718758994847932941}},"phase_rates":[{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":723275729534924224960923894059925127},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":10859407383185806571949424325959824963}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-787345586287337407839437356305912595},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-7088678319392919793775318331016179783}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":49467382973467432067840536476484365847},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":6140180321298199811219662664008519727}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":106067432508058894596253107282324293},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-87854357357362362197206381492914879}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-12121103967679281554120953641555620813},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-12208673905257440688015736859973221183}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":1497225907159501470220227654878558751},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-1499226173278673021950991512779618447}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":18659745485952488080219738268051358959},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":1020899869055998495299191906695173239}},"weighted_phase_storage_rate":{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":278604007990292723192228131795257471},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":1193467856770364702891270795955542595}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12704433639868646579762167521543146155},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-10120822339374642179770442557777900443}},"cumulative_boundary_phase_input":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":46514933453903258637438471779475562865},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":178565050463634111772295235971147781983}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":509899081683781910418287635649164784973},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":486695042883969273014421653605340800697}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":5727001119628461529063348824052268805},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-23121290300542081395438755284351305189}},"form_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":249741112511554238475452303171885987737},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":499482225023108475602611047886356625939}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":26719474650116014490009328066924635749},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-13231648778806158160367875210694234317}},"phase_storage_change":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":57770148705217637790225659075587744677},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":231080594820870548863858144444879736509}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":237761225351228925486369998110612228595},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":271140987321318403877494369986804296823},"time":{"denominator":16,"numerator":75}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-120547599367323765943181824038569270561},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-127169220465747176025277276969291709671}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":133378167769158567996784269816208770061},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":130606297282854215491584422058297581257}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":302541086891254120292519517537038033921},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":300255321610547796010148063847683070591}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-323528339360787581825417869995109802737},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-652297338742779298326260456916514074131}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-274991156097501040106566013655230115989},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-144525683320033282691755792870046931175}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":286343157297827254502351333709393886765},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":136038928252571838537453310203730040857}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10725100944331252592223829304803598091},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2680832458901894602689027935567689715}},"form_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3330886774983102351507689544552217383},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":4685328254356222279412138347277297517}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-5491547600412144976542420525132767255},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-3732806858276286804481716741964938223}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-13635163112285260116077208384425457435},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-14620129531367944733438311723406980989}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":560916264839386929324981779643455115},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-357593930250137988072165047805968525}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":15293753192775329276771253536455949369},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":14278615450675749220452015700416029609}}],"form_storage_rate":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":276637957446255343622479279457539767},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2997268605134348995969372421319293265}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":125276391992662646361999190938201442891},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":30217581710139002232753279033952186963}},"internal_form_gradient":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":176723209102339232895795463717386653709},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":704779524682112535063906439719581431465}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-708614639142515960283557276344041502609},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-355367763214184035216103570403311608863}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":154930435849443877729536326048996186037},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":307657412638992601718392855504270454391}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":345021299612734258041825238456626351},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-292301856123866156046418055427781139}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-303562966388537253082613167950576324423},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-152899174322329271959037097672675978077}}],"internal_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":168888446315429459187122771840366352203},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":41651193138836644953776460861193691357}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-338099774092707610723437422547780892899},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-342439608124525951762380293266207868665}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-85672256528107828459646368357259956627},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-91860983060553443514657344846190814575}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":440542604224611205634396193442499335},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1123414464242134437740528847653650497}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":96093485352476838718751454105081343251},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":89715186806553296967318632489843260567}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5632823474976570570953869145897142939},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2825763994138681311522859014163341663}},"phase_rates":[{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":705468829286197880420844072708859285},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":10578217472559494497684479238296928093}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-5975451160139508585769824044497933007},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-3378267794310698294328275591695634389}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":49315889401641562729894949346553011819},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":48965198000358628340158765426141884475}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":27455922652678245544061423820585349},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-186085141108197184878269616192466617}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-12078386660093645772753220021393132363},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-6083664847017024967251896652866160561}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":11951859267201185732191623648308045991},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11968792671778303602815754968204747147}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":15388936084308225198498768737313917577},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":861775730056498450786690809434752353}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10962728765168139700539100265993281305},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":6856312940325196442725435652073338883}}},"cumulative_boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3526882459762672525587759759867605799},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-8040939774353270527977657457856724667}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":750491036876631446073864811119243791937},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":720382372039670238440348963668573827053}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":515771412558437971966506347724392977609},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":61545104931827541991632861678025854469}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":11583809502688340611088055243672784877},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-5844649641668210574448708249233840281}},"form_storage_change":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":124861644727822619024820922248959739043},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":499446578911290474719887034247192828083}},"phase_integral_residual":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":3360908412925655435718350946419779397},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-6657992659343400635215305583584106817}},"phase_storage_change":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":57874556696159377489897355878884771155},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":231498226784637507599940695360700528917}},"phase_storage_upper_bound":{"denominator":85070591730234615865843651857942052864,"numerator":59519284784517220506221003425041981289},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":271140987321318403877494369986804296823},"time":{"denominator":64,"numerator":303}},{"channels":{"boundary_form_input":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-15390467969906853941149541077477953747},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-16219097837326440565027490639897521791}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":132863305441084801782842877748814122289},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":130105811978524095381944588587988305913}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":304090603100642688886428832719548067491},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":603522015406721891691381924900335210273}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-650535166067932446637051292525394919757},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-655817746417691274721308345334244075841}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-280553980949853316937146334603800678349},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-147328584441432397937225408709712976479}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":73099638172223560482685206412106444945},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":278082971996481747318751504883506356061}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5343005745336696326828481946066042459},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-5342582163939702702672866263025736165}},"form_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2866793079635836489996057041083712845},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3759954658878439683425375968652865925}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-4538466241140376045089999124336479597},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-406894714861878890949256558918121683}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-7191811721926163477281150267298624227},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-960135882206598508460451847042700959}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":282091415769387155244895495178228193},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-351294422804288054157883867055121003}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":8030471380636269594612223586967895661},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":3763021114787533332915596550724919613}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-758441037860214177403559225949035621},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11159687269917710697805210148193611995}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":122649220817216526236736850997681490311},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":118308330170077917689159402001099053789}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":706892171596683414436558603753182836137},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":352449315504770928301985731824257523227}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-44300241996179066317191643052122549543},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-355400963515290662020398483800820650415}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":308793754553802348288355726444729647605},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":9579983266629284960287920184324768517}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":22267632471097987452779640586980819},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-308694667551407197706046802608994249}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-151186315021606049066277982247673398371},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-76160844562093940404336195025554660423}}],"internal_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":167295878709964667489338073841007826943},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":165046953342677232683653547035491176203}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-335172589294089907211523327297418302211},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-339441249452222181807088817972544367333}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-45187485743208392229183651512516881495},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-3016355833988204953630930695952600387}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3544865277687402555516291767831473597},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2207247955858036166235360381614981109}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":100913879577079954982912361592502890515},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":94575035916158310274992695833762255623}}],"phase_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2787420423687380560322329118106086829},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-699186713179241780425311954529807931}},"phase_rates":[{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":685494638575569105677511263719776085},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":1282754686779393837100260053242467045}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-5622002527988291370724673080626786057},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6394501940895494297715203969920571879}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":49146052433143108933155349633035709785},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":48790454131894189725842151995280526391}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":56704060459661454450744117116067565},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-196521128987663048981584485996513171}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-6015512340884267922542349616997620745},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-24242749764221494858345823631174860199}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5959980845454772613362086565880911027},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-1492220923271841387646347395713437407}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12272990970822116088448836600569953639},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2198205704344760847524230036717006943}},"weighted_phase_storage_rate":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":3257858002170582566463098956629747315},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":2240370391393237462570245027869151263}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1282339430810274823244441615680978943},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-11082020618851978133920311952837510003}},"cumulative_boundary_phase_input":{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":23647468884974446754919861594178732935},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":181620270494040888852844404064658944723}},"cumulative_internal_conversion":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":130380148696061249158463346903727324367},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":248953271215671369162371120196504176949}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":5856471748847035474710283111554736081},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-11817273013014174456082203324983923073}},"form_storage_change":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":62396048523628365494467843616694034777},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":499168388189026922544933422580622430265}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":27053162897874112353905278598099553593},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-13399405899023444562557437158851847217}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":232013650089792671131429507241826035017},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":58003412522448167176894614075751851397}},"phase_storage_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":119242195766192757368328822179466883939},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":271140987321318403877494369986804296823},"time":{"denominator":32,"numerator":153}},{"channels":{"boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-62783325107795982211968867309579829529},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-132201332166762006099055701822686156265}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":132374585885509508109729732794631659631},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":129636477639830649300424451543276585661}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":611434217422784324706514816552723502807},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":606688916798009979313554559258752552991}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-654123435988927321894193825622194507421},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-164856745492942513092075288645019538163}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-71472734903394148527743535001188459451},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-300037565441133207616412542305381934597}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":37275656980969286983370868956214032499},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":283839886099104937647443558925610691861}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":2660423174594990603916854875678435205},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-10641739491161306706861064145969090221}},"form_rates":[{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":75514913193476842068234437362732729},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2862800460101292582792551941256361039}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1808083766263317265007200472617872547},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1396266791244244496165023833847065569}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-15126478562252944857965680127913856175},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-16098007562049439315267572210662109195}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":283697020083752054685156770470031247},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-344710867844569018321744774687349843}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":16821945010315153903099048849586161675},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":15820021196758875245195786835375948079}}],"form_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-2899170917781716089183563988658247843},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-8087326024223049605568089789891603971}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":120033737658307171919662619185345541337},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":115761297632818611505021154342655919759}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":706728235455180457569103329207883817587},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":176212460289303029929357952530927196225}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-708825085323286938443584997289672105493},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-710705078004826581808171388271487754201}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":76903327962657450909488545400308911321},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":305347179377246994295053314073380292691}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":91747843900118518366243224722473287},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-162585736963292966548046549403950619}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-18816709975246136719598904070227889811},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-18960896360232016991796834857746914071}}],"internal_sine_current":[{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":10357514442074855364598818286286616665},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":163509412061788154960716214531707747145}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-83071707977690277511348012969579780889},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-84119476006249170262621426194910876629}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-47521233925857349471166023357962872251},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-25286691147183728094215608499282394661}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3565041896561725935559761771926517333},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2165882260066120225980664836964413647}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":13211924715874391535353631342759767177},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":49700062371372491417034737734695242273}}],"phase_balance_residual":{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":86111901807119921653364940334215591},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2764853870029901822057626055643188621}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10614501378555967190757095320483597575},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":9911705519564508641142085386719127977}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-1310325387959705710113826717948358857},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1500874669181073466126187925625873009}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":48958179141896439491591767054845440047},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":24298756478528251224452113858278413359}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":58408491498909837620385675356192451},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-207010589711574048581827828022715097}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-47916358484591970909102700504308981107},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-24141763049472416548855871591387108781}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5940207194273538493420655420706958533},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11899007205732549936334851414565845885}},"total_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":4657779930807860094105030281002173231},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-79547992747109472664732081860841333}},"weighted_phase_storage_rate":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":3778475424294788091644297134830210537},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":5541790256315546480296663170344681315}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-4603597298045598509127639694592130075},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-28360978683020925303733859928613433581}},"cumulative_boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":381462031516282777175039576119233906483},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":183139447966382654274333753106181717211}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":527147176236978145317587572889222369719},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":62916606657235138842380013375352543767}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":23682688906018059286768759150907499191},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-23889015458054303528899813669368290903}},"form_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":249327281740439122361037503112557207873},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":498654563480878243279560119525261948741}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":27217001250400217225842422819365083353},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-26963592895731757095137257009139683453}},"phase_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":116313808439476344502794931177434791239},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":232627616878952686515901788226507779377}},"phase_storage_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":119492010702573850144716535387037286957},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":271140987321318403877494369986804296823},"time":{"denominator":64,"numerator":309}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-127871178598067201195971833133949344329},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-134509870256732742415450387960611615443}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":131913709456705551212106224778551303797},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":64599097485027149204702814887887290227}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":614837206953266541388445047831569922193},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":610007442864813883408734599589082999265}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-328906747850338495997820490275224190633},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-663133656745408018903895776057428377667}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-18187113440194102566321020226028475435},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-305184328010240809247207676952581832155}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":303752393151902477587375610930731870039},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":144668893725749883575265555621054941111}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5296192791992664068096128945368896897},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-10593294537888964267232991127987314879}},"form_rates":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":990304064414857735558627635367742971},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1995184422528420314992967754463780675}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2726219923248835653900025691513473557},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4691452832942993895976704099308280215}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-15863217503421034598164519795897507791},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-2103391972069076513114643560292919957}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":142638371236109507012065727704173121},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-21115336647434330378568150588749233}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":17576218525420530485272619337491027079},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":4145467570495703794467299615397917849}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-10682550563558261656061660785880994397},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-21028614172778260028704915009260925383}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":117435858963177905434499909252675733825},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":28308733527297288155799117320998206813}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":706405563756677560989651657387891711299},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":176159368262524400223452672096183461613}},{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":-5536583703642489446706228152257552325},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-355224824589704785049975086152119802317}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":306321595720658140677888531799799929501},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":76005643525368856294495653013995791609}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":188569413501268913043455051326357065},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1366889523522584998866139770516664641}},{"hi":{"denominator":332306998946228968225951765070086144,"numerator":-292626041099126237879897705844316629},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-301993165428237731525278543485410886977}}],"internal_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":164163699363067803214279113240437008739},"lo":{"denominator":1329227995784915872903807060280344576,"numerator":1265580071028738464565316424973356141}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-329446410600748493762548855064339903447},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-333553688715409966603112463966089380601}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-49835767571044543083032443364507487571},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-52864006136575666760470151443124945167}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3584893273563002419463515678607281721},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2122745167668960844793716462124940301}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":110434637994699934303859733606349234173},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":104186963721312250816857744548809384357}}],"phase_balance_residual":{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":85058819183799349530134515306986077},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5462171274981458749012323169400012089}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10228158296473473637338995747134809115},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":2382026040046367560218245986072079819}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-4832905083857518393630808596354799775},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2792434670494650725981668961480346189}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":48752596134739916194085478216996060763},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":12096673869942963509619504148275201105}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":60023508549333067705087270431852133},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-217547224329144946430273029303899525}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-47690630060378175530089416496990320859},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-12015926264468127522072743998235212151}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":11835225157759733694817426901701996149},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11854540958881670204941874328704420395}},"total_storage_rate":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":815443733885161211096583589608120145},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-7812010100243320188807482684102460927}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":17206100434639551344834329502745955557},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":1652075509066867479987179040644808057}}},"cumulative_boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-5298779397414999282594409686373002795},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-34666128851305272604458096864267103055}},"cumulative_boundary_phase_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":192276879540837156765786657881240601333},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":369306978627375956167637950660233151151}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":532651982125877109634829756135441544743},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":508640740794249352268252441500507513913}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":23937913484927652464231716551296207281},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-754434309474230638003401496353883251}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":497912525427871732128026061187536618139},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":497912525427871730653532088879371275121}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":27378635875413321626170940767522258989},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-13563083182405576512737395230310883927}},"phase_storage_change":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":58335152751072031081654271488136754137},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":233340611004288121769419399563833123565}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":239576802961727064344113692721850794435},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":271140987321318403877494369986804296823},"time":{"denominator":8,"numerator":39}},{"channels":{"boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-65016144616940538234179165580910146631},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-68336751592072156939810235938798085819}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":131480784745391553226002318378856314435},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":32197762158414478859757287686591078815}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":618385966918891917315944897264778331017},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":613473486561164455840259309008839484213}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-330799404488064238985024495652792037681},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-166732790122269927640770572529811336093}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-295853999241128998497906354316871158435},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-155044418383732612900049757574086725039}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":309028783557439893373395178881905113575},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":73641389398390688952211638503746962523}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10538344166350093060266321798387294991},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-5270040802483478794989724701735555403}},"form_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1559870496803616814335710636655528861},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1158455932962776092014551014194950399}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1870212198989735647202871872042592647},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3831077677985817939235987235361837107}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-8296672302869288024290042394372134447},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-2193635097095501263929769434939410331}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":573665028759827809467556489265848153},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-165350094381486748334822530049941709}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":4580808966724746902415728455643251417},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":17337089535803464057867211036613006371}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-15400393729675803689805885283879024247},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-3213879790530150039299669007281558067}},"internal_conversion":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":28715333128651708435985107126759734883},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":6920922830507401070596766549708115775}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":705928920947102808368795977326282557789},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":352133033758340996193020375542836889539}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-708381425266784166855981741946424891471},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-710040548008208047439887831355303770043}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":304920780595123821071433470874457832625},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":302587784773259930009096652728425926113}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":773431645914829887081347706411162451},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-716674298971478269312372946375029449}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-37264971570095431364032611130178758693},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-75125472761096189993923247871335617025}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":325256865400987220335725181437721377407},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":321007026712975327908525547304992193845}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-326655118272440391496752899148990261959},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-330672614059039023368648286667462700413}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-104259059023744269209692309383917858955},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-110264126491071352928563974615628285289}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3604443679946505005746767212765918359},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2077850567117030861723596992433963335}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":115128286378885731977416513253765905625},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":108932146240617282637967057599187674715}}],"phase_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2686439707116828445132212558315600215},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5391115139799640472886671368297543099}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":9809826265486987789831310566220922941},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":9112161682245017336030840516054338335}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-4398009687893030941065793784922293141},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5139828145948712616012223467786952251}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":758275773174269302129144268806554489},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":24079170832945429083041611131881202533}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":30773867397761423582188009785198573},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-114062257268229607919062748584289311}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-23723617718238543832619398818067121269},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-47826361368175989120708361718973889659}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":11784656354095333336138583203309408289},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11804629518278181448473957060059566773}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3902201803608934895547262072077551911},"lo":{"denominator":1329227995784915872903807060280344576,"numerator":-40453648463936346448554569699310725}},"weighted_phase_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":9651297766642369292676573677978288079},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":1919363039684186952945922776903614867}}},"cumulative_boundary_form_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-4173205588167043506160779036489082959},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-41072699313062037317565306483529423601}},"cumulative_boundary_phase_input":{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":24227208748384026753769234068717852971},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":744651037659454627121480392761702129579}},"cumulative_internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":269018053543749652483288481860854497517},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":64228929114641237883900002051598575093}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":12095729064472250717410679634066091993},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-24393093001818765260210064331984124363}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":496950191733012367188456069197391361129},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":496950191733012365681723783243768538835}},"phase_integral_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":6884481515575470812785370678022928941},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-3410798799612718783723575397431586053}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":234152856634257205406044911752084850309},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":14634553539641075173726679412920625369}},"phase_storage_upper_bound":{"denominator":85070591730234615865843651857942052864,"numerator":60065813524990123080164569074633217405},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":271140987321318403877494369986804296823},"time":{"denominator":64,"numerator":315}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-132045057985045805497167896647830120527},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-138687456636005076472201095341207698567}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":131075929883459275826236922413422912543},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":128415128988312636695834199457340296089}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":622076075264879175544358657965345321273},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":308541365802646150770802327724608278457}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-665472630039194677356414187711854470589},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-670812679152760390315910875473492752061}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-300462500103574622778508874623759991577},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-157371043579468944225834161308883626745}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":314022967572801394597867582517823589187},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":74877949951738808969575222197898668655}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10479834898059070914490060083040552281},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-10482365187543377439032727292777798249}},"form_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1154963880671086708229236737875986157},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":353993166369381375877323876080881067}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1049749316097558016175967411176165139},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1502782045646947197826747540985401431}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-8658190176376970153984078218872609075},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-4565845383600878809198248668110910243}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":576732805827558872914953655454517289},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-161638785840278651863727346493707985}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":9531242220562742783182435859625610937},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":18085150842991087295330812562497004321}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-19941498581754477801018997334507501005},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-7552925193733114648745439542539283753}},"internal_conversion":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":28078930599414181085304716442612695941},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":108266123156191527756692037923659645281}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":705303302996564522769483688793951166505},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":351870195772362035282945898716068966405}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-88490765130478571818318417743038292293},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-709482921718447598792344501576750484435}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":303413162497025491657861079770111803063},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":150522533019229384340020701628467152731}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":791430763161440864077898138603717683},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-750010363782452698019969093484570083}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-296481614268028941941337874645551478841},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-298902676082064273861086211038161483737}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":322233056359641690376032716716480771481},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":318078394151599002423461947198606398113}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-80979155447872597107147994291130749233},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-163919287007130889853081674208387177813}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-6800126662872301404376869385852884997},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-57376105258189569145737117618108402085}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1811859545872087649351261931639888339},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1015606444261986614259476401190276645}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":59886561079409560938024577702550897229},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":14204044256851014018816510076259016155}}],"phase_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2649373680921085477765934748149207779},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2658390280814073148805621772146508567}},"phase_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":4680246673104140032243406449000450645},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":2166213268359542680144292965830413861}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-3937858488078214182972741897007623031},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2334818489223071174956808571229724335}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":1509053269079565132459903248426207607},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":2994550647090423660143258095307162363}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":125960118072134416238733156724758457},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-238735713532255955526991085629876191}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-47186514446621410469485137541508928023},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-47571838401856164609476764241954037983}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":2932245754609011321373775433136957339},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2937386626926581788029285747569919225}},"total_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":728327685371802754564102924340213439},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-3179668652323214205762029306171721221}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":21398153952498083310147203183187927883},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":1093314135352475110745852559091890633}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-22882434445717196157322861301323368735},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-5946709230359346909649966603456066809}},"cumulative_boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":390707432080788004837485172968550247049},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":375335248415390890983298810430632477979}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":543300906574889463920071598054698875523},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":64863300930009547616849369461307518327}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":12221614610434744401609910807423929555},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-12321254655550587420573982902462863477}},"form_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":247887981409035547230407522238829735627},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":247887981409035546460800385474224889917}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":27694737195749991029780184172271985011},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-27444129269857322361256866565931159677}},"phase_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":117532163725821154538153103489419032723},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":235064327451642306378918523680709187805}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":241043645373412323747757457932103447705},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":271140987321318403877494369986804296823},"time":{"denominator":32,"numerator":159}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-133898541772024775872326878910837574021},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-70273903477793026472155462589249073965}},"boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":65350709502149222085902737462002980319},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":32017573370311684614855736147933301647}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":625924475263669673403604042141871115327},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":620828247418024452143922797649029537385}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-334714003371288472794530233001964403723},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-337385599386881216804035159690609985139}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-76202487853966668735801265792342056165},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-319134699835121046911344225525218937669}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":318723240494213468327643706760637438079},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":152082436102722298652436662229922347729}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10425519948638716631661309874843665339},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-10428727210282516893829209272220898457}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1533203220906904435362949304059081921},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-208399541075400896562704366919039673}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-266447788719087487981266204488346151},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1108273512185724193677697543243119045}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-18031862189036056215776724270552528771},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-18969594786458668913909005821016089111}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":36235076427744936766081967074650577},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-39447489436814756302935641627420241}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":9896733675980805423319800539360908425},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":4706385248668524554926658919974159299}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-24294699467951097943705779556908267025},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-34520959331902238369152914414503784637}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":109806309650405054397003173768554687841},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":52913793769498119184471917873373107783}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":704538736708128089031828048271062427123},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":351511134406821699793457021575515780391}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-707300354559234922694308184183520104573},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-708784557340859796421985199055008232617}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":18862572377193045728473508742809972107},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":149698395144182915626040332615940767493}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":404132267450557912104038762420435001},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-195857753444389613838613857990301501}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-147357626196821795530431761373109475231},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-297200192058833740262741157215106246945}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":319260051341650694535173244302092679863},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":315206461031597264015968259373542671899}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-80308612935257215059882936063689270847},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-162527667874874786619026431595870852993}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-113297531567238483511125610161985947153},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-119189479245427593779051113202382343907}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":910686799261345454196270120022449345},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-991423544138065669339583564556513151}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":124366023243984029967532242606485457451},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":118284362577443271770981671177769500143}}],"phase_balance_residual":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":654085394849151805002432369923663129},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5250550337404439246703781556332156853}},"phase_rates":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":2220489693193526385613146581302035345},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":8180329963304509111678151482118253095}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-862862656310711986962105282430057079},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2087929856921002151375301383816636467}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":48033146132142657839657947105967014203},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":11912619780060246501936993107603947361}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":128639296055384340463053306540337059},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-15585864801774148337994016877842455}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-46905389223023916372532245548299845141},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-47300879654024048017816642316302003679}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":729967562251444690226339425776531131},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11700555436278140112473652806744583035}},"total_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-399016239158099720633274887170221623},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-7448839102002235906497528396788098209}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":23496666989634898502439229782567823779},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":19623281127897766556157857620927588219}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-29158928591280857526338183750268880017},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-54161852293917871508964307445390635157}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":787541493177402499245523727574163273503},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":23646055994928600713496345980906326563}},"cumulative_internal_conversion":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":137112019334938050211232780456274969129},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":261933537802983414804169598995544437735}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":12346741389261916059941368060883090863},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-24890442657898554671255178088435226383}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":494398706090572790219257626667464422039},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":123599676522643197161834439996598942529}},"phase_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":13924520940879776722347212437449077755},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-431244706120517140245057850385939965}},"phase_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":118037378189861287715823187219400364505},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":236074756379722572661500827158374240273}},"phase_storage_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":120959004748394243181093663108722289799},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":271140987321318403877494369986804296823},"time":{"denominator":64,"numerator":321}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-135581940809320867852022308313226744089},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-8890673820413190094324762930922177043}},"boundary_phase_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":32589846498584459967940547452040515017},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":127756414412112099973663773638906907561}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":157480483360621821940281660135140097971},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":624705764433014300004258565892475034855}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-673455027910250786322140032410948294085},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-678824322067758921447878458680219360825}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-308886626191324288505544650091331049853},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-40407116740733677563225199263921461837}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":161558844984889326138927145934837092917},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":308512925142242197992396201139275508399}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":2595932223179826652917850737804071113},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-10388074053640744697409749817185749517}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":791019068436221929909347647696575291},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1152491914064025174272569048902182841}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":478069371912570307069403317272061281},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1465668944900727018962397447654000843}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-9369672653248082569738638182996606105},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-4916823953642283183789162804391504021}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":582754958528935033418892221760664859},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-307609682740533087181914754783520349}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":10257852115020523651256268631350821705},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":19557762510052230268701258439576698565}}],"form_storage_rate":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-3556128905141070775915204212538258217},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-38629848106978299590762517458798147255}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":107340166755983312958669540671614346351},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":25854505248190792172550792560808120625}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":703642474964023409820826428821803305647},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":702100841665260895427812153527537843531}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-706464243907916101497100181349438521971},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-353978057305163848713260252798008011607}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":18755628745903506091487401979343213517},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":297620634864772027821629509857997767559}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":102990766873202713835510312654857363},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-816913531006331890647796875096542449}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-9150856545654453910035270023803038241},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-147698171261149532209352842460362169059}}],"internal_sine_current":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":79085451318517579660490705167293390597},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":156197476767116939056801427882727529115}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-318611992289658199723538367423847810225},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-322326529511926680344370155903236266103}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-58871389547970724729844641477090097761},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-61786632047027675851627450915519808589}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3661557393115053846248090621941301993},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1932768638941491525920234351575953327}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":128903971384635999462353032963400095221},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":122885046044467922692606142443909824523}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5185310404056989237455561704239445853},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5203102363708765610739933403162755621}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":8375445114949446749383242517415611459},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":7658420020420446557772614476334855549}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2932686791689767333267712068561423399},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3660678993572858552752452609454189689}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":47760816411311820746434579708163703253},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":47367795204876552968592437796008410657}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":65565958562780949003374998093634975},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-65007913269156013960551825506954329}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-46604929688503441426675020282801136107},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-47013788083690529907499300437298976879}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5823446766778075790330297113536933227},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11669030654129366039683312791966641287}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2847473180942789954871839028774058673},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-4222896367278098504985857824257831327}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":25601558060185776252449794671532007063},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":21738262637865905570819086161766821947}}},"cumulative_boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-17757166033358886603450864726225691823},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-15207464414806941019926969910895566985}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":793652089395887085489512580221420870069},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":762662373763282977518148560778326211307}},"cumulative_internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":276739823828219459319934378272040899501},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":528714795340002603140692471596240398087}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":24942801147727112070076824989939718199},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-12568788380609597953370330388021802533}},"form_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":246413869414250975565530708471298924173},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":246413869414250974763113183157793405145}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":28000919663303178964706376270073751055},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-27753648285737247350564684612619223823}},"phase_storage_change":{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":7411988930317101182593318140759942605},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":237183645770147234998255424012561248159}},"phase_storage_upper_bound":{"denominator":1329227995784915872903807060280344576,"numerator":948774028621061890279888915658070307},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":271140987321318403877494369986804296823},"time":{"denominator":16,"numerator":81}},{"channels":{"boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-68549723952973293732337465649322524525},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-143791136591612563833811342728767170111}},"boundary_phase_input":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":16255856973180749580224647106702863237},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":31868379698668108089607059989788549975}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":317022097928203056854626630590454528541},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":628712427627501675153647038384251803521}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-338773864093924987392322769148454013231},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-85369022265225372292406321918279897297}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-312681975534615458241139315905969975899},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-163549551086916461668383767614981972289}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":327194308725735557527402575885155720003},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":19533988689179697345338868110653602475}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":1292953235691128482293276913730159591},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-10348916704413803566958400359956187131}},"form_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":42466868432574968147220712284412951},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-925909620416416001888433512614615925}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":295565597811759426279184838309046425},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-754614093702641183612063133639120451}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-19438400266064559141056402977752524767},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-20356107051058498195488403493211839231}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":585725487954943590521534370100991481},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-37426172742292770975475141168492249}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":5307224361208720429487921195994995977},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":5070328469532339820294139072945002779}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-32396288973610071550405132798517861353},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-42528661945622872935981803973069939569}},"internal_conversion":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":26229925666184379523912881921382824153},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":50525610866236732212529997310204016015}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":702614578976100814912753730634744945185},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":701032344369705824672139226478940486497}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-352733751619650854124267343249619721061},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-706998567299187924901158821494267934103}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":74570283948059482031943881934307320511},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":295731676928619571255772788532479222921}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":419206264831613105577946383870358245},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1700868786865368187257182586159106513}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-290839706443996768620180037418120783381},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-146745751413487797611233219076673693509}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":313482457145947909147118713923444176337},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":309646117005502964062726824967453877557}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-158025874098431985473418926005484397253},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-79913972326522442430789458627385796105}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-122135070946812602529364222741988211183},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-127901192734585536208592334751219119907}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1840110889979547711402951015177812385},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-940622314713356282372028086379107395}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":133385096513008794752443062654546280115},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":127431253369359828587601796610677566027}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5141232680760025363715494273601950403},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1289736577403179486532618792563180973}},"phase_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3920630897418310743477347771718916863},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":3553831654821882880126706515702844409}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2388950191847354681935090625565151221},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3124831081849037902228193453728607091}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":23736458596199766210382963934892695833},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":47067158212045224680747507873284990765}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":33359374611520694439715867121242169},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-270701674980338730784737224154974029}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-46288576927957850880523612325105364661},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-11677655857595534979405484713740478751}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":11616377634024999551470176518319962549},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11639382081762467842497342465085646441}},"total_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-2350620081457565961956463125646503831},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-18691974202263058665375096910107789595}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":27695048810694939626492206547224853691},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":11918343871679907135303353531481074987}}},"cumulative_boundary_form_input":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-2621304292956813718394272928567210645},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-67570067186959603009417786333993229039}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":799748035760829866582096822886434443783},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":768637694956783247784949884526411564427}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":558397758718848489800602421904341078531},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":133362892839678074196404289711018006147}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":25191305527578113142807115575123744779},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-12692040166104332512616879638761814557}},"form_storage_change":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":61384101212416350864875811010650317541},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":491072809699330805281060295769742079097}},"phase_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":14075170872641202056529421734707575393},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-6976546604725102655064085379122497969}},"phase_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":119195138991608581048703153045742818341},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":238390277983217159176223322525872427319}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":243948487376327452464922173411935048439},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":271140987321318403877494369986804296823},"time":{"denominator":64,"numerator":327}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-138449999491448815708771348223248051707},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-145173851961783432160130747712115216447}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":129762860630353622339186900882970939449},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":127218734292100300772544231952163150527}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":79786160698984584707167449734722908199},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":158203009139545007902719168503285555471}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-340850091512263716069009497044900369723},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-171783158002966390289850033257765346323}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-316185832543513808057882223276637401301},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-82662647776158897634073401905642569163}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":165470602527534719668074659789105682447},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":316245062974380093541947547721283330141}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5156625290760210648231451563988816099},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2579799792199982577554551531304942011}},"form_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-291790674014097512309707027140342061},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1256634162558328160015310961674678257}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1844635367989373893085052769643529687},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-85076326890673247002847353666233537}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-20128600982168590996580760679892749049},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-21035793063763101662834416908055573665}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":73589310049285190356118205318263213},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-290959522178810163617347104148228911}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":21932511516266202430289188351639122889},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":20995742982116087122482368145233730039}}],"form_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-18063871946649331914927713038274925057},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-46211554103281950563821148919718722703}},"internal_conversion":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":12819705569620849431896050678593637131},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":98732857486964347033812418507587734135}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":701521338455616814739978666003169719483},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":699830295201608351727977828229276865401}},{"hi":{"denominator":1329227995784915872903807060280344576,"numerator":-2751334901014232857827464182092394341},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-705945779541554663861131598820339777133}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":148187768730485261022052729592634353747},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":36718398648698711383934662108223707799}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":212931155116111117986515548741200493},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1767938493773192816412992206528519323}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-288751358768500817916661523861091177077},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-291519273464777537857448366974857331913}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":310685707916301590479815875009948926599},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":306963595184576355953702542655089461149}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-156777963146593736859991871772923160257},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-39630861058130315261253877026067094661}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-63235864972621142241215623477946960657},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-33042946475776644615579768990759761321}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":462375271667151798829373733614776375},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-914076297368946521149369324868279001}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":8612877131784429817750640415483554287},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":65960071909275356944450083570679567531}}],"phase_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1277310386684166127480870313727672235},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5126925207384503094080139407204607721}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":7290283355580271622217429749953262921},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":6529703921503085715766266696346339065}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1825942501713133974155495267234170075},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2572537689264349884792583031341303585}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":23584815899215328844634561002765424205},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":46751317178873360057611745586218436385}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":16944522937498101679930729949023495},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-70344037591610914782060352369205795}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-2872262879531762558670777818717668873},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-1449897918077416970735291112200975577}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":11597705058254637385030397461726958225},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2905334326545496245735589652815753213}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-6357412611428494002556118298225107695},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-10154238083638589176263402975770062555}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":29770331281870169827299307778324742419},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":25903077936004772211294342968178597593}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-48430712413470682730657023805040122743},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-37187545748834100695961957566499314905}},"cumulative_boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":402915334926438846314623104432661853285},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":774601073126725449383662895399169212107}},"cumulative_internal_conversion":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":70400643538432038542195430113601711557},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":538079674053413750552827115961615199625}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":12719748191878846582384398434196851183},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-12815178477241192476237168268086457873}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":489144078939503242325671997697010272181},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":489144078939503240654432080567600653967}},"phase_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":14148900734808137983576958530816629783},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-28057269510578528062707866847781294387}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":239693726288885417013253371551988779217},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":119846863144442707006855613027963606279}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":245104662200469229289165535516443845163},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":271140987321318403877494369986804296823},"time":{"denominator":32,"numerator":165}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-139629782704618905038704817207260092397},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-146395157953200706633273675538709215021}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":129507377587489899292979018608573765633},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":126992644944201195235185294839412755639}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":642648339311451778920113728891979345715},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":637027918528277425278152251577307618181}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-685875902825952185974306084717589144537},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-691361042423857453879134327116860389501}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-319387781924460919450826401734021278733},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-41737561857016982654888283407516708827}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":10448306523663272374868186649551984279},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":319604880317499574305180900881485738509}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":2573057740972176951908075936303655927},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-1287295679916874788709677818571666115}},"form_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-606541131255903046958341713991795523},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3135220743925010725917692855214890735}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":307925082707492813636904365262128247},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":541397792041375341243147622220165007}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-20809578922451317226488770090185830083},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-21705838376452971172623530779888590609}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":73961376933247424279408837200849831},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-282243246811989837453521188152146237}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":2828254807490624406078991706203074975},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":10850307045201893837502178400680082379}}],"form_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-19817577980350246071365186210979871105},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-49670083222267145697837985020692467421}},"internal_conversion":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":12532258115210844706318031841892619237},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":96467771028611506682910999371534849103}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":700340127518129132999986847378383421853},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":349252031866396286310585302597656661351}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-351545043508070785046147278059790556781},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-352416426262479795632040947790837313203}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":294404912041605103033942854882367135151},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":72916722107863341251687793813467905625}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":431933690750425674195306331687860411},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1834985755555913908648614976744240955}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-143284166719603820229444307724784536581},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-289453600369616309286328413245742168943}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":307954750952139394251213273945128759443},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":304351735486644441013074235477608769737}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-311128804492667382321239737768507029929},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-314502326339058816101792557015716191933}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-65375220267070063892625984384014651659},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-68190902383472059145529802359039920141}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3717704294766011193119693952172535055},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1773386621419756208452202055492619885}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":35540898102770242250510737111490607445},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":34087244902399846312086479626238122833}}],"phase_balance_residual":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":318035341851964228731474162087684937},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5106249880095133237993526595485067129}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":6717634012534688549542272498075101903},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":2963238213878360851793273057706082611}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-311122570767880207794508553043617323},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1005697416847148667738764388024430999}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":46855997021956112045948293740977510291},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":46420227030098146359881644255212760835}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":34372190985428158471847060240833069},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-292047053499940043581807096985887657}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-22804383400228189602262169183940865251},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-23033985647285249215907078713325851189}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":11590502540444884499702634975011477907},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-1451790178294360072504711722556536407}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-7812010468554626898385745724284981475},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-5434181635870971581440873094784654505}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":31823145492145865244344626697674760735},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":27933356678783259372074492641553849401}}},"cumulative_boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-27487929238874846952173156055815219787},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-81237364526724484515358618673875624265}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":811901328177291281658604600362600601835},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":780553853358484880410312206094766685027}},"cumulative_internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":283952372550330187551216351424761712335},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":135650400205094978732147142264288973919}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":3210982617095317173159195900004794585},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-6469197348123178776071419895778842225}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":487052097230417967798503517583318628091},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":121763024307604491523450177788694404049}},"phase_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":14221878878536384233605101942397787941},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-28206861342014096034774880117561252083}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":241092866014897273775089707130038836239},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":60273216503724317673810287796970863519}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":246352872102767088125580756467362366725},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":271140987321318403877494369986804296823},"time":{"denominator":64,"numerator":333}},{"channels":{"boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-70318066001367658587988110823454219381},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-73720845183801911871579793420464100425}},"boundary_phase_input":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":16160017434411789762237236764720430249},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":63399236597041210325317229356397505493}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":80889369615192552817057598358073787629},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":641358733139253386419733525980383468077}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-345046928652024788607591343531924426513},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-695626423164548824536773321461953452373}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-322276892938673137726104326748117804803},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-168418906085073011802720550121967668985}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":337395750888557045072199538114981791453},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":40326395643057925812815278212058644607}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5133631550414654287861925324926921393},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-10273548801699469021205496533476565877}},"form_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-901030115882110289974693672042161781},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1858080653002022520000722199057446181}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3036922241011362365473929653974352171},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":280803977214188826616966588098769695}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-10740486405461794728042315794473409837},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-11182928275139577554221922622221938483}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":37165652721832519144570245685485245},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-273261537873669169584582941044772425}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":23309064089762409579169501315669197597},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":5598875306620532365569829456108530543}}],"form_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-21455737119065907233127096453351439773},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-26447024678858403754029819695008751813}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":98015631446717978689122078790367501013},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":47131476514321350350590771642185739259}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":699041768898010373124606845378906680157},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":697064009396564407216904476113448734897}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-87715699470871216437601844040545186993},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-87951035164611420338647465642665115259}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":292345383475779558589970375333468898541},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":289496780953951918401264425275955643783}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":437424995189734648229349460745688187},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1901958373705409010356354539851953695}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-142146996632498331575275700984362941479},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-287292963992122560258302587049011079083}}],"internal_sine_current":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":76323218845590687774848064879841007411},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":37726727124331893139204892217303867851}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-154386716541451401285531391984550197793},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-156012552300742355378367713880425821359}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-134968932749519278598212720558629121999},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-140528821259200299507029341445384777797}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1868149464908456728311220588238690103},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-858476439892568112689330446527485801}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":36613792253225623422265002821463614977},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":8794692765822182768731567806680881071}}],"phase_balance_residual":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":316446750215080077130347534728558859},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1270193466473580045402781787647461661}},"phase_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3060180091184243969695124354957342443},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":2649879534718845384659604075414553967}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-647142312297297749388108546011555005},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1433924923122385447132324541442376287}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":2908013304391625918933858814506410263},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":23037421849006553543834148136101163975}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":69618350216394808930730194906891135},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-302706076730238173205050680949126533}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-5655849289932277473384982047349452285},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-22862047667434100958509074449619875477}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":11577732686195311821868875699514762035},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-5800822124759255607438044089035195013}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-9065484487326091270656252428618427829},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-5739409194239877573238603926803846699}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":33845989750805723195597940478084451717},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":14968206290378648607552611841401058415}}},"cumulative_boundary_form_input":{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":-962002768209029873390159335958269885},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-5509293360169119609582451519190258355}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":817961334715195702819443564149370763179},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":393248765894728746939155348173464475583}},"cumulative_internal_conversion":{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":17890600869522665011046415634150684415},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":547020176743597541523956453898610808731}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":12968150168140413094265618089771919551},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-6530816835543729058917070404262723785}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":484807783317172453959168465771110514153},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":121201945829293113055211705293610433375}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":28588081902416024418180167651845018513},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-7088693026112481628656103516786449183}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":242586385867148237943005563705952068399},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":60646596466787058695215674045903539429}},"phase_storage_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":123845949388019219820797262001176655335},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":271140987321318403877494369986804296823},"time":{"denominator":4,"numerator":21}},{"channels":{"boundary_form_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-35366421243351125030007433459071528011},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-148308538313765049979350501964161325019}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":129081189713503976414062830937244653069},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":126636665191006477655137655666717890487}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":325841479202569357538381208674900027549},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":645798617799483029835234708568571401821}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-347175172975607474125609494624848080423},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-699920136262634001116224189644093662891}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-324841965558286472954114819140755190873},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-169725660657956198870687631891796848743}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":340079029856190544054068322522047671287},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":162625786900464805925510063999013020039}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10236687480381417112539940501770799627},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-10243095979718678535374728930743692125}},"form_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1174494801083221858762701919644144111},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4254590618016084503125343418136323371}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1781829962295796950850882740006005399},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":829385668655845126582638671502574275}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-2767804654202133737295382578180384971},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-23015525401502719783968220810949364525}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":597598595664343796529247113372532973},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-264017145250889624410382789751285641}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":5995300409518904271471035585853918873},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":5769999269400922404522363120846476399}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-45949338596040135258010729837897166737},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-27937907886899057207769861201419023275}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":95832965179325064239864740364191757619},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":92122512237343497608799831624493358655}},"internal_form_gradient":[{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":43601773219105500431823325420521232537},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":695517275642462650174939537416880191799}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-700256054541509831061581168093379254045},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-175567520114990948699962123597505432035}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":290195688818522883141059428707266299935},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":287240477231018607928213482061336218825}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":221171487977555964395986641362395969},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-492200582146281726903564827230563545}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-140965667097610185788091377416263453023},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-35630028453040405958217865606802734077}}],"internal_sine_current":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":75675815031427935250509225389460196725},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":149676374713569114936020301541266213295}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-306492326339222620189517463596934303581},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-309618022259078442883246677331804029545}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-139125036291408982343111348341456164623},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-144610811039740441788607658784120120559}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3754822715869359472560021512068074267},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1658868647883888425737544656969107373}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":75339166890433874271801158146159881575},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":72507949263873648369990425133261337387}}],"phase_balance_residual":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":628879597043908104289255903720232615},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5048513030863789698554014761158366513}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5499307667718669661446161660865224389},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":4650965510252251775873154179895895773}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-17821018186003380686394315475851267},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-420154965014280778548255525724869745}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":23093039169712688536585821110098000243},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":45715741807391624478313031322402933009}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":140802142330470931771817708764371533},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-4896009727580576479328190050477643}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-44870765449662423730285343196426673561},"lo":{"denominator":1329227995784915872903807060280344576,"numerator":-177209223462695544222626719448195305}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":11557271314751115315789078991834261583},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-5790578034300450801431917476101829837}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-10114601808007457008423767305609172949},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-23965651328501425308830737851245118649}},"weighted_phase_storage_rate":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":8958684197008169562396740633071998447},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":31910164445296689106708984551592927901}}},"cumulative_boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-34099690574253123920048295637452592071},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-95100656496163650471101279086614195791}},"cumulative_boundary_phase_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":206003003870754050428463189837388526573},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":396216812735142961259197636978153176141}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":576991398067506142739728959997393389919},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":551338419504723017974368946006008934917}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":13092318709104534615413453209731030807},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-6592404123057864984405306232881501619}},"form_storage_change":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":120605600106692109183523643334714200185},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":482422400426768434962011143790962199301}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":28730571943804096561565360409437626957},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-7125199157927327661429538449378842227}},"phase_storage_change":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":30521599918322984542528959296043823665},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":244172799346583873093765659546029802467}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":249120561874786816375924683050074606611},"running_phase_work_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":136336797989146591869741906671772585687},"time":{"denominator":64,"numerator":339}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-142118153598655167783553825310791255385},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-74109182237270294844846088711068871097}},"boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":64461197138496049427698220088263498295},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":126503017627124214520995232538404825129}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":328163230450341248090177461477127361949},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":650343616739294695528690352167455270895}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-87329973786151876605490721422687322435},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-352105476802799473999986371042332908649}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-327071599450899486099127164861617939623},"lo":{"denominator":1,"numerator":-1}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":163750212742899147346807172560242022423}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":4723620338587010027132700153562983293},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-9453726188505963525856289054105355475}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2849960716789189655162365876435168223},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-574556024635875786974386026578865781}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3820477345859492952994885972900952487},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2139641316668036428134485944911541427}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-22789089656407118151885848851911840669},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-2956881690790116282710480982310020423}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":300270766800886035235430925235178555},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-15907057058211153754119094490451951}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":3080260658554717105986034862190628555},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":11876857226911780407552783550945599245}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-48720876957774365352952200537218212055},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-14460069639480957049593561321942042447}},"internal_conversion":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":5858225076827331444439741817320527567},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":90050246839592204282474576577793563553}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":696103546873431204756730809731100922567},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":173474445238291331189506695432974321219}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-349359620103203045666623679848435249321},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-700821628007502129150769799212287010769}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":143978833563583348946596578096413832821},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":284912676575224261010129355855058657527}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":446696606880013458879623165245500227},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-63608179155005035926687270862840583}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-279491236012530072946346419988388872633},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-141348749391674530377910889138109125183}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":300211352498246227505742850588068019581},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":296961863255214696318713653797225528179}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-304275216232063219250209678654204542483},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-307334781160513807702005008077688550959}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-35797018323283873876467702024692083653},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-74314542378563167255527337522256619397}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3773313740277750200612338717804034763},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1599151795017914516907722281408169241}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":38707697024228631071108842632919771153},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":74624494823601786588271839260903084477}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5005460220961947248146843523365373989},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1255714892933030575604910672515555453}},"phase_rates":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1213819846064600437474148294945919493},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3986440869893527108174160551452460999}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":582688889017025463710102526208764743},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-231500171926491175443561022937092629}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":22914943062249578031282411479152030155},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":22672630413244699275987938608543149387}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":142187946094662569126558357036032409},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-323953796275005108439083700676617875}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-44482411762257712023393395157434770091},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-44992704331085070685415823160339975393}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":673209156780679279615684458197278941},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-1349403921324123374964329905604087471}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-10944000338925506694845993552576454009},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-23990990692256055927872024379096958563}},"weighted_phase_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":18888438309424429329053103492320879023},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":33849287865667772270502220908671211225}}},"cumulative_boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-37430584799221604414975338418174262119},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-102048392330907740612805599903276902457}},"cumulative_boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":415027626357375103173849733741414404629},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":798363454421557370074066925481544078459}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":581385066875126641323058766360383785595},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":34722470301583056409381871361443313013}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":13198199529309211743012345654455447365},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-13308182861821924437873365007156651629}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":479907531553039585423329033188727000481},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":479907531553039583617361359509721958099}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":28872068640400202675484291296136139611},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-14322635851295187851977021907018290801}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":245850456186830931426492450417296432475},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":30731307023353866011704435235712402431}},"phase_storage_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":125340400866786167967785185022379127237},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":274495727889421303797589525699735801049},"time":{"denominator":32,"numerator":171}},{"channels":{"boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-71292404252856040772855546955586157925},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-147881459400929205448239977482697974895}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":128797874853823284805092647841741293341},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":126389451156931484950409467958267483471}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":661050788412712534947884610593394266863},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":654986020288868106769884637038198684813}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-702951173072117487698562046208678554551},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-354257590006859172579121949964589577361}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-164477117859911486384407896668483597113},"lo":{"denominator":1,"numerator":-1}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":164671720596348991298297250369555409653}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":4308249414691207064126541804191211859},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-4311539701817556799650434135728060723}},"form_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1652351814153468394956095986993329119},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4843315428034951939723890467342290361}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4051527747303222957719543354852667117},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2567585200825716944535271919239385561}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-5856010519131802853233564456576104899},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-24287046152225497548151169712937727201}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":603485535523720652419954340961135227},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-244751785653384243250472200907838191}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":6322842674998217734786025765262357093},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":1526017932255962578545077455759871577}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-51230776005381928930956107373335151665},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-29752077496419021546252269508471893369}},"internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":45851866458254576026253711582842325279},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":11004273070770607798628848312622549939}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":694476621687797858225834741718641013413},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":346095163520841819633123640663736643285}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-697092272437658210614633598246425756999},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-349636648840245757974043989188935131741}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":71408994027199780130670046544760522917},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":141251862973169466554345072280281539747}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":112653324120648655262271681122941785},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1050952301424594866339540498842417829}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-138486001078489958720439782490385110933},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-70067100124901476657317576157987981855}}],"internal_sine_current":[{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":18613008612305071928696872809475138375},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":147317597208870166833325066828285134945}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-37762202187588679378673373486976300169},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-152572260389779071882747187966459941141}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-73588798504996092763652219449836747049},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-76300005769227878299353986810337458729}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":473976431237255749307198261868033385},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-768910411761655691461672537816061415}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":158910368780627499850200663042804774155},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":153412055207091801933358773678789292895}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4994615259126878053697636356694625315},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5012065449424044335400308507866187095}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4190082945540924619497137529482728197},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3304007665601181742955660467595391793}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":151501017100985900418300065691590331},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":390234699102209203530596019752876889}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":45460377522593899757428251131806971315},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":44961864426237968709393929016142359415}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":143434667116277415174731198868559441},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-334528507451055658733712939730712923}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-44081463241342450949243560503160135397},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-44606101331971308361364112153498534355}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":9941565738165002518474083300372797987},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-9965596502714868271224540114618057495}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-11550442505832717979356426224057693437},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-5938132538650916252960746546012270001}},"weighted_phase_storage_rate":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":9920083374887302737899920287319364557},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":17875812419117189040330776416447353367}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-81544832497148462652405884363434726543},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-108980335740326297118191848847778370031}},"cumulative_boundary_phase_input":{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":6531973852332212287679204573050081503},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":402143979972269266715558684646043933373}},"cumulative_internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":292841839677794003912760025910637626795},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":559686127226867880474595759900326464435}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":6642315549896464045849162946500772431},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-26863793172312107473279774630331955981}},"form_storage_change":{"hi":{"denominator":1329227995784915872903807060280344576,"numerator":1864355678461435310702345948588090563},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":238637526843063718849917196413754285533}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":29013273148313274186384668163643519699},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-28788972134391495977717740598941750849}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":247617553737263799791981985634456132855},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":61904388434315949092656171212785554275}},"phase_storage_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":126174938160274153324826660828950248253},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":276406525871655292348342425450083967949},"time":{"denominator":64,"numerator":345}},{"channels":{"boundary_form_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-35715701672732430922987016240250687721},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-147524861929824855985802739040017569105}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":128705363353091422405525543486091099597},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":63150376442390272377874433341309818723}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":665861465161763062702177334505095805357},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":329858903374255608985287105935777933695}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-353637892040748434969556796854807820541},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-178206768378100433190755033340176964231}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-330478203269871517302801394910171552465},"lo":{"denominator":1,"numerator":-1}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":330776867945722409441959286343406950405}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3981909085810158997538914818206609971},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-498156772761038803124600096696863185}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-3712355298017031461450811072730961343},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5082291187540975987333739164704930463}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":133638487016347087886593710791125581},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2943186865811917920826169070658018405}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-12023930590551566087746822398008128747},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-24909868236910784166401737871130378179}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":75804634890483819045475710796808727},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-234736816906723055595078745996724753}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":25928735796508608269398571657923763405},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":12533684685805621377342801271613062295}}],"form_storage_rate":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-13369753245928921016148342282147338335},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-15271214846488860005703288089757719291}},"internal_conversion":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":11218556958643863064891064268640210585},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":86082030774488853926131540275014995823}},"internal_form_gradient":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":173188977920491639945493837399866998147},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":690391101288702105781899024705738994679}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-347687646022756533168098544673758716071},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-348816577849896222928702358852068181613}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":283234038793038580088557739251520146389},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":280016059852773440194078551477527583075}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":908060161968049109449789162264236021},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2168054185256351544949005133051095323}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-137186003046004851154133010539002402063},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-277756663755877168909143620933809257935}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":295490078874575156617685982809802244015},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":292382900946389834633673481750005994191}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-299977948772387009552038220038151408905},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-303037985238392339643275915519649797337}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-151097168042201536803843291469088229055},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-156513318109937309621523554742334598701}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3810356545280007786098955291274322299},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1474894919042427050386077402924853443}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":162915051790364279690125353336733165587},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":157502926925351343943483285984333161349}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4991555049636805950364342519628976703},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2504560018203392233873386572606594119}},"phase_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1752725903516050488355519541483464851},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":650668806974647219000209147929460109}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":925845762071619803390650687272675635},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1023114647564308286935666549429561459}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":45078097325793731106858671590335123609},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":44565940070684915106852948668009454347}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":144522263402042117318082802394170813},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-345056540474620137843586997113744895}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-43667661015582964551726500038465889383},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-22103173006730669305313702377352127113}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":2322237081648768338111299570483876947},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-9313203505921354724743400818256310341}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-11935160718449237877608674075462423871},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-5867661710939914002791480573291990407}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":41543852265266446186984695053126929469},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":2350888283887236500727951879116432221}}},"cumulative_boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-44120763280392896725232974954240865245},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-115895563643286837242526352240279193583}},"cumulative_boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":421062858502849666624098597600660476339},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":810208307736012621466543097417835662251}},"cumulative_internal_conversion":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":36868164888442466029678387557625958285},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":140930305604855511375595793962679448091}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":26711452298639215865186413487917409155},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-27112000579519240773417272753473857301}},"form_storage_change":{"hi":{"denominator":332306998946228968225951765070086144,"numerator":463415147533959398559612536228863289},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":474537111074774422250970978260059744769}},"phase_integral_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":7288619674115756786550095191522750821},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-14466173184440549559968021768710361883}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":249472148217396192137889277261911332975},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":62368037054349047156469493953295609137}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":254113798102074490507370913046173488377},"running_phase_work_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":139202247293138643872907009675301580157},"time":{"denominator":16,"numerator":87}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-142951448804151992877413733523795520601},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-36787534329954319285383800342432583895}},"boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":64321400007727705695753912575253982377},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":15780425622930284240369339311129135031}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":335375689284172823186178271872206357711},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":83066508284276289305247509216939925377}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-44475319078751085544568538551255572075},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-717138023459066745606831033685228854257}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-165815884936009226376468170515278066417},"lo":{"denominator":1,"numerator":-1}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":165898533358244654889811505151828158631}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":7481012058706717596316439550014402401},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-467987438649059349847347746151102981}},"form_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-2035921984847663546768844390698590001},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-664018455704497270990088049200004611}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4492725276308280119310206775133080623},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3266429644922422770074163459701665301}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-770641249983541058972541825265798593},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-6380342137004910433941914284078006895}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":609402822278708015723288779986808965},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-112235589155667581242618001830025347}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":26553881119083169433582353896968161471},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":3213329829433543252305909496605163713}}],"form_storage_rate":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-6933038941206588828250860710478575885},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-7821619351883980178150917354711198583}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":87866293007465101049763958624523579633},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":84204813731457848919211876135887326099}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":690948716756248301023364933717874927417},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":86063459820133271456850245253568477139}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-693576157803618175477993063797957481837},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-173977163594938343644450922018546389677}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":280755241159040118677523959405865872403},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":277453377387535331278581670563276859715}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":913851155317885130007841219877986657},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-558460115384985875998623813895698791}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-135847318602343128945101631001642216415},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-275165575169610056314285857804433194765}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":293255544566742231892263222936963991281},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":290216554865995547599616301526574519081}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-74484857188249165783747843953623674489},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-150505846294310354517940387796840920731}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-154946616928099069460010837123503207049},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-160355487880032229565429988504756266795}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1914495429547675484608526434732984973},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-352598502362767538140973246518806253}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":166842955696016805454945195929661214437},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":161519574171349805432835096759845543529}}],"phase_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2496599854467318022665010414162951419},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-312719585732762129128119879937207693}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2802893669431496829420798766334902465},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":58875060726334515960452925870901627}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":624997897921966729005914436357306919},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":52045161387357217407844400349319223}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":22341792214709190589009243766803162737},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":44158076488767345835367163957666990123}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":145443928619080813507664959879456215},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-355526751532762919868795549739324367}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-43241544522684990619928302803332547347},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-2737122591060496047948518544744569155}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":8812732491634101511094377889704051705},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-4414916557050945766527699764388358625}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-12093999844740901707486108990993203627},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-23138481902798473018961307902064273097}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":43370311684911808918520776692835403453},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":39434472912273368406246030935625315567}}},"cumulative_boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-47471187861740209058297359333704822759},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-15349153291269159013566976850560662883}},"cumulative_boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":424077924128211902828587062252625506763},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":816125967344611478056681599659509087887}},"cumulative_internal_conversion":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":148502342674951095771640471620634968839},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":283834161531542066085235616272293755387}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":26830990886950198511378531603796287999},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-1710056709777681769058317745363285145}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":471706087619881058573313949343898495709},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":235853043809940528332517041944658833759}},"phase_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":14647784562776644936930943803786855715},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-14537679711489646123794745267150011595}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":251412165770360384843981600784542923961},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":125706082885180190619556700713181739781}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":255962080559802420026018590707627849911},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":280487525193339673486702891960663502751},"time":{"denominator":64,"numerator":351}},{"channels":{"boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-71424326630901740516704255922020535759},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-73379451404036621155079916636903710933}},"boundary_phase_input":{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":4019063933354080195324997459674089847},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":126217280428568587299210161588292779461}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":675713200523047376120833793046018360683},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":334710809620799239135638850179786473091}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-178982626922552387817277776408495079867},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-180359858432992222642003565310920226311}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-166201598982794086644365762129950492809},"lo":{"denominator":1,"numerator":-1}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":332393199845658028826029394188071411505}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":7171821615712230398451336069310782741},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-7178692478797058707226178371476260955}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-4381704114035226562215783889426899467},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5532676389284328182728958134907772207}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4700235431810895005707381098667526373},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":883999770341697545271610841945522133}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-25261802842024294970925916988194924037},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-13060662616521587046658679808284697257}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":306194790568074328779287701384700879},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-213958170387880834416273906258869439}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":6791632610372615581811582275519648607},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":26333793957833035164549861011365208721}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-57182150304458912527405452871107946331},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-63967652996927274244291947008333871031}},"internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":43029846371836632748171371603591730721},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":41202465443951049692151522166694346397}},"internal_form_gradient":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":172265644628234759289538796336857348175},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":686547651205704545604521492061895922075}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-691702615716503419257752886533120028213},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-694107494219285089905498989393013137429}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":139101542593691893626062597174987773393},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":137409608041211745942510337460162924685}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":459317702322971545596699349078515189},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2299199605924370655548936733192305509}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-268943330791819738845769584513669373071},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-272498526059564186326445548204788897087}}],"internal_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":145553304800508224528691545124401780831},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":72034530105785604511915693174057302785}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-295983691612779791526926676475001187371},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-299067193634291532084547510387158075369}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-39681147112468642617884013378772227337},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-41031281727079064782749124946314004873}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":480969652308063812390226056444909807},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-672169416266079671850285932655532509}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":21336543114627479695932748526457645503},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":41365026819537774346519413104890510329}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4995547904165975011699021555974081997},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2499964054086224079537931159482647139}},"phase_rates":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":520992625850073455048656801669514735},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":574785460610082793690615887161253103}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3155174385990303387388117080403327613},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":289436705588220663002572124733139603}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":11069349047746944226117529489864226415},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":43738836696157398290457155577947744055}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":146205365548625316819252515629014587},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-365928982437801393780868931285398819}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-5350457563389606636023699311050578101},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-43369487407635296228396393703748950569}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":4256303832053519649055329375745048045},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8523858731198340754262341816646786585}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-12029014715397615712839012934024546315},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-22762466125671255537270934951116982999}},"weighted_phase_storage_rate":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":2822070974316331050910402496067712501},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":1287662089726750584594406626788027751}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-101638406345127456290035742660099070745},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-32418137474820426335456139247298756491}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":854184444156454925950161620694762148297},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":205510600591175157646583018995990077981}},"cumulative_internal_conversion":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":37377713674822754212918934535648537507},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":142882763549613635769777609436928776437}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":13468037104181061543277066522241172409},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-6902608486125413058852897312534208329}},"form_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":234397289253767480411920006901501212301},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":468794578507534958881255620660140696051}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":29436429678267833535206966938712732131},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-29217976712195989856195416401410479925}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":253435413245804396714836090352296443943},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":3959928331965693640857121352275571291}},"phase_storage_upper_bound":{"denominator":85070591730234615865843651857942052864,"numerator":64473159991660696515328163256987669687},"running_phase_work_upper_bound":{"denominator":85070591730234615865843651857942052864,"numerator":70663347489500095717762795736761760637},"time":{"denominator":32,"numerator":177}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-142552677530263523780950802693076408761},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-146352819971355244662657812058689228601}},"boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":64303452149712340325621977205669008865},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":126222193502543813931949744788728392459}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":340369669044113664494199062823002513793},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":21074344414876470503666988873042008255}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":-11253801237845652195575616206985946407},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-725722641407656485465828354218488570173}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-332780805196835204538692757168571524763},"lo":{"denominator":1,"numerator":-1}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":332554901758908430336179012552211911885}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":7039696146569413936309402311292485289},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-7046638086801601579740731268583666397}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-4640499861983005734796739840056588547},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5743693365760508512522168538051677161}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4898813286933456952662344491331465097},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":937663843490742355703013408487107961}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-6462879524124567628954892830440642501},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-13354770257990567056835150972955807043}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":615404305604593315105163070825907891},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-50800308680433018386901030655335661}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":6941607806804441447267157699995091971},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":26948557515841910147975877311277247309}}],"form_storage_rate":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-7328578407735261404627409083110346345},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-65268492577560043879367711497286344815}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":84330823039505081481323822464373730343},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":10085562070362967436166142135314246569}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":687105252123078820072923996521340529509},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":85564852431686238379536532092412573461}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-689762610387618838256770865495904799533},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-692237580039398812129883263274302998931}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":34447644527782400382660738391141696507},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":272117192554385938731508417863354648911}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":922453595953303435162380915254510993},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2364065766068307296713795779446091013}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-266121613972251209008824558066236875105},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-269759003783830005644980476552493084575}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":289045124370664423731756624350286336445},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":286149332273901523029138926757308041107}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-147056069710161907408437153020652456015},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-74301451912985250024942052026086477225}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-162429878672205124514029261524118396651},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-167820992531530532833767966967071737413}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1933349645474918380153681594692301499},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-638375506202168695977746852724051255}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":174461632719667120056127587468811831005},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":169322780633221906079064734576498245949}}],"phase_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2497754850412090571075339369223663517},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5000016830918718940667943044939122657}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1350295030822442245533437012651982507},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":401015427736829665559123688388159569}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3815477793717921816171659323955345595},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":371437121639583948504814075994131929}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":21930051617876190838533052244354950139},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":5413599536914952407135750899707904645}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":9175815598053888863519749139725127},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-188126376232049699633769384790284065}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-42354570327276979822817852657805081217},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-10733369723935460774877797491638450459}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":2097219842698063271616348916970013633},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8400328441118978528413988931663031263}},"total_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-5870873549009588822121335801040390805},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-11173050835978910829060418606700711147}},"weighted_phase_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":23443440081931456796388300531400994575},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":42922390905602222221246874283884922521}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-108320563104358558967267811536337027405},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-136532838335438982435386641929446083555}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":860212892795490457855688681057793617879},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":103494883460641546483049027533866494415}},"cumulative_internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":300998213063570434050570003374197059361},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":575313139974840655867672741048457948211}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":27035059559496748599217755405346203565},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-6965125455970972269839164077285418727}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":465815361198898422031503854524358068221},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":465815361198898420054515538902915416409}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":29576947087809861525554948845520656513},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-3670020521856055062076240556913159201}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":255539588645801365288807162368058493111},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":63884897161450340372851503888507599015}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":259903281675787221480618403090886597789},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":284899752820649801988015940009335669667},"time":{"denominator":64,"numerator":357}},{"channels":{"boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-71029986912555990561360527730643147533},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-72966796467249234589835404675625512839}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":128643186675862058317998717366747386239},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":15781861151463615999220548516922237799}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":85727741807532771103056198357109572095},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":679396563839392062988605499543712429385}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-724534642263655559702714860059075729971},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-729978934850725873778096937527018188001}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-332742891745735416427629901067681402519},"lo":{"denominator":1,"numerator":-1}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":166136179299727802844018692951889818803}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":7105196972696662124063157021902941021},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1778061553162868062509955594596528235}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-4842351729993801415187979567385561775},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2972938550949144975868980775077252955}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5088960530458527357919824372143196727},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3907746251773501609459614009830893235}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-26429498472691237733885246541682227967},"lo":{"denominator":2658455991569831745807614120560689152,"numerator":-213170632459011128085842532103569259}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":618454052224232884498339015916745565},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-6006373984598877665928370883557727}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":1772104593656114849002997532735229611},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":27547811242600835603177845980789483943}}],"form_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-29893122839539978981717967417117248225},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-33239270154360363778605566091894046803}},"internal_conversion":{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":2584177491532585181735929551746384825},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":79042150282721849092171717495113588207}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":685084698952135453158069466533021638267},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":682429183911883179336053539538234847373}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-687764275392690467784723249455639313087},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-690307011472815789017713743954954256797}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":272893117223481350614490679862362004393},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":134675498348296070507041471813033774185}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":462675659755773285798293980298491403},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2428371052206146304919854801733964975}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-263233102022299699146744904116073980949},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-266950588163591568440191465191881505401}}],"internal_sine_current":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":35888100235324544839664817483410555463},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":142121897726762074466077543220714155875}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-292320043870247683121850223423063082521},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-295442717849461556108180140771998767545}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-166061436479738906194804623899049671823},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-171441994980945736013530857036784627669}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3885861414100976713605309066491181535},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1207653144622636031431724912849578445}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":89075692365164418005423809981531151743},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":21636000355558274636983876838184935941}}],"phase_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1252173280233067343963716785395829105},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5013280928315219674310059582850546277}},"phase_rates":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":75441235013973826844344112287788823},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-359982013634836510164415885495439969}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2239557241229122079374165337301846033},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1815832210228836083200676273565008343}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":43432288541873097254881454677743607823},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":21434271275495705389230584627574417577}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":147274236596870452654993589416028887},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-193243628309937606311550743886501009}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-10473712343065546910610350075187592651},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-10621626416881101170843381599603919999}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":528897540456753423533749750169720703},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-264812427957681725030370431264560407}},"total_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-5608171537740743204683212606578796019},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-21890784843895738005694191895004841851}},"weighted_phase_storage_rate":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":12142475650899617888517377405269226103},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":44587755464824989551516940288783251755}}},"cumulative_boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-57489812188705341541197680505542411243},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-17921684438030449772272963889723246923}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":866243042170921491839344870934359901609},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":416938632808465613932049962982388897247}},"cumulative_internal_conversion":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":75734086545554968234217987634501711995},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":289509120384671621271934145153020698829}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":27136600637668287966631786581235985039},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-3513962760532641558932722087701112901}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":462781365902767932332316365769491407313},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":231390682951383965159943381681659985133}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":29717717918826239122758584333456040773},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-29502510230260532079561627615614646721}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":257722291171317721113114609222220139307},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":128861145585658858607957476506351928615}},"phase_storage_upper_bound":{"denominator":21267647932558653966460912964485513216,"numerator":16376151107646680384285462149616196089},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":287224801401578249295476580628318503951},"time":{"denominator":8,"numerator":45}},{"channels":{"boundary_form_input":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-8835484914061062129941948966239473615},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-145502976567873610369780764853551200013}},"boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":64361413527634100824337329237721567753},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":31577392171656008770412111715490675721}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":690953036520192153356978628226508367337},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":684466257541937018260134202993088690215}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-728795763420509148240247831264430569119},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-734199655468054684316881135035795847387}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-332270134493700349234273535248593573905},"lo":{"denominator":1,"numerator":-1}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":331536389051984722229008972374068726329}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3691852024532790450708853055038210617},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-7390937725020331712159265691677446385}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-4983793306802102254741215279689718779},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6140878006954031136908633268406896301}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1317857634227503290740458547513573789},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":125172903624221102918449330871214951}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-6748900298324531684773435746970732755},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-3481259705700773705587285585799525245}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":621545954423216793312671717781482995},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-22621266805332715174517563908485639}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":14464726084839797917963883387478563003},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":28130433426530544656926695668871080109}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-60646240554010982634745652146006022219},"lo":{"denominator":1329227995784915872903807060280344576,"numerator":-264079442353907083028682862080472381}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":81154359107397112535887636458908094689},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":4842064497799815427101087912341797285}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":683009137776519846982997496022880413331},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":680286399217630064867186637006030106085}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-342857795781759020402070286247675274473},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-688324109006718838795626974605058756847}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":270142711763885420801030138627565906309},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":266524302710959842536572946510255756311}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":927392892640380307143358036207347827},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-155760601247103358494088564441043057}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-260281080705432974921147735330537153849},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-264076993466012047238109876740936381309}}],"internal_sine_current":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":71324747293680487086545637824633281763},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":35300744402653089637232760731296320121}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-290600304574942273175606954490157423205},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-293785130704366524919652909222362429419}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-42404591194052625427120526593759697329},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-43746799666670865302573478391216743835}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3905288408568868663619865157010197103},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1137068889768446550720810700053669373}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":181769108817285445848531078835418178623},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":176748725990170227608561113211147222907}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5052481947494693493719449007877000451},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2525578659541282278364826542001058663}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-154605208895363850621611932822990993},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1131765368580771442665096104229587297}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5144318954393564181085970932536663201},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":4294175903374434256725654106658342341}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":5374318489683933601147250321168951595},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":2651166264410618718899282157329091259}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":36899790763001982135146940337942987},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-396641114039074186998416151856700527}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-41425020587570202219609393728994637633},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-21014579433480981899445592805834457829}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":2188714713490052173216731314128520889},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-4380383950751415283309344457120112791}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-10438549027289366595265392735074413573},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-5351424867802905749253803474657166979}},"weighted_phase_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":25103845763360808019740129705465804323},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":11549659442847147564581899698493065405}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-121606238062956479679851822735764427697},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-150193927530862673664267184470296187885}},"cumulative_boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":436138462344568594395813247775198149293},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":839798026649116729508552196911432296191}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":609676802947598985523863634035025012899},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":582649789142693104114194106240297745621}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":13624892026143258088289627276688005633},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-14182459610262780633329506467400339719}},"form_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":229852822832058473313253088161688784501},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":114926411416029236144338199591114976441}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":29859807109893301463539725740047662243},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-29646104735033043228668520165764999821}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":259981030811411045448228288616454945535},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":32497628851426380181095483643041694143}},"phase_storage_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":132124296096298830307406166196716142025},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":289627135546444084677432389310098552965},"time":{"denominator":64,"numerator":363}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-140475361617350103684262785692737562099},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-145062764437573011611181553680217149315}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":128837181271564681138022983318707326265},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":126375943208691658226849207951878782461}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":348062220321531432731313512036715411609},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":689579852531933578703490112067385589249}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-91627222756571866191415840618194029707},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-92297017355827894903309064236604652231}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-165675807197391490721765761614921279355},"lo":{"denominator":1,"numerator":-1}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":165169262872865264527303528506600188985}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1969721411437000732132799784460021303},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-7886393016085542913361098444850624783}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-5066644023211984037986360074481767781},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6332085819497979555330587502787882479}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5447368841338414598517582692326090653},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":1011018005441425367664461602357619609}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-13774854065085244069487011980437887791},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-7100531593429690880709252637290050069}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":312343595092038637756639771043414041},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-42375921732776253033401630416328239}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":29497007681926308147084938483773607879},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":14349669360915877176010446754565086261}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-61217457923312903477385647210165707041},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-34329170166615284250296215541221749337}},"internal_conversion":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":4981463393762817381064465815946543013},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":37983210434256052602632353666105678531}},"internal_form_gradient":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":170221744544816458931517322229798209313},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":678098276156797203768387047798644170109}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-341812344994813947698953433935371396721},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-343148683510126214207092493337016588461}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":16708359290042959231571687729450494781},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":65910210298079305606931851892036996249}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":58040515827217525156503914759091759},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-319439942115049392717886793292836575}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-32158611952003394474404351750099322781},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-261142020259475215280765047701425131785}}],"internal_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":141799809734875386368947540190204665569},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":70150966010908397275036745466884329227}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-288942125120910341565161817147450479511},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-292224044883229078568897012812903764721}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-86549960670286604751618304502564281487},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-22306977890500945466192498383771188797}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3925025374947894334523143921761012833},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1065023075238287503473737140162195329}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":185335165272842772495953745795246012467},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":180323263382783452201790211210860839565}}],"phase_balance_residual":{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":40033878546719510088557963424870989},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2558414541821278653252760005686473509}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-922342615269220759296787817714177219},"lo":{"denominator":1329227995784915872903807060280344576,"numerator":-7471232247335302364308744588791097}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5809309151355932761634516049738870557},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":2478594998566339683191003427366688601}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":21273743775725823449262094677435667727},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":41959743076662663197162229906956157007}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":73899479948040446040206507697607653},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-406723566468792210230841160137986217}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-10236404110270890853141860001188469877},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-5195255421662419591629001413442789249}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":4633114334017563664049936366645120329},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-9266228668035127328099872733290240655}},"total_storage_rate":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-2355148140211556514058118248762031549},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-20904409013820549874339675107320476489}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":51796865362466677421153174215117580845},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":47753931319410018626252755975123022185}}},"cumulative_boundary_form_input":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-16023877579846220723756455101888937615},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-19624218076734238572942664974882045845}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":878316167561241783219971322893460704505},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":422860949493512075493967876767088307059}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":613412900492921098559661983396984920159},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":586210715120904609045690889396495152983}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":13692187850647062598704964277915752227},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-28620533645826509197259873250344403311}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":456601346208324825659559498153270290677},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":57075168276040602946543808666441126991}},"phase_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":15002119464248051319281566991357677519},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-7448053754434505802933293486152222099}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":262313237422599155066836904119907048997},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":131156618711299575481273629776178331563}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":266576080870616441762811449075459750801},"running_phase_work_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":146052726220168587087140216748482775761},"time":{"denominator":32,"numerator":183}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-139386414685879656453138700589987850239},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-9038422147795729347314540134539432349}},"boundary_phase_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":32245076044250574038866186893678962535},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":63235594076654413300097700283663537689}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":701327182299635416471790696672561975637},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":347364449941959493789236583355003316915}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-737191859587563654701799120162571730597},"lo":{"denominator":664613997892457936451903530140172288,"numerator":-1450194292804903962931859268206984553}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-329994052192283259265650656144750790703},"lo":{"denominator":1,"numerator":-1}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":164335548288240757592970074249956478965}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":8561738170540993557678504509867250413},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8569519590347208021591773492466229919}},"form_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-2546510435021734312897598391360571145},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6513395143859524641085699273770354569}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5614081510014546711813811288087609937},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":1005906441766181605457396889601001573}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-14045862942691675614975461255183650523},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-1808867981833712494670223763179462033}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":313942473585236505020557919089104281},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-78904389760143851162988642019899563}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":30051121875808580639070268963660751219},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":7313730932688383867229249014820603331}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-61508101339017380701352298877912457207},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-34809923665824503164500478941528731195}},"internal_conversion":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":9792010868072232268216189524924577221},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":18636228713793323824500459691212802491}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":678726623614065575200681877489684957863},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":675874444503322584178225815664013678847}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-170375217205654514302393847758782078077},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-684235326124734923908475012575831300379}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":132235033093717131909503520407335379149},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":130352324772583625211559441033668429899}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":464575022006785283576358519136105799},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-654524130503705139020050197011186211}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-254201234895594171424645797236484622299},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-129074703764520635544704965719244743287}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":281993461342559084971845765754925295383},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":278895063919308912188001431022640535007}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-287370895235390483900141694103825853493},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-290749317124666091664559187455884945157}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-176505519336357132592954892816240817477},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-181847243617362775869675772962711487001}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":493139684332593360813395943998893177},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-123942725603226815301162251224805099}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":47204191858585881930314965533120333049},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":91907053473865013391063309443211617959}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5194684245258538778985014408341835089},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2593451412726162157535872712871427791}},"phase_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-848947123023102338742495744666220255},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2700619357003401546586936144730732117}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":6472153439306407621772341163955314377},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":5618862713080371794597745420955413195}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":10522929583392723276868553037789011887},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":41492433662153610973020525737312781669}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":147878822378811870115968546914873081},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-13021343842823683428877230516716841}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-20228691536848904568908624600971244933},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-20542877132245530414151121675313994499}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":4982625163197484744467920741831838849},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-9965250326394969488935841483663677697}},"total_storage_rate":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-2044578971256968366975350025410041127},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-5092840208818082446652448624733919449}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":53329785453989507233450898776272292699},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":24624243248188338271195581692060892297}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-134724758827170374686292517405267181399},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-81886280612360352797013612449980470511}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":884362119319538765852258732936025509981},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":106456279491463812779352489116971258847}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":617084904568448185660243054468831636617},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":294852504002370428631392362794298776725}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":13774614452942541576974576518936712943},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-3609808756921572284736156507495042675}},"form_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":226740837842952617411353326863255019157},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":226740837842952616348030642501802056909}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":30150937888461619223180951481086002011},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-7485210515768494250872102246670148063}},"phase_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":132358134625861967898878904974012218085},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":264716269251723931585985598360747364279}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":268974723222103260141472178143601134195},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":294657111314797908589474007347427956531},"time":{"denominator":64,"numerator":369}},{"channels":{"boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-69050529080494538184832155355424089049},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-144160797564177517249644911321910026201}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":129151539890160351782735440139120229299},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":126594788168964516986111730221240623085}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":22079761928935356963371470102206858143},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":349952331911131584648679476345583787589}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-185327288595043316568884161744328808975},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-746560964139619162626806144971108210271}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-328187225776436493308650100168866046579},"lo":{"denominator":1,"numerator":-1}},{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":163263652622220373295261256930933414755}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":9433844765169866681170606690691159477},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-590118735904626067342462866855450931}},"form_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-2530896790365532244146004723221047641},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-3342364439632012380184382462302626725}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1442884461371108705472916008450642449},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1971736826389149221087047096748869811}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":-447212278384951706802924474237779001},"lo":{"denominator":332306998946228968225951765070086144,"numerator":-28778600633689224557785954114151369}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":315573192695376324652611487368701141},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-72944894249944441654171904888644365}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":15295824574085086407099607257689528799},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":1862315562829082554965810470324657741}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-61517597307370543183497584411584903989},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-70489857806107271257742053525063326819}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":77053100129355822189401663055472066175},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":73209355491637107384976720219633962735}},"internal_form_gradient":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":338268381200813574769462384414827845575},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":336811805956956398691142879010695601671}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-169838224871849426243641097670300107663},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-682146745288169193963072321454086072037}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":16347223213628251800747066919102113651},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":128859822322660497375470041125392910525}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":928963569492709948630799003720312761},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2679823704607436658567455086387017529}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-251082024820176589849677535213436861263},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-127551530324027377493426388188038232619}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":280480945194798434727561573264053456391},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":277280281505932287078383157642279394253}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-285886904235070372486044044696860572223},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-289360941672861118029803407885394012881}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-179834727471272674022501827369518936799},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-185160991398692118983012712842195739985}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1982804847683340927781177651334440339},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-458326287785019617935846818858511791}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":48053250112543935563920419230500450571},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":23402547563399147105005615412585343983}}],"phase_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2631686860336388500558644378976696889},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1313829677842156651202122394739334591}},"phase_rates":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-309926418398195491305332436409576651},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1746925495172648468688252407474280499}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3565498568346909527870729750051545883},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":3138663284072446444354637905848489343}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":41627862084408236874284897004894496453},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":41017355377189551415208347252131485273}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":147849144037056209925461109616342329},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-213253594601554358953364073166380955}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-39960945371653057383841141327597188251},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-40600913100009479004734429500309065405}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10853473848123928877862952612806449815},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2713368462030982219465738153201612455}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-6712535547089071385670228487862953301},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-19802992118952653464791823184534398619}},"weighted_phase_storage_rate":{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":1712658180008795993682104872616310959},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":6335858210894327224118778792566116025}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-141198245928466737641120531969838189747},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-170530098610541526715104330118175473501}},"cumulative_boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":445208048875945016171037228346273385365},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":857584366627130713968543900289890724983}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":620696768637011739825371257424556889719},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":593136696543411346671455509348892895453}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":27753276533338429943759358136620186051},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-29138648242336754451653423118085875225}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":450359874466208249900110537367337608003},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":450359874466208247732597302336632824747}},"phase_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":15149911435981543951578600391621205091},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-15045990173198313973150417751169395599}},"phase_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":133593710431041031023164921824288122723},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":267187420862082057724318111841315084079}},"phase_storage_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":135720847832003109168674868362609031477},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":297279401208478685670618947343653875277},"time":{"denominator":16,"numerator":93}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-136620396882460308380253508503909389701},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-143641792130106301452724847596163561449}},"boundary_phase_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":32337447574324295755721622034009142473},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":126746171418904418093424906034652041431}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":711790918864419229582959136744274229293},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":705098165620491314255148778673851775115}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-745361283539727271980057965318880648057},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-375274076459382281003451820435556818355}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-81480356811836355270991523358600681309},"lo":{"denominator":1,"numerator":-1}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":339995086484150051033600842788206955737},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":40487663783532820405992168244404001381}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10434701536831226396787666515388891249},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-5221510988453376060493549928327298279}},"form_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-2485956740340446474229812020887317465},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-3423018254563859897924548012426187359}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5889252117629080881660988167109488111},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3803023118013526100393885807132562855}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-7284811001661611880960883106844528017},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-3748034325082681090850734126407086659}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":317239298751434172066449084126611393},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-133751331550829334936029364826546583}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":15559234602438313034187428054354023895},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":30325600563314861441683310892264725919}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-61246245171151816671445154533997514861},"lo":{"denominator":1329227995784915872903807060280344576,"numerator":-278159030014879453433374410946050099}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":75854707175557920422296759158375160915},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":71960845422123258384492026546777155339}},"internal_form_gradient":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":84290752947974740663630116622981674937},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":671356526331657761825367551619940126205}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-677193466322971745741983246600462829601},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-680040091077918390225757018843644118891}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":258594003063676473209629775324154819389},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":254691676333150394633984488493266238491}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":928159052086347250736745963704833261},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2740622249697300258861454549609147339}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-247915255429210263192320422458478377535},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-63001738321142800702459337983181235869}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":279062246651771966051504734251423011523},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":275759992911088989485472283806899885233}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-284490192920505090966955766138139771755},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-288058661801312234630909338276135813049}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-45771817451220445899245032017572490917},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-94198376808657038680146833842200505025}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1993273300774966523110641300922483821},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-420192200607938165675960441115456847}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":195523108490001245912357896311709064627},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":190541367890816928390934624079320543191}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5329108359001255325410598396386429371},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5320787918925729601211165055120724063}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-3265025676443771033989563932225817597},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4290222295004672741309858668459833099}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":7783173980451482178262997454483852651},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":3465396889651311722200437774638374335}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":41156513841504837203475960041199195647},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":40535439252781977182574028847989175421}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":73860550557515057753808633184060663},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-436183578186955991804587048953501585}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-9864234592362163903321153846870215297},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-40108152308767856150820179237169248655}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":2967487035599454921098383075044328761},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11869948142397819684393532300177315045}},"total_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-2512836284402031837453204630667102487},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-9570277363780472520880276334025067427}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":56220572602347752996538745272663309887},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":26034078478124097518591648267069345245}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-147602327032332064596444915180958942389},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-44315826904160064898925201837311410111}},"cumulative_boundary_phase_input":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":56029960573254739862267016301495217809},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":863525593412391858566673192760265039425}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":624252458035866017345166418010105725387},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":596509861172573374408228573093273074609}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":28002631574692578128483205343225399143},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-7350236468227065504394100393759446749}},"form_storage_change":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":111812296282656423235252742771813208327},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":223624592565312845365572550627054498001}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":30450795053029802073414648906064851747},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-30245577569946824528233012064701966561}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":269723930429555643294921423656224165785},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":134861965214777819429905337832974221887}},"phase_storage_upper_bound":{"denominator":42535295865117307932921825928971026432,"numerator":34246764145158838322018778362753809773},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":299969507999502463388043687730650410335},"time":{"denominator":64,"numerator":375}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-134951590044617238077497725104017854719},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-142268386684529716872375102780768881447}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":129570188101505307338935592072434347309},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":63462534041029460810472081573405617541}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":717014158962779960667149773294887713581},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":710302334658391534810123689373729381593}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-749342406191302566284575661485118955169},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-754426341920749672691629455793791135127}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-161593775979658745161186843390357662561},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-338968594466769034835894325184950710263}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":336980538226161214625568509500441433335},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":160394150853158603379715217647614535119}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5382847153237310759404992444966384809},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-5387097037390580886360959141156385353}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-4822423078231773051392666620382083555},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6857898713719604279797313029215405285}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1427088924792158255658951222269943147},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1800908825888615348936663703653389037}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-3705585147037655186969750580259384963},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-3810853164327898934993727776272921923}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":637888566894572068017759685314987751},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-121398288322104308497499509866859945}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":31631487269279760172156010786289078739},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":30840490089263574836328982828400451707}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-60697343073201097096107770758716726839},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-35493551169284946646118743745701429323}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":74738681780828506557982155894927766779},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":35402674652426999128728673566059692495}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":672100217833770824752271677820471524895},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":167277664992738538919264615693348080853}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-675065407093610966214470448931136570265},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-338960301604224956462200304397899864967}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":255587893030273887240776543130992124705},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":251637791157965311473944864806145258445}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":463405791194476501030485954850582423},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1400205706580104742485628424328609541}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-244712687683014770238056947349057867859},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-248864264177117273284213258516051009163}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":277737285214093045400475987549762273195},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":274334421812515830639218094673686723651}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-283180553240404398707342962581377031227},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-286841970083137042608474891615816247055}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-23282878150369902628003837932583060395},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-5986074152480972203098691695376899993}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2003986035564908998110654290269126553},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-381383970751098482688705530984998263}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":198746496054576728944771449248431932167},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":193776514195078546823697262919469375625}}],"phase_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2689355428116901261709189981946800577},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2685105543963631134753223285756800033}},"phase_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-2026685243070815486185869117603031801},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2541359551982233861161771761866494769}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":8420456710755250290225590197999229367},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":7578088659504316392843818320845853393}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":40678076570210673046672783073062099491},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":20024699165758106227107206515962724563}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":73753322326011640215408090320596041},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-445699319095407337552031466019973505}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-38947233882054972426932678257786717447},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-19803988901357753325648383565569615365}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12211072686733915741703556091017988983},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12211072686733915741703556091017988983}},"total_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1566122957868439754863691771469828691},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-17592474629845846480265689122601496393}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":57565097157464217586380387215777069457},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":53394627708724046811971798368801362253}}},"cumulative_boundary_form_input":{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":-1202563928247449200244747039415701401},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-91966069121238795037046695146047090881}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":902552971739333899077784866702318844975},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":869475205978738370517654950407771816069}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":627755833744342353590071831567680464455},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":149957215480309601394136721560022792695}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":3533262392172316545369504645302075379},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-29664828112529510347078829869517652203}},"form_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":222081411408069673932704766555206796025},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":111040705704034836402916345163238258231}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":30603614148489113632617171921780426507},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-30401123435210367492208922755681711909}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":272322986382885130560200290761871778121},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":136161493191442563004514528853272981143}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":276569036492235662933740787354474119065},"running_phase_work_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":151362054909047746750618990231113837097},"time":{"denominator":32,"numerator":189}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-133092613585202889350477745282042556495},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-70214709687188466359860247813309395131}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":129813264443573274739727966462468881485},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":127130498193001636280337360461894413171}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":180551051027508915905667262205315375517},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":178877164586656898927568287906704942411}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-376620576164192776517827590442685333921},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-758211443705547340963666030118282620815}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-159988595116452824963256602571492660039},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-335899252758239486744859224253542941385}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":166736158080038882016868580291474643563},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":317184574795368028510889894441307835533}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5409230029832831465670234423425268139},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-5413542760170532479437727909339919855}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-4612465847261977574561943982320776279},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6673442559792188165750839281848293561}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5465888694818100084610870526916028195},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3339544478847193419052327259591133581}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-15068951270750467832869308540581292381},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-30976938756426271542398110230875489405}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":641383123703336242318899643029508669},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-108835821788930858630474690006364083}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":32130634248376845665557941502719304217},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":489713360789255452302366284983145075}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-59870904765425152693949244810227062187},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-70213542307316126090274536350169902425}},"internal_conversion":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":18426539199556957054769666187638123445},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":69740054549286117094430781969541191797}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":669869411434001452892630976110715902105},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":666886382720808094750133000310657937277}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-336477576095248975625375439131561072547},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-337899946108425133945672797489182427533}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":252542604921531593720727858663769105931},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":62137449696126735990561206406797625335}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":231250262461165554174579395687408779},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-357388576339655947900810172295998827}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-30185019249154475535030411801078547525},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-245678891899391476536888729266599710793}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":276505723770829499674964570439747635715},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":273003538398249678202807273576126298393}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-281957528853137624258861238024136734323},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-285710109592119935986487689207034209991}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-189362026437968996441066941327268534155},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-194633846455779440481185001707151627939}},{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":31483820461919917501280620213661421},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-42739727272439141749014698063833731}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":50470682254940653172720312777823880061},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":24615678345924685428346011365011791233}}],"phase_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1354434243028009754061847591192920983},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5409111511436636988712403392942380501}},"phase_rates":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-1210618624189328943287745147718995683},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1467350785861690718083876098374246915}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":4522986741434574932376365612611213471},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":4108386448672020849982112942302332509}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":40193403914565367746534303266159690099},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":39557929081050239164006032474890053995}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":147218489447970656014919603771841075},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-455041268232251474003683546440457431}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-19216380083307783324255719549079153615},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-39101010059127556445336240121063389981}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12270094782835990822939976430610918227},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-3067523695708997705734994107652729557}},"total_storage_rate":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-64301649908706601027697420882091179},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-7774721962232802716844877625092296619}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":58842078366885847077506086076113603323},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":54664098382850520656584781099985309187}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-160166899077479883069631265355305524163},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-47628691818912877198832572131147984389}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":908637968510126396331209615130247073795},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":437717224040767661109147882089711558343}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":631210809844259283037841143977862612601},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":603097926978236192315348329144913414145}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":28530786355914638291968822195262889601},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-7482491177070020113852889942535092333}},"form_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":220556973029249660905993431407792183095},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":220556973029249659756399159426208359553}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":30758095132735292680617383513166727337},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-30558308161878876825087783979505352937}},"phase_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":137490866685005665930536001857363615711},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":274981733370011327190773502005828306713}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":279223478868807782911276186865798614517},"running_phase_work_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":152770020765945102007930642992666829825},"time":{"denominator":64,"numerator":381}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-131043013012896955630576800595080032499},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-138395656286161679100927765217675809673}},"boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":65039140344846275914151341116890841781},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":127361498298871235899629587814535608905}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":363677547598232146707413170801910713355},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":180176765399478893779436185790883826007}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-47315560801374569003546399944125580365},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-380947535642996527479871014060168862557}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-316282721163118752706154285012288966989},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-166172599268810696378303314671074321019}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":329467651170959823278144268825326210753},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":39135949963168211662874525855134739099}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10864739775981348843822366695679188533},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-10873458658778827170394381046004405621}},"form_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-2170648069368195799608193699510565635},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6427540218233889367093211902915694347}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5161631899645132582040884582555220369},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1508020866637344619445238824329702497}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-30618937613707152369734793920859525027},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-1965914932828653303135786717521353189}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":644968898971740029447569684140660417},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-48034700112325929975666032700717221}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":32615866855745990226971817638722482899},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":31829059009379395233991574216670377681}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-58767916382430854621656934972725788233},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-17289697679260113566571047562066525159}},"internal_conversion":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":18189420238658832133671747848204584371},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":68763000127749475635448463549270832907}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":667644299131354013025383164078715903819},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":41542464544678332497687520916238241525}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-335432576179660476797064461225539309457},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-673687870432284741143464893914613020381}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":249462161805535958240363966678226782617},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":245431731706688594647765107616622544685}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":461406026529572384680683331633357917},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2916629501310041606513297826440269219}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-119107530341773177327618692612205451413},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-242455724435028939646529440280101000015}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":275366968993582801724294798692846037619},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":271767059146851823060798912289390927167}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-280820416601580191015761214649407577103},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-284662076048817722208107058299280560897}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-6012014341746661521986521975636006881},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-98817662568911504956650414075831449089}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4052459109607032053541433168788537109},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-603621843961087830763101948962892339}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":102465767704474431469381286204084550603},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":24998484488635582486762898713808943201}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5449092528733338587025845131059867699},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5440373645935860260453830780734650611}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-5630133960442910129659976934311299131},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1662523582584605679364125394474941891}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":2414643594405724072885862637804233711},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":8844887671274463186835029312277703621}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":19851568082870630819473422470527470015},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":39061673292723347393439904451619992399}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":146870099789143284863899545329906513},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-464196002301142744548570623934167225}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-37913104426722214099731604296309013177},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-38588027024761288298838773213928322833}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12319151477828834531609683983191551655},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12319151477828834531609683983191551655}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1284993490538391330311506580051350887},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-830242737564577395867737646530618787}},"weighted_phase_storage_rate":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":3753306867060577871998027597048571195},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":13968726729001803983100096975944050011}}},"cumulative_boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-83154770156229713932407276441599950343},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-197002063664065337503186277519170491135}},"cumulative_boundary_phase_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":228683846979363933674540325839988897553},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":881404518314294911401090901108229473353}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":634621326139007814062904596699400972171},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":606321192609224448985759975873785484437}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":7199124833913941972579576279898854195},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-30196157545733509171446735931367713461}},"form_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":219057814140407439686446001737105205041},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":54764453535101859628330413485604169753}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":30914085365204071547631753575909921107},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-30716917767740121619189193204959796009}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":277697277540491168885818057984738422289},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":138848638770245582046606067140605154883}},"phase_storage_upper_bound":{"denominator":85070591730234615865843651857942052864,"numerator":70483602974155170565606765219334739671},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":308414195308231285712401327486170105775},"time":{"denominator":1,"numerator":6}},{"channels":{"boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-64402377751750408643118423022300626663},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-136169142704654441652957120503797240675}},"boundary_phase_input":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":8147803149979820749494584462464970197},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":63808469374876566141128039771421070443}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":732477678144581979477638952165336168641},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":181471345257532504285566284333867798245}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-760758668833051825384154541289594556077},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-191364502761038281386821372677317513359}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-156048703937443417080314324207290188539},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-328299409403903780605883578299741193951}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":81241255006188086244885588219663777255},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":308496086607621711660673159939118268861}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10904488828212932282043140068883571815},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-10913266462847115116657448419486519281}},"form_rates":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-501036143840564988254422922583275719},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6119503523580050313731223817715702919}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4795524234142714929054137868751349745},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":41114141146870132554119905762646879}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-31087839944379764154479215217545378995},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-7979993503942846730410517358664548255}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":648652277165792112598648798569307319},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-20776204899401017073700562782229989}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":33087167690264996742199759930352089079},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":32302691289228936578995659452307811663}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-57390812612076359576856033487004214287},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-4239077051126777301465255727383349899}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":71892789148319495579450202825954174223},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":67873841264365149794057946947909454573}},"internal_form_gradient":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":166358538812423490547010023184424059199},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":662499169780058564744888950733199349679}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-167201166837675907394326919760169496735},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-671593752688851669235983592372652894025}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":123175297201189794186656020786302408309},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":15142976122923600815475096694772948085}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":920333789083983414841422998896139785},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2972888085504305849582564466632220641}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-234921625393270834253566900795391321851},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-239198937669663272852243318483409288781}}],"internal_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":137160086313373682276334068384336634669},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":67656111866003990058512749972450824847}},{"hi":{"denominator":1329227995784915872903807060280344576,"numerator":-1092844800439330573246989480196480135},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-141848310460387395526581510347442039513}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-195330659170477587014377448043425029495},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-200559111741448960254112492329508931531}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2037801228678342891051044480316966351},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-261081490725738018040185645621508727}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":51973201471915040585980816782779907731},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":101481897645420634098109073269564919857}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5473562454969356812158130325944519931},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1366196205083793494385955493835393115}},"phase_rates":[{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-200439820810846177752465172432739307},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-7424950344274297211146471259934259243}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5127619138390785158791804568892763919},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":9460691436482530360152589914111679655}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":39207914832765313041388709901586653645},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":38561272049373368903967143660384943865}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":146475671827209785169353737779279775},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-473149834067011472565611830738385793}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-37388937920521573854075441132204279115},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-38069693312457077712706237961469344895}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":193110990612936614200140851824740189},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12359103399227943308809014516783372091}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3806899444326633938107973555828272307},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-10799008503051628603132509161945102265}},"weighted_phase_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":30598856028201496757482003521416243297},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":57026224314976808220311582476188496119}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-172347263226686028675106905041540584435},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-25423124028543251806958580317848248349}},"cumulative_boundary_phase_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":230211560069985150065070560426701079465},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":887386562318189589476821654836800198707}},"cumulative_internal_conversion":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":79748912578791911302273915619608446761},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":76187847364811445672794555267121092515}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":29063043377679345982545791240828344739},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-15231603667912183614413651203574591681}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":435180830067824896909233590835011098067},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":435180830067824894514257117508177806291}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":31071429454418476065088765674047716753},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-30876770219176264672417233165574600781}},"phase_storage_change":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":70116672785568193780929773888495085343},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":280466691142272770205508566404260976959}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":284698770868390503225507549264089989283},"running_phase_work_upper_bound":{"denominator":85070591730234615865843651857942052864,"numerator":77835865340362258719481449892458894435},"time":{"denominator":64,"numerator":387}},{"channels":{"boundary_form_input":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-15797519798550571564365032493301275185},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-133752308571297013729312454294979160071}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":130672522293932453108917438714227923853},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":127895565604675982451814161176841242253}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":184390456571929664093575101734495196913},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":731033579295029314851772187939130763781}},{"hi":{"denominator":1329227995784915872903807060280344576,"numerator":-2985784636649066867725769193054173821},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-768902184400571303281571124369211499715}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-9606734171879378242831572333434883965},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-323755838493396425734753675138399982055}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":319964205666588514739301449235988823389},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":75852511315956189001267862121628825467}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10937705883905303777477938516882777305},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-10946505364699258642673909382049474761}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-3612950878759036526445530157445315401},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1437193627564251274657739366545037569}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2183834394392343380138530449412607133},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":136593335867506226393008689895125763}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-31544686813602374816990383682088386223},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-32373016124213262715690098989536229043}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":652439347315413665870886653971285223},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-34974113091708585113570872849979919}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":33544545269542657257079601005697523911},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":1023830231055737175354105105052506381}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-55742578663487032194698156503051196629},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-66215846858539767596707278937021111907}},"internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":35555408447282031780443445195719282167},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":67072024023904677757136359275045186137}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":663248320630308927413013893936933722811},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":41272187116983314229685891806999294719}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-666782963053554983699476902891312645045},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-334763394112914776361541556703218865585}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":243211931469482911969030360111706275971},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":239121471221787880761473860339010285053}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":917659921083887370174796045559063233},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-378474602433317045554264447124703097}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-115802044156347829925044357912864489483},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-235912740702849902551584331644721082615}}],"internal_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":136682116842334786523260662624681465939},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":67393728796923354912259519730189456055}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-139399948563055154002957247139749347257},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-141406127740136039566173896322577187451}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-198201112706808088360987193334079403421},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-203405659260744615142947909873338402753}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4099397320878046323818771078084113765},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-439497667018921206530147856459094645}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":210766593973610925392437430545043175047},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":205853282074102047436911932195281925325}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5491960358380886692616585257208781363},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-85674388712295809803447099875657561}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-7192239323501985652619073160680631043},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-4095949673157230937659784735507051987}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5417592954024348565766338933457563225},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":10062208271757513794883601431841634575}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":38708381112295501199291924366371719063},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":9514341036088484602039710533985373433}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":18256264064727407398530096408895483},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-60236103812002286356721823211323019}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-18430467747628689690364816780741327361},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-18773339410607568348599481005717629545}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12390873371626804666343992657698180471},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-3097718342906701166585998164424545117}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":6534130405005773388845699539560262653},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8098509466098924072346813889880458095}},"weighted_phase_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":31138354534246402791771928021305729641},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":14529334348110210881090116261785163453}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-178271333151142493011743792226528562629},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-209654631692625561974230163837863134921}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":926971514762468683999762746646533751791},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":893381666955908776154250443641964631937}},"cumulative_internal_conversion":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":80165577521533497612200987242995782099},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":153161695011153024288055552244496620805}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":7332556001645617932826181868501681407},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-30730914662556483421996479391427037955}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":432322372358569006909296772614130073927},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":27020148272410562778991726645375666013}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":31229969655861559345791994695738906835},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-15518859139177118646169691765754246769}},"phase_storage_change":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":70821754109875588650608635098434320495},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":283287016439502349555201154137038775033}},"phase_storage_upper_bound":{"denominator":21267647932558653966460912964485513216,"numerator":17969591211989750724183894299540617709},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":314324734717856586847540537668547268571},"time":{"denominator":32,"numerator":195}},{"channels":{"boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-61885939239975241601692528350714381481},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-32786989476334646818945271607746468095}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":131000135359348676503376392287818731885},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":16024508493607672665280240153969824875}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":371298631203077346354298273962925704163},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":736141450288187224741926694061397385277}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-767847095203810573421375470324774189697},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-772223202428915397920736316127074416845}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-302232297076202492139399861503407649717},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-159354755456879666570733440103156500967}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":78616587813677958761550307364692144917},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":297830838363338961196430392708349710619}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5482216620616027648339523291090121343},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2743303906394040653422321803229973931}},"form_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1577463980498453569532326202443049029},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2657467695943457923020876737369478497}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1939169052588630155181610223495549705},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":839467126554150253433091390181059137}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-7997394715835251624862520275558576061},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-16406930449549452555831289676667738939}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":164083963266908566845165083468074887},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-56606139163323925330939977685720725}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":33988034016912647157174067767472738597},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":33208728778487694628172095728539681733}}],"form_storage_rate":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-13456681993474210657764078559279636865},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-4020886368751390810643458603820344249}},"internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":35205456102752196423389503126611575351},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":33178398345104844674022862805843541117}},"internal_form_gradient":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":165274045412234822911083599291579679195},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":658256322610462818437666476951552526417}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-664809287836079215799761163200836419773},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-83437029776741313993991561134073625745}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":120025094965841419514577980317084060623},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":29492160075741086480200090409456452207}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":914888423890465349060165354307950571},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1540633372484998999818358634089832487}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-114133351544686109465806433797419670679},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-232601367336552161618874486245554500605}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":272497801561583764530275447295601898025},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":268617424969390362384202616509026591175}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-277913875756625115512367744951011639219},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-282007255817063051128449653246176930609}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-100498225948503434367163642047545698137},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-103087784336526487905285554064352560459}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":128871243392804360924626359148174359},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-177833430943579929012805511982160031}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":213553115954985525407145567038001912281},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":208656596731105779172529727109577426113}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5504448306829237304672007240282127949},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2747832961242564993830883304771237453}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-7962550306397001676323257989521623295},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2237212912250051812790226257048620585}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5698485154766849507186768005077812085},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":10647556622298192305190638907688417747}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":19102587158887824472459903646067895257},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":37550584468093122033793692496754170155}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":145609015039720829777624891520081683},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-490398833446649610464809259477305805}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-9082443534990901183774580890632492825},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-18509828690773000925336344951413493609}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12414766032766589102617773180926302167},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-6207383016383294551308886590463151081}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":9462876076289383149078607981699028787},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5186509153368395802626437594536333239}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":63289604050186225780134922218817576247},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":59147672746653857167668900066589174745}}},"cumulative_boundary_form_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-46018284988722542977975616689852008973},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-215802192219438308252782402264315597689}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":933112146107438153210858515035025254849},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":899390857641011653403730533699703316265}},"cumulative_internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":322312565840950499656150331931043045991},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":615757254889465676340411852366034315199}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":14798924005298316503214675696006842599},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-30999081046386828804008014889886505243}},"form_storage_change":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":107388227670156000273514700373433100677},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":429552910680623998596390182212791550847}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":31389543007313731989354741669185848049},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-31199622251548095969461399161595942461}},"phase_storage_change":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":71538817241606096520196152876700768083},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":286155268966424380900985263507394997189}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":290375353361741008203798601928034286005},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":317354891217972476870446662668990939649},"time":{"denominator":64,"numerator":393}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-120982899551701587715916319368218773163},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-64179628005242011567238950399829562461}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":131346099078843215070343762761207162635},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":128517044807443577921431857284297241469}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":747573578717046576245821161123673675863},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":741198637672453424944759200067575028815}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-385604731113680699848482783801044147513},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-387706742719056270042344293157000834277}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-296544308494161288035530973473385600051},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-156578309638760190255561234750370384305}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":308474007186354146721048834328054066221},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":72940306967626640528989058023639122617}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10984756725967107344370962003782007759},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-10993481266139685087234814050170081749}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2634017325653922756380438468084699549},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2408859175887591954414815321890368243}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3327978615518706967385462665861198261},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1112127958544495447908640012310146945}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-32422639675924599569476387894324183711},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-16621313568442131887520721656966559041}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":330173570986737563626423702406911509},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-43085472960408895190723233469414077}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":34417694200764685655230283553838191719},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":4205155351590908715498930027309728701}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-51647277767986610025652507924709284989},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-31092166508489981616208814384402887317}},"internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":34896023900430654785366752324791540139},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":32863610758265152882227215435583916087}},"internal_form_gradient":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":82373393506492345623919328989934708763},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":328106283856138723057602000025621593953}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-331446424025734347584227186832979844555},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-332755676166679708549956006843204115281}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":236869364796667521158780290779870950683},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":116369500217113957715157107521975851753}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":456060703526112311112461774504059883},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3133207635785461912915232132833416143}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-224913727284482549802433596788102268113},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-229269067097067748334162845070248028037}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":271719280055053494753315675609490610047},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":267750693534515445557930318272363665071}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-277108547676901644087110986383729534307},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-281279668797260959046966629924833181195}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-203717453231747353286809886408487764859},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-208869586398520610202106727472806405535}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":518635432510721415007468080402425225},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-67678502664431132817518680551527679}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":27031593813655591689852973588554078445},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":105687081278094423002067388839278346067}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5510851147090182634249319956792840309},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5502126606917604891385467910404766321}},"phase_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-4361454984017651592761927926753654071},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-4846852169094018138855300201060246469}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":11938810426623394568345698449220766055},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":11214917776733856587311158359653155533}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":18849465137213507865664474250809091779},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":37041562369374147720738237659656683695}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":36292157658074077684113781220825083},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-498665482968527118702830222980181119}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-35796131466547887486139657642476526783},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-1140290791455179714236431685788615605}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":3107695397181571543085302045539899991},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-6215390794363143086170604091079799983}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12588570385685840959295164666797716511},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1033791030792329408956882394585605247}},"weighted_phase_storage_rate":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":16058962038418112746236918147876750375},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":15029187738848826103625965994908641035}}},"cumulative_boundary_form_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-47436053342844045959021511057448322721},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-110909516172464873418605526932149809585}},"cumulative_boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":469634497250879464458640439457228420299},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":452707547058180285559398826004952374729}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":647896633922566373198428796892535298871},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":154709554599513258605780163453280076833}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":14932862242222389476747700222379848165},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-31267510013622125374698750041830380843}},"form_storage_change":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":106721227634392016634851250098395096123},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":53360613817196007998455500327613953393}},"phase_integral_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":7887494986731422135893757859307529703},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-15681167981493006673126700491232259049}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":289068440140719886463943886554599569399},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":4516694377198748142936044126857375237}},"phase_storage_upper_bound":{"denominator":85070591730234615865843651857942052864,"numerator":73320326073473904077090466752887433607},"running_phase_work_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":160215388051852947247080112550668266633},"time":{"denominator":16,"numerator":99}},{"channels":{"boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-59008255667606857813518181744722443283},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-7836857351599793332560510488177514235}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":131708696319562947942391424274334565223},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":128856970617843473807798514439295515795}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":376240129308261957518148925605207954387},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":746194655187416195622753958074305960341}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-774440301249655810391060887266858979743},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-389232850461493783474689576522673682263}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-290349261697054736888868044210810256491},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-153547313128299247004930671225267637033}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":301991176118754597269053716069971717399},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":142602700120690365546819129791275098213}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10998814944666955669322444095948716759},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11007439352138149746282133978105647711}},"form_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1025086717123530559389554064350556391},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1064253996327742859471401339570835457}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2717214772506083286329987705619561555},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":15179672227648770002278971323568431}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-32844015298486372883386177258305394543},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-33659456323262029297472214341733431269}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":664478114358494440095160781723829173},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-14696779524350636741884763737663909}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":34833611824919479066672699586112840827},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":17030101325829325902874853114347646899}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-49208715941134509862018813549665056119},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-59770917150395266662886364839713141237}},"internal_conversion":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":4328314596059787419402008289239837065},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":32591093369897613894813455082613227441}},"internal_form_gradient":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":328465314834882740351415877466717107907},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":81779138798280037017237992187567946389}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-661042782811742963816358963885157745003},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-663581344492797474283384698051770690303}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":3651147170311910118210832050018397583},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":114765269897868806964263997168914079329}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":454732457554481718194007224454355613},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1591764080349881374893201948733512961}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-221549412398205360047609458617679203173},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-225920095803369040874005427969817437721}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":271026832298208164208488864600274921663},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":266973195819596704908707155828228351623}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-138191015108081139808903934463266491045},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-140313659476484810954230674159146058895}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-206365034352231138436150641912782255907},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-211488601417973007969196143564361166841}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4175039125079689280198705728576077203},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-184685178340515424699261043298808965}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":109433019007165586478016138849939997413},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":107003282430230416001444129954153993139}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5511005994903416766076065748609947099},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2751190793716111344558187933226508071}},"phase_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-4735603633805064208005396179889016209},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-10424346190354529943043209002426415535}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":6229479283226473652496138293015487703},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":11762500635909782930967805317270772001}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":18595139843556055751756513556558506317},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":9132729999760659402873330965968879997}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":72372918404121249125688064286557115},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-253337121623808484906490009894848689}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-8815171030569806255600935402657402305},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-35956299990900741969055989692745698201}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":3109743535602250378648321845486931425},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12438974142409001514593287381947725695}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":15906227134655782001423634010403013735},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":626605420970115400380886701470976481}},"weighted_phase_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":32557471537895145931721223780034034927},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":61024127992335497463648138242655094199}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-195276237340214326756103373768361019941},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-227696675358629591836631436730432754847}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":945442839641738442102080476927316273343},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":113931908076758997994192275921780840845}},"cumulative_internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":325571434934805606881490151554732588335},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":155473408350370233931439853806778824351}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":30133666005148346102485382806129988157},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-3942001060174649952879771597044799973}},"form_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":212165312023999844995806680651406265357},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":424330624047999687383838756564745756945}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":31711104523231996899125996938367272103},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-31525706972564744742717169315004442829}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":292023499267692767089683901203148822193},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":146011749633846380816801946192598266555}},"phase_storage_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":148114071023326211669075972497720106679},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":323549206240257506376321061700200975939},"time":{"denominator":64,"numerator":399}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-114876013336130599208686718235465762309},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-61122932003785729244555276275051292419}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":132086177495725374507011774036695148163},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":129213366761857061683776760491079416713}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":378653350075086497260024170628203722197},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":375559454368270603371522520859059932225}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-777522560884697427416245295788801809699},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-390686927693482269137925527259348124275}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-141823111891975491783882169447973256937},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-300522353111459051152508244685076338775}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":36877917801807761948864788410533149635},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":278168996078188260597504724228632152139}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":11010817099720800133715285474136781053},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11019340441536147411701943402990256273}},"form_rates":[{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-87719819823939728121501777184582143},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-908222540496865580628488978963385155}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2046851431754814755268630200460145315},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-199349014912736362959688285557764383}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-8313468428565465125487976425288459173},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-8516128030213118583575149966470508495}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":668733172154012537637932108950752095},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-15538166955031418998006213384479305}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":17617949234348687864153889248298954875},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":17232863528178157283296304305392976031}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-46515865233918186358600868424391343875},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-57100226003594944919346900018271717517}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":68795127774071801701041761620184301065},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":32359590836966235998397199325787229955}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":654945643789859554012441203405680023599},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":652326205596542167354585153786360969785}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-659265997763951072257391453845303193893},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-661734631212149378376932503147924571637}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":115237952119081861183824647097154866563},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":14144667618597301085974924233812042389}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":907028704949585206679795266731699903},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1616068031640804948091563341745186027}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-218177993488110759605683970446156613615},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-111279352849789513090381590135600176719}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":270418386590361734288117212291826720649},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":266283169978863714460082775956772608839}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-34466527768936258423696853847834231619},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-140023908140219452341387090048428237319}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-104470125364127792140405273237759662863},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-53508410513495300192958689863721825765}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":131305451303177767249082809633444861},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-48814591156178393116482152749636753}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":110696839771895520736426163201015840463},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":54138637460439983784551079139133745979}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5509822445966600914627041338698231283},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5501299104151253636640383409844756067}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-10204300339700593969166785164171059657},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-348086763259211302848990067337381637}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12956046087375977499124166645861236169},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":12285480905175176056570489774489654693}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":36681379423078066264694204130630277049},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":36019100318266050791078938391898195487}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":144358101918966758836123969755772537},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-514410431216847244761243125689740303}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-34724106137504179091700608281643069437},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-35421318140222382024345870832024803235}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12444693445548071344094963844225171181},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12444693445548071344094963844225171185}},"total_storage_rate":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":1213262262489604658672573236575125191},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":4765470714046703954230091957004214669}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":65928061433751860897362040209593346931},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":30932848358820824436788495987637966093}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-200661050465345448594010563685648477549},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-29178368779248062994163561735152351689}},"cumulative_boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":475817189605925284516048326917643179207},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":458756070590517016859982621511133037209}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":654367641484020829467716635685411315783},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":156231836260611630087652288165976962553}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":7600418277741585143443808816910329575},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-31804523099247026568412200514343132985}},"form_storage_change":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":52737758489928544621384486756291294375},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":421902067919428354305293871485419705249}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":31872895277435140603570365019682015471},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-31689639194955709425736375557342588759}},"phase_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":147508697487224172427909486178268387053},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":295017394974448339255751125614035919443}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":299212676963562820491020074474142777305},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":326707034169404048681487501171378508201},"time":{"denominator":32,"numerator":201}},{"channels":{"boundary_form_input":{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":-1743199299764451837957579038319515907},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-59468520398842723498846357554862335973}},"boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":66238383989534495927824926641798365863},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":4049461035761561513141980536689489471}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":190510560292825558546092789174219857715},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":755960720227593061737435658434274213649}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-390214577529199489458753432997989616375},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-784133389818597231668087476701990838081}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-276435795529144228156002550896586801935},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-146720009727283035266326763329880900775}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":287577463841372448466204375943780485093},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":67664802222145786773394037065023416597}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":11029442263390307540705140853253005309},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-5518748015462719876414102308006052847}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-694356137271393881639621904020363303},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1472787811181835098071829007099895931}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":658936068581534828341697032686978171},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-942128935653071303473350202241028697}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-33652404261802819706933803133517773543},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-34457979804228823798311487367688089891}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":673116168090569609343023769300286687},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1527524161027630336037635561436565}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":17812345537644965842501328891527481567},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":17428980080482482115083399684393914659}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-43573443048940288075540351846392237207},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-3386251491324094348998001356768061101}},"internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":34211113677332423899072620680086073063},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":32167077742677425690723611205039714715}},"internal_form_gradient":[{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":40816341371211392174583929826378763331},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":650498880993079092658917374449448164691}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-657566989401084572876216508013031817095},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-660020150113912459106712464348068941315}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":227300740234402473107499412405033211639},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":223092985958767913176737062972808379863}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":452475958659664130648624131304342813},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-819792902989353529825330692535546537}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-6712611305722931598906609594396050519},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-219189148132862824730552173160042093949}}],"internal_sine_current":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":33736455388707979629321858266270103817},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":132839311623566701214671057909673518757}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-275156811567925908550141751081827339393},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-279538564917529326613231744251052551569}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-211444292009027174835219191994521064899},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-216505872421021469350446805916748018697}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":528664202171461471984206424735630083},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-4798858682465315815458175460558313}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":223836535537073442290005476362748998505},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":219019023121626436450874299884928183965}}],"phase_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2758893995499735230817390758728139969},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5509275787673582522876559031130780115}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-10917950398038951505890971038841548325},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-5917559047147962822377294537002128259}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":3357278042632544212537498133499240293},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":12775792219794330775817418523763894515}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":18088018188376005045419672106842184523},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":35506351484468712424236384378040872121}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":144027570901859262521807461698870129},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-260948185644820469454707805639818823}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-17093524325765542755876709945345604215},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-1090157387420212489417970386633878261}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12459158385079781585641903420616568551},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12458699949289025859006744697050169113}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":23104870731764303008492565484955559677},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":8453312844855048367358050134097544565}},"weighted_phase_storage_rate":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":16669578445176147771008229332836949221},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":62633336706040557951326071842386522181}}},"cumulative_boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-102945324182319402053941650400303512635},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-119501062010688004640662669950993578755}},"cumulative_boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":478922113855434714012665120353977477607},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":57724145795917273499354888364206269289}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":657574933391270744208254693874169385133},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":313971504290411264504557245607190161733}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":30670118264431673339226515606649391325},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-32073282202753749759216582370375212699}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":419611002823878193067015666919042557281},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":104902750705969547585288702675796786791}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":32035656777091827546880425350063508425},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-31854163009549445436058439289943439853}},"phase_storage_change":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":74511764030124364832075986325798607979},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":298047056120497453580157310203631191895}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":302231701477906759697613716384739643723},"running_phase_work_upper_bound":{"denominator":85070591730234615865843651857942052864,"numerator":82475304782511724754053937373393657937},"time":{"denominator":64,"numerator":405}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-108087543034280046784099536575002449441},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-115460825712354391779633006374524728945}},"boundary_phase_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":33219577757001188685672704842399180903},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":32491301428920444712481076718160631341}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":95834564128323881244397602257656891233},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":760706411043011444525093672753315395055}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-391589904930480428437048848213719330099},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-786734885552347232638020322764245856649}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-134359996751333720592248161673748881255},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-285849410498812586512511188270615859753}},{"hi":{"denominator":664613997892457936451903530140172288,"numerator":546215041199557608949301518938695445},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":262684484276958901606701306962140250245}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":2763612617711848889865616232362615893},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-690770915422428296008449175593306369}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":76856203963474356223874229344709757},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2195507158826230174473383399298281153}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":66434241784123384598722943125903613},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1741440878610287041452307718597267909}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-34039781360958356822143561694491826655},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-34840098813092313914553404287789917607}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":677644589099349525341509868548344229},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":1578336974951564912465855970086103}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":36000152852291723277193113335336670723},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":8809265220531133473813975174029254821}}],"form_storage_rate":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-10094497153374401928192197175017441765},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-25506659547403333458629350998835891699}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":68126558586232232602976021386823567947},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":64028386628009388507401752745004498313}},"internal_form_gradient":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":81408330272212792869891394663826754083},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":162190642489185249516408461533737839435}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-655960119402291791385432621650633493793},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-658396624406070393465230028648701422809}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":224125658437531625392910610201574197679},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":27484007443673951851468486747150954699}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":451732611183298989585476604718783241},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1662784768923613372010888329310637277}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-105714722910580815163127308278100499957},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-215818636176362137287655417319627601087}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":269444346159930790546391496619358670689},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":265157243015595734221257601675023830201}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-137326538635857026646531071948080140239},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-69774294472416999907951178200127156363}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-213878254106779095433677193597775059865},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-218906796963106576624125716983835262605}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4257766525718781105247034729130755537},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":79335869526351581371157387998653453}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":14137226966108664849530283877863649575},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":27675122900344678741989741852618615665}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5522958067265779973527519849976634411},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5514468774630139307576042549175866731}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-11611920123832299362305724000099928601},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12511057932681980944843203888366330705}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":13875633642978662829901362378221671639},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":13239907186599009000513314080865048607}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":8917676603514729384161291446773707581},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":34993725125081244878529039892430868661}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":71895478025631233221877999829678057},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-529280830544216044456103956941408857}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-33650041417617947383526791000206238203},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-34348602758819379943984335423716422911}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12479236579890331437415716137608028349},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12468631463166147948136960716849699001}},"total_storage_rate":{"hi":{"denominator":1329227995784915872903807060280344576,"numerator":105404752278194212920730533733304003},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":6161068265279280005227161038872287585}},"weighted_phase_storage_rate":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":16840401299178831555118951333948897957},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":7916931953170653365964128009427044821}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-210957251944370681300887966577560265087},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-61103587556660655348998909268948251045}},"cumulative_boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":482036449270153575451946936432952400817},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":116209806469074869921658551963994428375}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":660768365825000380111519194876676739881},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":157736084801002617273849737093575602331}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":30938925246989675446612950421288242769},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-16171099828136089230395408806148838195}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":417468914224357523146016261719797647913},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":104367228556089380087460102671704699601}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":32199306310354589632803292081440757961},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-32019167098343518814410235708278572455}},"phase_storage_change":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":37638674029744146111819064114589930635},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":301109392237953162994084688783323819855}},"phase_storage_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":152641254025683288666745033549793406571},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":333128559336296681808494924491602392309},"time":{"denominator":8,"numerator":51}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-104443637963090963084441937868572475971},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-111832044467981452402097073343826344301}},"boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":66645378359863530856172165922154533141},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":32588813587431787762181939709647750279}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":385601521000730481069885136484970309637},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":382653585648600512137840191317890983387}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-98220774444950037834922388023441851065},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-789188879244622019471530241108688022701}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-260502365536903023845702159515439255687},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-69438481466503332714110127900538665197}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":271287396946704230777674671768276378797},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":63563626890171147246275424830258043989}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":11103638173221542268300364440349891793},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11091436865438067527857317819539635345}},"form_rates":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":227378428050510418738348040811132605},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-691662860339342879942399442684040351}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-310932349841760055236486706159810753},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1298016716493297932603092121775355361}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-8604039599356502363361572824669420441},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-35211166963750149261049077747764126549}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":682351541335038819343246608131509309},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":840900381693023846600120413921033}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":36362473133403207005983790875082243219},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":35603201038375211503072893810426373745}}],"form_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-18468938277759138129986190511007730825},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-47616107483042486406437346374266683327}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":67918967345486544205861909313845427989},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":31895264869620816936912163940730495429}},"internal_form_gradient":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":162412051557247495118674683567534033455},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":161775285350342337398785760002038989189}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-654416422105837156520494448248498243735},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-328457235289822859159214696558513989139}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":220955545181872510447781803486818706753},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":216638922586848465770520791617374473539}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":902549399003338305231805389682478229},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3369989095132668111038225931600405783}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-208056162023816353551042620496722658441},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-53122330248412937023092871744579615715}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":269074330326682370691839800639771507839},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":264716388101195434315647836317691936769}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-137108932652391542738351023971892172695},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-4355024160083080158355200840618515111}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-27030387596534055731679149803864693773},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-27654785864410273609941051073446960031}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4287341178847660183305013286116992145},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":169073053537770033739260081623975839}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":228472156924511489608995090929475935141},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":223701509652880125510869507507182195193}}],"phase_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2777351930189420069360543005063421857},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5545996333529456785985480535398628629}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-12271797335665759478493726426591714819},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13167620618402421476346858905892945795}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":14299801830852138768934029280845085725},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":13671592637651480365325624483703944457}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":35166167219259628048068558802735510535},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":34479155395799386651072344117939006127}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":143645198236000644848300606794904439},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-536350422656147650084899822462599631}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-33113166626818647259847922493491549603},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-4227340723797515603688186476401598121}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":1566238053419434009372983627261537297},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12508995592722613981805216922553826843}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":31053114309101170721614554512856955191},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":4084530790978371161524294263295690867}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":67990990864619446981586935534872416841},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":63954230646955971052534523427449446795}}},"cumulative_boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-107926523736945285097735591207574799949},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-124828238655539625988671968694392432035}},"cumulative_boundary_phase_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":242580225690386089230415003355276697279},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":935788854300242419578677529407514380177}},"cumulative_internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":331976033709660030935584485937881622159},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":316967260142768710341617231871872946635}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":15604475854143086450518706936740763791},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-8153006315671288236724980047765591291}},"form_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":207743497341372170803463970114221278391},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":51935874335343042341099733658693909907}},"phase_integral_residual":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":2022781667477204798400345814725185585},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-8046272228862326953423927180831620291}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":304201293560557634481914090567354105219},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":152100646780278814212364920477017207341}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":308362968135024719090092450690987843309},"running_phase_work_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":168193191238003468119212774838680447923},"time":{"denominator":64,"numerator":411}},{"channels":{"boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-50318019181879257428485049699686727981},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-108045376348673573317585452943261363193}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":133712329530691769139025814852449206263},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":130753905074494836378416289555355738089}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":48475434568401893781829100146095102089},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":384895011407131234601513641402434100735}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-788180627366304290390539672876399710925},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-791503497842312899003531705581748515013}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-62947037950908978359382092296893968305},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-269158611850272226352750673799743948139}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":262464650423014316390377958382425709699},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":122690743269672564363722844470046078503}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":11160797609801113572621474828077852217},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11147300748706709690903549656525595097}},"form_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":901354893233067037543608812311807869},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-509839548866704157995600740418942711}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1207894438662289884548355967862720413},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3504180297464247433292572593857915305}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-17390938544579775827799504878151261961},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-35571336245079566388818175376986298199}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":687200869833100869441063393434674957},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":41303754390675340918643988142462051}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":18355946023652822437594173418462691257},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":17978296957469380244535694072555934163}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-33264295238912212552964167474308545747},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-43994247599767418868874887662472055599}},"internal_conversion":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":16947272878174451419749690348356748865},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":63620283499960247191999810640874965229}},"internal_form_gradient":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":81017632727644567266041548887033378147},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":645517906135938861480168566290274315069}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-81615083574132585427761486069339987713},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-655547473985989872703153262510177759613}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":217795510142646068043415454726579294125},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":213383184088064711638195417851067620825}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":28197695683975656845434315929870187},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3412335463316317346642547663217282753}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-204691968479179703360636421452136334955},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-104583770964073411738320803946846411077}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":268778291268785208497253713503273625541},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":264353487306584709819632802613830387251}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-136924393653727283728418452252886652895},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-17400475486090528566541195778447302805}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-218540979082733578708457734654799865925},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-223501297251828613535932006986998234243}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4317810408416370908274333980204172729},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":259519142718845635602048517743172983}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":115333810355196968085990171824073371045},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":56480485645641536433285634084882537561}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5599815430517046905672890072631028113},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2795374793426508693321255349643535137}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-12907355642697313313034871598403386905},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-1725359572129800416230714333064014993}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":14704094868452389859433122719460935239},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":7036407326114188877694676632847679117}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":8665808005605787090534424478931149247},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":33960988520303365510294670150659435961}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":17951210607622913565641623422587279},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-543090056474564791432328441174300385}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-32577738594671879547706988521864820905},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-16645024116122919641747541010706297547}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12591805027580601991295414148156850099},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-3142310580705542147636777400815158785}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":35300333753401865052126250760251224995},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":20507048844111085691508605849815115161}},"weighted_phase_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":34282314496157038802545209117279885371},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":8062662055484813070047936689035896345}}},"cumulative_boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-110285180886095875289695827912247615323},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-127360552163711662863302877747750120235}},"cumulative_boundary_phase_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":244147167052073883400012962123078836415},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":941917943600609365033915792980421680399}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":667129681083977771512372038816080134731},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":636916721074598057270359454867536907265}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":245941491510009358642336649162627425},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-4110398956416261805828025890700765041}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":413676127660455929449972790464852977195},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":413676127660455926486356175865978783757}},"phase_integral_residual":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":4066421023681537166990291431688260077},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-16176158213806795845339556868411680519}},"phase_storage_change":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":76829907676520972714366521404461906571},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":307319630706083884639013279887955077357}},"phase_storage_upper_bound":{"denominator":42535295865117307932921825928971026432,"numerator":38933605427573695498506857419562963023},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":339671947133697476329692393624778438395},"time":{"denominator":32,"numerator":207}},{"channels":{"boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-48335668706114991052490945311089227527},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-26026383473406221194073887011557156549}},"boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":67069270251390906046648845776921559629},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":65579497276810050871710575295483192197}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":779876650922245311627439630108770848067},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":387072193884431082489689407869283193113}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-395210207828028489516445969898331557399},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-396822740949218410671328868450396871755}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-121291864010826576517405722397078207343},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-260070410694348367607863600714396384285}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":31650862353983613385982476696218271503},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":236078407203047659662096828075681338727}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":2806183895222767467037412390752589235},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2802644049901703662661989459048653051}},"form_rates":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":688887549963881141172175761410007887},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":423854009525747407588690839072362033}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2157676920439233127656580833128382241},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4464225987270083974629330213375300089}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":-549018407942525732515691651943419569},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-35920874531077520820243605040892937195}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":346100834133396993429762270187694629},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":13940840693964615157671225390515789}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":37048733422249077615104321838328238199},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":4537173303629544868830820145080671855}}],"form_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-14681917207249960283502148887236482509},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-20073500252777157641497507595418854385}},"internal_conversion":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":8466864138285310184079354158441919811},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":31758481949116947170570800354372652119}},"internal_form_gradient":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":323377912250798469694204536586098636429},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":644003950247721383555468598669581099889}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-325757004994397275778009845549078629645},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-327150094136660230956927411910774199963}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":107322960384248016115056673222999383149},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":26267011786537721275905721558145695613}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":451459940358078655338356196463787331},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3452513986875750705579470206187646111}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-100659080313760266330036111769011904341},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-102929918407160492928193647240976582301}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":268554176815045160564830125052362637627},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":264065140621910366504647583454777040481}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-273542524718085337843646065844397049225},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-278152745899764672593045797332843993413}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-220773401225958788138338176559473684205},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-225697511074707697000852681647406277429}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2174615675829559096578777634223998863},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":175185770836099480004390213648138455}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":116392028744144341437685955421654851195},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":114031602549970484238933383168963674569}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5653987103199107390434310083265606975},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5644441322803039551479471001230616963}},"phase_rates":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-3379086589559984256562326844660069695},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-3604135323932664129123510862710043807}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":15080617548897623955163498312742693067},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":7221402347585094522124084855483918899}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":34161959304817461165752016218149018639},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":33444198128644440518286189197838784769}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":71852081115960470785298602105009051},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-274742333552591391849712512213487855}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-32040780398038074574083507659773550393},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-32763610613090116913056771889049240433}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12660773476041590127090727087485909665},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12637068314361267070634196278635174917}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":39714234136036807094216329632223667863},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":24830134776190562917681604653029489287}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":69078068550536727661220627406696632881},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":64977135281744878200676619843867198057}}},"cumulative_boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-112550915356695015495281340973704922863},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-259601051228686992200494609310167207323}},"cumulative_boundary_phase_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":245719103073590857760481294445975435469},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":948066021470310307303138659414373229667}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":670304755135834762831401796625495854661},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":639894078757327771067600467400759343401}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":31753845275238023513601269516743612653},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-4144506452320741564112052406749364997}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":412046872803878802380707127607335748731},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":412046872803878799327942695424091088959}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":32699987746633081779730944479432796275},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-32521079455927040107287244912716609615}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":310461254081108626251467807268310171281},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":77615313520277154966759366367606447215}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":314598239823195819006793428948691388823},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":342982333537035659974324710383142398475},"time":{"denominator":64,"numerator":417}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-92554044174143649053129716330938052931},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-25004406285507992173913290478052202373}},"boundary_phase_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":33642046638718719286754450826853111059},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":131568221824069243585753063808032214071}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":392011991461120576546136855251620541417},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":194589290901707069929714400437710124193}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-792480163514428018034554999375060169351},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-795609668710886883329559462797829682755}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-232898729292070403724283896414531976931},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-125248787412187770438391572679430829071}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":243528541857222509025005696656954572899},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":113180019876269100821255460515847357719}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5648396221293727362088270203947835145},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-1410204283002729768988926068662635707}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3766517280805698071205540411329439729},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1416631472205109251143399867708708157}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-789611116216212082261910750139746271},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2737070547283861245196177506433881149}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-2217648872019746122887674192701673755},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-36260060742558147809175268379064507729}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":348672150164223916290217014923304779},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":17581144222035912798157688977489407}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":18686572416153885833312021834962996591},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":18312981694064882824878451123974786547}}],"form_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-12621878545694562312859348007236525899},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-36080817256513786149582249394663815197}},"internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":33877430590825850527729437742787661695},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":15869268902013847336439481372460021851}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":645502472893414870502785847411043710539},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":642553913907365323745048115518582996945}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-162549412971853160311316592439307302393},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-653181328748328473300003757199314453393}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":211510111249439841043256655692591044873},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":206901066564246381484078294145024535259}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":904456225727651641247805516895494721},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1745215224389796659943130205001315153}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-197931697220122736981807873653179657925},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-202570912535550623569452457264411831141}}],"internal_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":134198659174532479970853196439315734899},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":16490563243884158416577894791748540877}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-136648089819997384519401525277001846941},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-138976302047381020707344493531188136309}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-222942380946525632018902612188234893027},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-227828680895080680469597201416971498547}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2190771730934566150942647016823618243},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":27616396764825332167717109816729223}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":58705598623362720312423933369713622715},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":115063857510797204734387320202704419665}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5721630060824850031123856628453149757},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2855724876619495648866484389244086141}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-14096320493323111260533269037789398933},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-15010440522179378843469726778611689373}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":3857173543736295028619601415532987281},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":461877044165956345158300618628202859}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":33662879719265049374949806654950263915},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":32929327474685081665916327266910643519}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":143948679134794839038150808895532047},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-138879814860433718114553727644875815}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-31501808007150892432691840073600142929},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-32240162056668866992274271919639739219}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12740636929815993045599447040613584061},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-198676538182258089686616052063344093}},"total_storage_rate":{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":1384101050370414622990604654263655895},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":29298843937066710353944659644420369353}},"weighted_phase_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":34767495351621196280709022475455020219},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":32689830596790248251763454519542092275}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-229440301534053014539928137400422566957},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-66072344351804935183275837818700498817}},"cumulative_boundary_phase_input":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":123648037004890398863523954664242087525},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":954233281868313553096220834280374739701}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":673480764253724686318376431413882197945},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":321434783338227683721591435079047798749}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":8007315854522607125315571425724523613},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-2089438127021601232051310488480006623}},"form_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":205304726343663027605670902293095848341},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":102652363171831513016406831549444881255}},"phase_integral_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":8217618866519377612208035972155321785},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-32691736282001452793610472056877637175}},"phase_storage_change":{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":9800718533770824288333642086097307153},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":313622993080666370671398295098963465527}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":317746137500523363463238421559246011501},"running_phase_work_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":173157364681333911732504383577920551351},"time":{"denominator":16,"numerator":105}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-88295885911913989010714150631871442011},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-95786137038049505136476409620555082827}},"boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":67497968859542507738067071863189717631},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":32994861182518211095728340858185103553}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":197003842077648958951404049730299964955},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":782420412078342108971096872613973813097}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-397177921163671898686770310036179395183},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-398691228894505111418872247129502962971}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-222743798577499526583199256890811830385},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-120225225580621465541644374468589046303}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":233445462281461073704282701815937674831},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":108121192285160777480669901525734602899}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":2841601461094392004696790831860350975},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11350189815646570684426951216940317413}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4834111655396555104532025705739378485},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2467054511993877485893879636665247335}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-4208154752416934556348004160753600785},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-204120146442725555853647630098169381}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-17908895786840508105232800687711897959},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-9147298706409005531626583627145320559}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":702628170560569081842084234803706551},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":42488116438658916416969009109098917}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":37685407637600327458292186344905025427},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":18471306741109550568806235751668692609}}],"form_storage_rate":{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":-163392014125032998150486540016763559},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-15901402398186616805027268341793201355}},"internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":33921635465593663042543282582612678357},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":63505553385667713354426969170967943375}},"internal_form_gradient":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":322191640818592829168564009650495479391},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":160307327066744499742947662963407712641}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-649006096014805800465017391184199583599},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-326097802617652848032594041475139726835}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":208391291980852804443176241165028429471},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":203681398153926006683617348987902267463}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":907062793878087395741836324704539753},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1762995678842045131191711321585585499}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-194562995975993175260882739614618742111},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-199301654249031793777982461239988095655}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":268304227567179361641900666313538482099},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":263701892153899484965565955004053026957}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-136553193223773562073718328146990960545},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-69450892602919733710840982608754823589}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-225049821751373359958387882790813887389},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-229896691329967605747460401670312536537}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4414742997676640126328096252368821095},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":533921417874234323116101760701301471}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":29598049945455468476682507179918411005},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":116058643120146777913138997210059359855}}],"phase_balance_residual":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":723481718663858545691008010045046569},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2888504883963182422449370866559471303}},"phase_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-7323097213310262735064968289987237637},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-7787242344308509536323533133421080943}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":15743220942903986198990128022214105671},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":15083669629542448325410692479546718847}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":4145813027007396616304478035483512481},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":16208450666032884646589735051475037849}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":144363527340442588425199047936825257},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-561178953874726157449050478465884289}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-15482831276173927510224337955207010099},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-31719843440125255380431309353891861877}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12816542048168823653655631413544363113},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-1598685254756665349833262119475230835}},"total_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":24504924870096081450046292612864847249},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":33910569769117703666753896138706146571}},"weighted_phase_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":34962013774098193331677431173937715025},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":65713374565490937276808432822292549281}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-233579171186173982774805363211291540801},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-33597419072609788910796960371970689347}},"cumulative_boundary_phase_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":248878057654926325252158856325277684057},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":960419818340035717676669898191284446617}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":676660917578624092228614864156002136541},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":645846389491408541506671634337984719843}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":32306704057141671348401948320187542577},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-8427001356194552781930770529345689845}},"form_storage_change":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":102343435241917975392174474920601686911},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":51171717620958987290760802353415979545}},"phase_integral_residual":{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":1032586074887259695597790295610203069},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-16432092985246415262969863009848541989}},"phase_storage_change":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":79200413789450983926796080873702202071},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":316801655157803928976024064943428932407}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":320909223640265344026931516721620857399},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":349665841128296759501963790963126016385},"time":{"denominator":64,"numerator":423}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-83902553536354865844076380635857409377},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-22854112777689650728556692042046175509}},"boundary_phase_input":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":8463691349805630530101202767498274415},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":16548767389070786336234922720547951799}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":791840446832715003579100294302418639607},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":786323769385177832157967186849314344663}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-796042867115760357039814648051550683005},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-798959262368364120057053565795272289307}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-212131421416155184825479879816236276157},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-114970616839975678803125032461552728319}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":55743729517042548884967868494197138793},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":205742804717540569610210124138786236883}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5716706888561030182347988632867542333},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-1427010295513099222924630315960534149}},"form_rates":[{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":93072210885974134208480544945744287},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":893367751861805254429290236334434321}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-1326151316772598189871377106139335565},"lo":{"denominator":1329227995784915872903807060280344576,"numerator":-29824601475849859954825213841728975}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-36143725923874450001644434786231776753},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-36908592998384208081552578856632475487}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":354025905673391706485936772032400033},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":12463330510681911038404773013853437}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":37985825482921483317367303819410585717},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":37247647603185368786305897011305293865}}],"form_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-8191362313059082206143856183675697337},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-1707542061351946928016305189419041297}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":67997962918828508779212540132837021817},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":7950039088439797267155384816887277837}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":643406142639909841654252799786581642433},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":640038339238418796093176460937087394705}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-647947040183257800480308747633502547267},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-651350371315096846676368035119559083593}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":205292540574613913040823043521311333977},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":200480260925652731191025812268603245091}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":455434108475970050359378600825061895},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1779552123847344777991353883796659779}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-191215847780161496746344955545662892195},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-196055788069336388620992427648915897383}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":268271256418920558543249203251943788871},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":263620404474388278223936295842013133913}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-136484822440012449118926698146289229779},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-17356369241699400412900070003826903809}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-227097727671613869164660206520901407159},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-231903529236119015143690947517086061231}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2224410368888000976188262837239076329},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":156618830286479271208709564136863409}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":238671980555380183985904510290151460351},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":234033872147337249362304297076662399463}}],"phase_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2926223530444712920938090139852947525},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-730114110577451383935098729038562949}},"phase_rates":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-3791007791911977640898601486255796087},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-16106703863599990450226967235154054351}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":2002861802337604217006852384761225209},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":15352350623319270559276021449889983093}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":32673322612343291523970487388581874419},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":15953712259335294281649160296011013931}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":4530286851037568784603470578167765},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-141612258499992819390871776601899659}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-7608236842930031020387231153372677283},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-7800811948252981363216170311906646261}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12888210626701355564602695947702180595},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12859345037414274212908370762253977663}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":53861898628509043340255309543901092951},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":2416072688945059276539655805116312725}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":70244623254627207752543021911252487625},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":2061807375148503102277980497267677011}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-237512103383190617111246443553597356865},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-68266124681673780199495015683412293171}},"cumulative_boundary_phase_input":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":125232499891507440488276415922091805255},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":966625606110937262552757994211489928541}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":679848322090444178577640451974728871939},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":648827654149573465481854903644317449031}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":8146524116080963424513677667317111463},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-8496741705012841607017062244964109271}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":408349251887202198381929551579936722199},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":204174625943601097519162879720637538995}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":33216740819009002076300503203132823569},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-33038320142983979285181013803555618335}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":319994024839502086051418045439893880171},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":159997012419751039569587704964430687337}},"phase_storage_upper_bound":{"denominator":5316911983139663491615228241121378304,"numerator":5063815115392923469059327876866303033},"running_phase_work_upper_bound":{"denominator":21267647932558653966460912964485513216,"numerator":22064521561405378651522276483276062063},"time":{"denominator":32,"numerator":213}},{"channels":{"boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-39689938858203212763306573875321791485},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-10864261388845873216038255679655254131}},"boundary_phase_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":33958835115539147557996932845207538015},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":132797636628105427591412565325673019425}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":795489049527350995301932898219273563961},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":790057043658308355400950327393430600887}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-797536310901131677471884655776023643221},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-800342692580652191961108199978049605299}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-12567246342461129372114474805100476451},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-218983979962008261682530386028416893669}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":212135483609738512028744401472826838849},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":97439983477138657898950350996770939581}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":11497652925631209662818184348051452769},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11479150415115985451390770154605470877}},"form_rates":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1783030548785934127835648686437153447},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":2367007255780159720033903261921507505}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-1611360229503402880380165579607076333},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-4390756030480080098050979480759507363}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-36460519014341465533939593952470148697},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-18609293410877890266356046249110626225}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":713612851626871648624162657788052333},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":57251800418156319922697477914160077}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":4784340453245870019717337091276099327},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":37541398145919886714841601102298354401}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-11657221984294838752878789377857423855},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-22642329500850726847260823321861986941}},"internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":34108349315335842065371547291693533453},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":7969902025105117164076133963916644553}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":642578641425115499434360571829823300731},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":638988938843013572822976738175637755407}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-647027882512298779978509659058587308271},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-325326325845568860177578124380589723401}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":25277099165116284614208250095451820249},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":197300692477432465480431534687216086677}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":916001853043264131649235943818020241},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-448709748675965187949343912034113899}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-187893934564598501195550020996149596891},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-48209230290523088937568350321980115473}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":268294609557682887002592201463511484901},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":263601015596524380289387599594792353675}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-272882333121274356375825437035800991413},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-277643768288645127302328926694538992435}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-229088197363052234680349179549465327437},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-233851277872443703068910279060745893775}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2241880892178243103461241425464731381},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":22482729449808618406388157639803177}},{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":1878806102523710863295583010723031965},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":117939780620711400818836246007148055269}}],"phase_balance_residual":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":739488464670259367253385822432658479},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2951829936318973371752209503927230587}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-15647944476471639327498371329992744431},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-16605177473227362457739898076114895233}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":16267206581049019558346643740367949231},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":15584840281797290971548029782301168573}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":16091901116609109524751293823456966519},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":1962586280202331638283405238862374947}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":145786222793171377256909121527400627},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-571314996122415183803291078608324325}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-29904248462940980481413649376051413349},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-30690949213569116258998729409284084361}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12956078213162537782711248055458810119},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12925327857923185376761166290406021569}},"total_storage_rate":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":3677476483156311227863610496493112281},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":43530134887826979328613417339780547521}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":70496845714795818398696557321747220351},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":33086232194338853087937120330821267231}}},"cumulative_boundary_form_input":{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-7538532348473349009618951089200274213},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-34642324593439040406749301076689986623}},"cumulative_boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":504113640358111557036667876142605427709},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":486425247663939852235552729105565425663}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":683045979838756913771269034533325140701},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":325908183704493942209191726940393095369}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":16433680191774106053170362055918546539},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-34267813642585975641581551675664412369}},"form_storage_change":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":25471570690313985829420610586193961927},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":101886282761255942455470262000812988379}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":33392347276659341646118371893222094231},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-33214050541453104407692904997705437401}},"phase_storage_change":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":40399607845722766543244349446378475607},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":323196862765782125247259393406719227279}},"phase_storage_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":163633809640025286004564225339875079529},"running_phase_work_upper_bound":{"denominator":42535295865117307932921825928971026432,"numerator":44551364163404403706869037300553083085},"time":{"denominator":64,"numerator":429}},{"channels":{"boundary_form_input":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-4670863164245863356017567089297373165},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-82284708040893442995488263139935728289}},"boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":68120962974348097472033494645344481171},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":66599630498880069655395938166967670017}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":798951234760272717094741176836877641851},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":396805125145934650027128631497223228899}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-798832398519881089363215526679625490141},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-400764602919473569646371400229518329345}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-189593562838390565530974739170339223255},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-103797307235923115278620864800262683515}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":200946981339159437473885209049038622963},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":91836886589595101592428002224177539865}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":2889739716986790762094426325345840977},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11539231667196576672200782344601489971}},"form_rates":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":2089619371956264020308343157569176621},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":1486651294787462844490211290530149225}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-3814081359622962969006388225269965987},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2492139169798707934979383099254710539}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-9192129735749309908972672948673550485},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-9379880558744751903813684677580256975}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":179826997529325077752750450742818765},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":129354373822504653440046691870815495}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":38552448204305084030366715345691353535},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":37824218247675544962411535711755878463}}],"form_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-3372833412659304774498454382004991687},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-17775853632202831046559797625396108347}},"internal_conversion":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":8562148582865944915240257268495419033},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":63980082347627670398113649074542381007}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":641908029580367127893472300631941365469},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":159522184264070439929470228669313041525}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-646255696455509873050866211299537740635},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-162527279563678890455544476624340922251}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":99583418576672226592774011994706164001},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":12134099231618642112291139571456704525}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":461296681520499313220012758598088897},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3617623110782525212331662239251458527}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-11537551082003819881770769947112553885},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-189648529725863535026291398769155559439}}],"internal_sine_current":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":33546294656403895681475782774318809961},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":131820023952847399380890718430549060665}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-272840721216671061736126600558263379211},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-277625206469946049213806585761128655483}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-115511708994697277700259983845177335523},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-58935527709804475228927381162514105377}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1129886348710475127105057949400872073},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":406378750510488480351644265128026877}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":7569755503534116764839257371677867909},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":29707071543668623638574402922825401387}}],"phase_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1494511434692335828058703978283428995},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-2982532107214057276415787489465547719}},"phase_rates":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-4024026384042212360632453726105372461},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-8534020555899608310986389009414854223}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":16475031033066556355737056026860383889},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":15780030138028280131983975344123047617}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":7924596658233330520086311591784875743},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":30899229962874814500186328150349031783}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":146835294191750469928936798656616625},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-575762600324518176015342539198332903}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-29380132574018454555150125205560302679},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-3772937619497678982515159255213327427}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":13019898291416617436804112141096108631},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-1623398695790600287652993531263951769}},"total_storage_rate":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":7991806406035414219013465666886965047},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":24260462877218789473280983805909688775}},"weighted_phase_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":35340059036800961650552317049552851875},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":66296779386640409993121765237215485897}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-244736182524331565824819610171381804689},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-35124461554616150424300990118525547531}},"cumulative_boundary_phase_input":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":63413351312191765513208680775513243783},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":489547105343574855500649413707142035195}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":686256785557331643114484131009010922839},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":654815433769032931468295031181155364847}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":33150406010882180486846799176933061657},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-4318806961251771535930219711174607383}},"form_storage_change":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":25435634208936619285045869338117752891},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":203485073671492952501111381574116129543}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":33569479698228728783663935894388668259},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-16695641198994263681628439258823583629}},"phase_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":163203452414023398335239316149830907905},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":326406904828046789379786982709409368423}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":330456210772659356799033107696257527849},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":359798187226035316743043861227056535681},"time":{"denominator":4,"numerator":27}},{"channels":{"boundary_form_input":{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":-1093287643433455142308251984061856759},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-38767033375638249746978302222498281415}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":136635920326942530172509021351957900115},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":8349517287277151376539087953093509919}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":200554331135077137501709364943116908673},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":796973647668049373953751606279574614763}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-99990973071079841203525533256986892005},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-401257840888495634450749143573682194581}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-22212792278953140336314163737144881737},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-195790917842318171171228898823900870745}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":189430404194795229823118506007985990775},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":86072641389003540761549771550241627527}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":11617166336155092100688307394831110581},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-362380102103194053628173309191064977}},"form_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":4816671056988980575522651496899373251},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":1802238055327503286703038365436055141}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-8850137466637424954307234497266720405},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11193569992755085905550374035939107073}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-18534043444526223771102757336936103877},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-9452939639573671060812010101921627155}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":725132973435321451623970365370534811},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":4507678790565745112989488958369935}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":19409682720489987878515745230500682011},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":19048240482852356127431094817758995721}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1656207001585220180798338227486010109},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-6364736125854778257284967006663983511}},"internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":34418550097666891154629869430372472409},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":16065173353384046803117489705669860535}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":641401197957762591987519511619762008431},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":637345034172278782703160880464153718131}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-645637206720285002458446141043076820799},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-649726067246686070728437324226674750917}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":3064770346347006143671660216760872533},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":23877211358664191365035136657054866111}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":465386136966502627951226778142300801},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-910713031559203386830687641604042893}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-45334981043701319559819498221060553381},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-11655871698217696193022874003057821397}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":268494448675996116886508237631028889931},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":263733691857960247012891011787217534855}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-136420492370069492044426447969789950613},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-34705274318506835067354766665936072209}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-232905658906550604680339294466625916593},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-237578285812099143519214204173210105193}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1139036211110064283916812206609801315},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":56645162292735476129102303225267805}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":243909266572800392433817287762401919361},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":239367249458962631740295105048212666397}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":6038669059743261825984060258459507547},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6024937709822629737460614951526345585}},"phase_rates":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-4126687396717906966667280722589744893},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-8746746663651407039958301840203255083}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":8322661589997802581244418568126844323},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":996056073861680221760610602640260019}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":31217494404005511747122509190750721033},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":30401409719850850302978484111483673601}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":18517126036165183494912047960367711},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-579777922843409983922704291495472983}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-28861145312329749314619082271423314695},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-29681433549060334121257873615227412977}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":6539714307050379414941293807612557725},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13044694195327244356772380807574922171}},"total_storage_rate":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":17284409614814670340137847604931177831},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":6702602118984269588501064195553018171}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":70793845460843901541349728647210721433},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":33175144601791856611289223788876056195}}},"cumulative_boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-124008022727315965625872183061783687483},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-284630101815895289308187136781563594131}},"cumulative_boundary_phase_input":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":127627303720049209914146906598010615887},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":985356348652607574533703143379104202829}},"cumulative_internal_conversion":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":43092720289311744635014417579256771383},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":657827653772792440243879560500968463697}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":16717567021474736731850560951655866395},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-17417396587254681090925182472927981435}},"form_storage_change":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":101658171499961656099848386405679150589},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":101658171499961655181658987549671251073}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":33748037457197808506353436325945021989},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-16784957253391888838938229714607046201}},"phase_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":164810430740408734439912949218470441345},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":329620861480817461391419232853902370997}},"phase_storage_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":166823276920069460535359299425944058513},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":363190775987601239069295692283116463399},"time":{"denominator":64,"numerator":435}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-65095819925213889304455275445449636679},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-72668034258197336276210775385893984137}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":137014389247436748820739090974451276301},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":33493474999734371589001172854997898665}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":402638970437599815713879847939955472447},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":800137773041464429844920314786038601639}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-800819559290915871739914820072859687029},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-803299427076578225485546802002134968021}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-82711071380464184338247140766027865427},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-183592501590873910131151472399546882779}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":22200978691816241704387553731004134697},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":160316626477592410421387395092077580411}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":1459013692108660079523523468413166667},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2912445530884685897680586350756043307}},"form_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5477083024319844203476338804276097965},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":8518557940404177401024839046207317363}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-10108608338833955441851619594814383135},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12453769257547057735921490630537364811}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-18679798039645644719486884650600098465},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-38095667466089478574509210346626756335}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":731082579491812199680668118608177487},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":9947743765832444600575233838225453}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":19537930394483242262475235088522899643},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":9589644598398677998789180362537971783}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3602877851393578621724167406354829887},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1877884579260931756702108562219055967}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":69234063731708905868369186599597586039},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":4037425160795102141359172190308967543}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":641064650821609678571120382702443001421},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":636764773879905555925984634307105641703}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-80647345780884471815104389479084049395},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-649509397676799293037153259726180527935}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":193154654730122785169867162118284674027},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":93959794099037364347293301707700331897}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":470333765459260190689404445377041299},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3665279872210210512106051342951016571}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-89057269392689085579028389648583934761},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-183376352579167819514786385235016254355}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":268662725514755905112423919100958728259},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":263878018725132200475964215306627970631}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-272879218620421767189785761813260958575},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-277690636504629161280626269731198903713}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-234737265167567115015275939535707997597},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-239362138090132799232999851113576271085}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4593527321797906484629309474642289799},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1000056279505051916711794025541672409}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":245520874374629139454525116637032882281},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":241014056166930639274433467648940587591}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":6097584372541713544866301219619324061},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6083091301947713715724492831113385113}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-16878182476234062923639361645089271721},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-1117487645973795163218051534681454905}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":8388561591990782173524632601331573571},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":16054506773946806790377560204584158729}},{"hi":{"denominator":1329227995784915872903807060280344576,"numerator":120084055005888219173667575315003011},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":3738541420689623726267479876089209855}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":149711887351730807543326869821955611},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-583347409477485462615928078831464817}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-7086952321056511852776741933180634855},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-14592626479568394397322977839690759681}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":6567216375211861287216028706135276023},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-6548806133249592849912203339741726495}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":74440298491163872654225973446368162569},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":7352619631965459227057426106189773329}},"weighted_phase_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":35418710319885147016250903020006666341},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":16583123843191850210816960774598602625}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-251067412013626332312890707160072826685},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-144018207960874144723067258438888687319}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1027440979256367276914147397673512330673},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":247909093803764442301660215822354077207}},"cumulative_internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":346364435683205884561405243444982239487},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":330427861321694383424949469821850094677}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":33721435796045260954872672096778048511},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-17560358417549851121523928115449681847}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":406540742517685738358637094862700863227},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":406540742517685734566871923498992288595}},"phase_integral_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":8481978362348603523604802439108241125},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-2109364957183631473626136577877229433}},"phase_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":166417708649020207089124793077942397177},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":332835417298040406486230272783776470391}},"phase_storage_upper_bound":{"denominator":42535295865117307932921825928971026432,"numerator":42104405101487379174788951097943880659},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":366585256612978510064248458029812141319},"time":{"denominator":32,"numerator":219}},{"channels":{"boundary_form_input":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-3757266613892139265218465859478565123},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-33846284948505470576000154946005246433}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":137374375111116942439919250067972827419},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":134341312198219707322663745010751432919}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":50507752619527687606565166995008761933},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":401546739169256622488698121721866678555}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-801505252570181459224477563982492998161},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-200969544621587707932369080407695175659}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-152774632599487457720476468237180235159},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-85510383921106728512835830106563122429}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":10343895324749833717170693767641528843},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":148210912402103991551461669619362770019}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":11723622528135092417561568131334979431},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-5849962635848365024264027212891511571}},"form_rates":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":1539775043738069004983784395450630661},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":4936361691152856854949292242615223013}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-2850176584647096963143475996827630119},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-3436565583611384039671671420271885553}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-18821715364540000952734597797115643547},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-19185815966827038374960096629983280385}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":23035956452473479717280445691436719},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":21761835214121094956021278629557073}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":19661169007534318372225074296242055617},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":38610920717092495791013320085608330863}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":9023192842587780932652023187557117411},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2130511993464386135839705337129471663}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":69685679100506572156183802840310593447},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":32496070105731814833545382474116315423}},"internal_form_gradient":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":160226120284160261757240072434772951075},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":318177258622644441869265929241832179733}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-161221583602583075370631653013006570187},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-649464591155224561472055945099930758251}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":190197191246534621749549258367945680367},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":184853701098456685338186880764682306277}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":952407040482082295113333610260354361},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1842411923652624519871798512176411313}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-43731947209805814874634462506778554201},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-90149379757658974328738808381110213171}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":268870935773609541368819944691377763657},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":264068993588540874686775806222729467165}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-272951451033128947017605864919540975481},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-277766382694740524962758538271837688269}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-236520650868788016703992609264558007035},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-241096073978038320048587636399657097553}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2315826929904162525258928795731740339},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":546934573098515976255829440338653403}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":123534768230114281568920468898412972507},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":121299784873155736268239221836259902509}}],"phase_balance_residual":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":769324752664795691439862128197160893},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6139335949365246459882541764934555853}},"phase_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-8604393539931847171217545318286798963},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-18225312615548550507549996098211580455}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":8434779298664741914758930891276473759},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":16132015210101061360329416619413161821}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":15135411574540275711987485667266584511},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":14710190139325552036765811593756174409}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":151580288328246264973821612836321639},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-146614482430381434804625713468089089}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-13920311138948830960226409638476237395},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-14347719405099875394915572945246170119}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":6592340830205257729993713632417151987},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-6572861166009517009658779149319808197}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":79833423961619281630650862383575244027},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":64112386956823680177106238017676169057}},"weighted_phase_storage_rate":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":8851278889878937587249854899502265827},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":4140181184393004144559121459675352545}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-253885361974045436761804556554681750527},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-72802376283917669328158632850991341623}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1033880403089700883591018612520448556959},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":498966812112174658993695363168397641123}},"cumulative_internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":347997693787124007346315801324052019021},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":165975557303950281122635954812662148481}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":34009193397464824896332137308824062903},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-4426013515325913721537759888645537341}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":406701917477595272074241425155507290335},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":406701917477595268158524966984257988787}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":34108994190979770266479989710697303641},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-33930943032818693440946859813063602557}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":336047230841081073561239113399388547845},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":168023615420540532829763966728368180239}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":340018844454957797575636637543809712721},"running_phase_work_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":184989086936949879550237396634899981517},"time":{"denominator":64,"numerator":441}},{"channels":{"boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-27519017476782563949063337043362701307},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-15653429341661209597110665266788250403}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":137712910951744310244012324911701059215},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":134691671393086980850787872245140655705}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":12667921212508193569419864536425755813},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":402915982808213008281433681372041772433}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-50123927251448681449576028695038623827},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-804250104033959598096514846624289248721}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-69891594232319159105552489096501830617},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-158098853803239443864483090492185392319}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":38284462122672175586900187116392697637},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":135852125118419315621432025251796503697}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5885769824077124253043444708948328961},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11746430291063555403100888593877393343}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":13722504636702546504175935482293316267},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":5634277812122556124768289368959156927}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-3180865620171638496201096246167410007},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-7534029967376247096640516353581917999}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-37919984961539161280881093186114882553},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-2415002822559792151581650761311553295}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":371664933867950599800328527823080671},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":94511685130961626071070900489046733}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":39559218224257648945289989851440462337},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":38853935210621721737233064432458086439}}],"form_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":7298120843411868364842672153538682083},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":106407983579511594057771781945784403}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":70189520719173054311076259702867896853},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":4089901212832145413252569747270856741}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":640926347187081497625386654156247442353},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":318060208896999650491308350244413051253}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-644765456597221978923386275443676711857},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-324798346641258167821560536135074661189}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":187275032577911476573618096192764761549},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":181822279991126277661952840697241614413}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":241529301682802752995372871800005991},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-925351138748529897942946677987269401}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-171782635030536264590901780264489846111},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-177264005291581065106374868332014986835}}],"internal_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":134557373865594051145666569968968227395},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":66075622125082154387664055504897742663}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-273053657263339435954074919596198441715},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-277865244303026720613343229722543239153}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-29782286544851716846179757313069077929},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-60695641006019664097839525595961378515}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4670479303345959765874552564506382387},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1187668862743282960543044456324482491}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":248557898710166591466223141097205025731},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":244126474841485993693584210131576502309}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":6209516941251891483367813600582998767},"lo":{"denominator":664613997892457936451903530140172288,"numerator":-12096647535510275480105768377771259}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-17497029544437422409731469090864382499},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-18528451336828063888323873058188272637}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":16921846657883311407757357080157567217},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":16168671917255726982898211081324819051}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":465714799257349158015560062150313841},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":7234478656206590674284705711863483015}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":153762329057406770037547319372468205},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-18409275978442852605040074689762185}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-13670027751230412687896317662574402577},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-7053110668605754520722852815674407217}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":3307488818886853072604889817986366923},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-6594406257693044374939949128381044477}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":85307909301989554752764770449933121785},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":69486063482793093596005752568213567647}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":70711667615165818023079426142855757619},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":66081008008248722586157055545948466751}}},"cumulative_boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-128232634931246901066014622201248501887},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-294144523137232154112092781141488163443}},"cumulative_boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":520167847895281949066853345125342272055},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":502123648160450135107385703924143125241}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":699285521357959251613463302321675970707},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":666969655125425233550483246561101736479}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":34298280049479584299386622550609527003},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-2231052466112049361778398725479909159}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":407123412037672663737777087970223100039},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":407123412037672659692979678311500420389}},"phase_integral_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":8572789984381062255795454622761318291},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-34113105764673405076399964555514164123}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":339252934900465267624489924017655552939},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":84813233725116314876705869783517160877}},"phase_storage_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":171596959191943723224122991121128907971},"running_phase_work_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":186683020332569332291611721844791403815},"time":{"denominator":16,"numerator":111}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-49867471264231013177796082739902363179},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-28718799333758705729161760505854485143}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":138027034707175628100671658299405879847},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":8438882889614327437867793283031755059}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":813138424598936804981820963056935698353},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":404172410959252230529162722067079542361}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-802250723203144329220484557848635855657},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-804413802447976002068228613548598344849}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-126472843792489637338655328875832207623},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-72425780459847586622382578295966326375}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":35134784750040528768786021999301687309},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":123265018537988426628834959155478871075}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":11815695990018274345418076692185062609},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2947283940944563688154423406717227293}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":15163956194331591657389476624243746413},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":12702976696907058552785447968231961313}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-14073820624185077073485335517218476265},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-4104022124795123408331134659074757527}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-38189661708452252060399568349474086597},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-38901309476968288650682421612688983421}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":374806096360153901957403277874197253},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":101967413929496028921050478028109285}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":9946734706469504403634453818260070641},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":9772016294033298299265659285796772411}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":20313437898628632991769025627764873767},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":1135816888577987568497247220582200131}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":70743142136633168478391754131428873399},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":16483835144031942526168617486822195361}},"internal_form_gradient":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":320567725355779289862338705054541187181},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":636068197884340825930086603683003981447}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-644821245312282352259448250679115715425},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-649910296734185681144538139768085278343}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":46097529796182251317953248389660096437},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":178827398821255603054196674321000718561}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":981922463432487139739197654399756023},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1857472923387711485017246767896007139}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-42170465105904687017844201537174937243},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-174274740748454296675115189194434459123}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":269389763930898339623889419703410199433},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":264574295728871831457132804955908641255}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-136590886721401592272243137306342118335},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-69495751906776106645848738504613570389}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-119976360666353027329076256181272390041},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-61106034033933288817912912995852178041}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4709952315382910566825828804941327751},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1281360314025817102920744059141350471}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":249988709448409787821332529286185305571},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":245597556800758134485584066167505185991}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":6262149635192005516783326822969898923},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-195167119592716849320314301698881223}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-17741465305915382839005155689398180323},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-18787734570687018835078763466303076877}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":16933296232547585149985155930198357601},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":16163821270174786363616142882651415249}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":29346598925553343219427264087615696175},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":28461264482668606551876669775445406455}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":156277813788251169549562932165233079},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-591251994833015372549378233714640549}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-6711637974089018476194941483901826575},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-3467085805771882092818428038408043583}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":13270044064704881488484119331014869577},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13226682030239795557150467097093016353}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":90854571631016709036045290847813980235},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":74932881412704819365725108462410500315}},"weighted_phase_storage_rate":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":17635283433097019011069066305012276617},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":65846346304080918817747130697752899267}}},"cumulative_boundary_form_input":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-32350350947250578859342304472616240881},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-148418455287386016387100848094456010713}},"cumulative_boundary_phase_input":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":130850714130307844462615709279183649341},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":126322057311013876974146531601320008347}},"cumulative_internal_conversion":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":175650401536403482846471978949146674787},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":670060374214931222774139862339880898109}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":34588560365280460125013046847521178817},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-8996693640542413641348326707561062705}},"form_storage_change":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":101953006001359912531237803249622513875},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":6372062875084994467902440206022070645}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":34474284824938029596185275625073682127},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-34296201660096427263388153271759966319}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":342449137167435114003469612639047049755},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":85612284291858776415849414655457082575}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":346356997851839664456799735464890669203},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":376745338827531532926785811893588296619},"time":{"denominator":64,"numerator":447}},{"channels":{"boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-22305483658876666184796269970979174849},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-52170409877950831152326815882562027163}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":138313803749141927894957220883960127571},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":135329829406728643326701621651953012639}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":815290620161417430019237549836032780433},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":405312026628344293096879874253799625231}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-802307767938054691991229601993128460011},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-804368300819978244873433391233284304901}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-112870197745751480102320633880713326491},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-2051644825596916238999727711266804643}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":127731606110945300297592549547350141571},"lo":{"denominator":2658455991569831745807614120560689152,"numerator":863085965704833981169537980909928363}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":11855927915560391020549606417158109295},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-1478485221369076356794216230320503389}},"form_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":8319630342101052919167931588768403175},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":14172734118651395350747395097170954761}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":-241385169366197176700414951564611241},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-17787203600572653725200540303777134293}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-38452871596603443910016478921822893037},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-39155835228203866433700529116664410169}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":377994217135098104023916336276752127},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":218813501956386656640478808530470557}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":20002976221802716002176249685813507319},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":1228555275824622837579332936789279643}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":26166113384150084717348916590965215289},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":3726307697359508989721356813837556721}},"internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":35672039939071989591415848519936301847},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":66480595346540524849126126056369133157}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":641536516731216585268273140278522771697},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":636203126558146490282407113248528791479}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-645058362946493878352579401126867084377},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-162602381541080434935085815058540613369}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":90772103497493188410952315315235767425},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":21983868783993886222939062577176500579}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":249986201073413644001122623316007571},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-931343815895059502279079415390845797}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-82814030170910284595629736367770499817},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-171333420644377771438803423510065212267}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":269691535125715917042532792316660997467},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":264880141003512549263429909969884505489}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-273331710066088927362304770841763459681},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-278115448088613653441438565109467960677}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-120803258917321002809354304887633078989},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-123011684298097692038258909268288220899}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":593751927825524672740013208014558565},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":343711445126220085433585563566920537}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":251364812593386924530522850748309898821},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":247015694659815501938829763309834467689}}],"phase_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1578076794894716429116187633057919947},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6294745416516471899376872477819083229}},"phase_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-8970372417753423432911138453740764347},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-4750443308816459397342014882210701561}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":16903309397485190531480988773474784067},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":2014613002104785570267651087868068537}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":28893657932950323947566762150697784557},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":27990731082049930220516418987820713231}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":9946634901399563302912500132861983},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-592911888071067366979140841659936651}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-26360524518123459423722999552865446933},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-6817140203098927425589070821601696743}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":6652375281767901201654392982943159273},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-3314785663966407105006257834219909951}},"total_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":48232085046156807288841795867638652011},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":80443693775522967105339649605122138069}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":70298056708163529860334675144312088733},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":65538462986084931146454222349771911185}}},"cumulative_boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-130446973335512159164781543045354612345},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-149641199268900488992233507841703558225}},"cumulative_boundary_phase_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":263322293148300945892750448490601206427},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1016920044241551420949111391325495364243}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":705945859889901930410083151595330727447},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":673176652121800309876442649498773201225}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":1089996586720902609772702550834382447},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-2267360553738087562182450875697047095}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":408774144359068215404702115442066323079},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":408774144359068211085600851493468749237}},"phase_integral_residual":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":2166139814556894225696520432990140547},"lo":{"denominator":1329227995784915872903807060280344576,"numerator":-134687887057983141068370351861018817}},"phase_storage_change":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":86408105346139949537543141664501721387},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":345632421384559789581056334387210807331}},"phase_storage_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":174752300486404408041606290876012463259},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":380112520471403473694559144463631624483},"time":{"denominator":32,"numerator":225}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-39274959012576362634216999281407593315},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-46818418657803118139993823114583411903}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":138570309535881789285720295766180080291},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":16951493929064197514648381905978974125}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":817196194716132562179452118877730863715},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":101582764681288177100792046597369929981}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-802153260843950652012926745161104729181},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-804113050550659266288618382811467748099}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-99003313388084858956970643718878076537},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-58743917249652364944929233390633148495}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":114741212279946004813315964737563740971},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":48754015898661103575973429831125344695}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5946036800271389318291612247276321813},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11862510417921202530911796613476920039}},"form_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":9072482206395186904040635627477521439},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":15674412998251319775113677362722016595}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-8422381597333053709672660337129130443},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-9589101877466107754207611746009347743}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-38710031823336891026325916400847758735},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-39404039655249819089071606913143656719}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":762448482268370922027899027096795875},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":233643457895503078118454136415158417}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":20108362885755999514349642394896156959},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":39531518115244619367802667383984167185}}],"form_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":16072762281403207031270815677824887893},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":5213096798848198171231835232024520313}},"internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":35994928312945178925028068411491297303},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":67071869620066753565952229975680544063}},"internal_form_gradient":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":321066887619231752838079662781676893683},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":636529999048405656378582668355461518611}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-645481006337922438350518672507519446161},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-162774506259864224260083620157099450873}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":178738864026176144712351744233562431349},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":172954641707248196769727775718412279121}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":255075828532654735921970748873093411},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3732624373162869450422712848269797903}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-81311816427495286533631028953922507611},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-168442294728891344571971472974250327313}}],"internal_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":135007787042348141839586528925016557743},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":132607848336610431229364741486996405967}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-273499365191414342690643511414001644571},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-278258343873951914116250333826770114891}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-7600696974776392863890311097579451903},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-7736965093918357542911670349354896705}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2395302550635001822439673261053983119},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":734012570883828643633619604603669079}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":126344570235217405783048921380311876003},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":31047981724026081398551285278338241387}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":6359804250579689972168309449056450437},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-792687091966354499539710878951897565}},"phase_rates":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-2261702383356746046383560036781073591},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-2396159840843858612106363657049529409}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":16831382646152769794081954758476410903},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":16027458305464689553613836483359939861}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":14223586866198041372144204635083844087},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":13763293079198117158106684524447284033}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":162386315896930868175503341476001133},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-594065619694157987169389362273047885}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-6470588758108326316805615992274755247},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-26808423831844963630338228949136817225}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":208342044457794755072619173379797555},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-415188129619638570097674274930939063}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":102127423620009326301840859229555424617},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":2687791574233656012761803740218201155}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":69981899057202912239299227873905648831},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":16289235795021049930862594689721088927}}},"cumulative_boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-131367480187369417664021003966012602813},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-301477011912385499147279226141903213883}},"cumulative_boundary_phase_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":264946163963174560610942483206611129243},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1023276854464950495017104534540237479539}},"cumulative_internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":354660192209620270467152266504454018285},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":676320646010240938949846660278883226727}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":35172119999335625332578970291143678607},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-36569669947310644935832469748437623287}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":410015754097191065135146404428123691451},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":410015754097191060670430055328445207657}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":34842878971377302985917395960636355633},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-17332330412685027615098351378665416881}},"phase_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":174399674508543628534358698745982899301},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":348799349017087248263726569790230456483}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":352633230418198066127772772641676498933},"running_phase_work_upper_bound":{"denominator":85070591730234615865843651857942052864,"numerator":95866002460614325873480818136890322561},"time":{"denominator":64,"numerator":453}},{"channels":{"boundary_form_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-8466480536335732314013812021906773131},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-41387963313759550413303043523310280951}},"boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":69396846124269519625236685066373423321},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":67932847274816399180427922711764802837}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":204712075717317384639716887343482798505},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":814451955550849493693808212632316642459}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-400893462033781783582442777722874523893},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-803647921636495259043502221749624029013}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-84901601564111830478813127672973507713},"lo":{"denominator":2658455991569831745807614120560689152,"numerator":-808034975726532061073864602936837361}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":50797176531714409751879684763406011179},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":84390475361430133718505442098926234169}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":11923973602712155492318985344803735899},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-5946433190165039994179884585719433411}},"form_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":9838734046512200993972388347622391409},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":4301112410183482746807325685151434129}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-9129460921374489101964212491432186031},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-2573230565162150993692505283418795981}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-4870195628150743752354513791535713213},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-9911586440283050709035144540166287097}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":384490641885443460093524305721098709},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":248408415501990120055001588004218183}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":40419738379075529714966152353560429827},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":19870898759001336791696769088210359331}}],"form_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":19121428106860035766521955070786196579},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":1682449703201457799936364567432017639}},"internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":36338991888448167021698425168989120785},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":33853422962383733227013984160039469105}},"internal_form_gradient":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":80366368112699982877479023577280864541},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":637053118113633448982105206368063105463}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-161523223309546595547339020424040083609},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-325989472249613895419343283315966704269}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":175975467773658140067913518490733539911},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":170079991865174630225976191293417408195}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1043113703625650327685056351317619737},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3736629101170316847608006503715149671}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-9979423121508138922172079406163239361},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-165603399574977019993108235791357867213}}],"internal_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":135178684585495444438970717901368994363},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":132788297347075964689024146026273432283}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-136840318617190009591664522338126213487},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-8700234034674285656552595363435322783}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-61200683227774020001424907485303651515},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-62276334292426884025696429609558599501}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4831651903685332890851643306104009433},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1560796106461866143767347205823148251}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":31745588287931275370257150252436770431},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":124852539123010278024415762149462792835}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":6404460160684252786140986703883975009},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6385427034288061132576644374068809359}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-18198944459297132551812525440126246657},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-19289068189442573539745294822204664873}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":261204808110154196133898532073121249},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":1986890038575858305778937011919695193}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":28007365559086222882141491044388870229},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":13534535713185944959340279771220124841}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":5188021941841142352514047095948543},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-74337873994035224633602570730573071}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-1588274518993572362725131271510788901},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-26356599635179871851724137622263076783}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":3339323977816885172272772507697101887},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13307155562489273531567531527608372821}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":107835027147140788636643891931007732271},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":91620614540706836462850590517511381297}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":69592170933420717103599981789435339113},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":64701419289483511663868757438599099073}}},"cumulative_boundary_form_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-66080606368825446284229899421533181397},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-303417072692717978072902806307058383303}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1066290610176848509908635872051417025409},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":257411389724241133110067413073616357451}},"cumulative_internal_conversion":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":178181791227195639148147190092125191661},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":679494404412964413939879221293886926955}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":35465089585253287377696983569835976321},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-18431159063990526413618945179008905859}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":411542421305499723244673398556664519973},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":205771210652749859314215636162175114669}},"phase_integral_residual":{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":547313554537263634424937993184149763},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-34849744285317256565768954114114287077}},"phase_storage_change":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":43993307684820856056359615436218780999},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":351946461478566839402987696643415811377}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":355739375623023839945862385264474402007},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":386796205763884095968756650757530098453},"time":{"denominator":8,"numerator":57}},{"channels":{"boundary_form_input":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-3548796331512581695145688340522566009},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-35885453210134945671921912690605542699}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":138981155270769800547028840687983202629},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":136088306550846024752395709232883910233}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":205060158141192187054069798305371536041},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":407993510793525773645007539348855936215}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-801208904325763702746348102082146767667},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-802973195365321437143913328011061595861}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-70595691230076731143895286258669670483},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-44578824107116697652202884789620567721}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":44158867484670088275272937779344284571},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":71149005521166795746862581592088390479}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":2987867860950942950798840293736958945},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-5959398731174945207357030589093077667}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":21233042009655785013697067713141734873},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":18759146569185227690126839086214143845}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-19687859286386729768392429163252523831},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-1375428298038501459598123173008019073}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-19603949071815797527198925232885286267},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-39883181175438357308974543739360440331}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":775574869591369778966017633442033599},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":263091789754614469938243873714120115}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":10153870367113205430979817174972036917},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":19972551382665509639280163548009882153}}],"form_storage_rate":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":11112305825239883675674047263698930891},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":33096795312507198288559687976488403213}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":73405963426957742264439255878855086619},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":68383205067290708571422740570453430483}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":643931218926238626030100886573819108773},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":79722034669651110903055302094277958503}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-646897250784681828958379611607194480671},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-653054934324515750611480490036866890581}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":173255203373301615447810152630765918681},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":20906041039429452861014585194316682073}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1068487850424960604806772899468786125},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3737330053567101323646452404722124197}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-39192862354662488779593943366832892511},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-81409275620597538091697291448347936347}}],"internal_sine_current":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":67678099400692738186423660112097033569},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":132979219681166425622107554502662602435}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-68467859316601648720631146574831864735},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-69639676620178924618034002022398633185}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-246350489541459821962026729073886829359},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-250593417965095755923834804554434302347}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2436540312617109223812411234335962243},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":826527233912887250297783286774204585}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":63798649101651886175990918623789759801},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":62745620697226632399607078756537602845}}],"phase_balance_residual":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":805762486928769704971938458455074945},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6426367372258060756581223048132054267}},"phase_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-9127843827037351524428446421267382531},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-9680034689786188677631764565225679479}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":8280086025915169025664841002798722845},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":7859812221462328856549798700082792799}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":27574422033252571416099939117923030201},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":13309199087628891934129586079666035339}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":170055123028766180615042073521972321},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-594814551991102157991864802293070333}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-24950951110659181727119069370487531087},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-6478344314274311759390412534711653169}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":3343703244891723937488588383546694801},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13322406474940917478278768917916553465}},"total_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":56788833160138987415214075038232573369},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":24317094535932057376896141261471530273}},"weighted_phase_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":34564221509659220063865980510834711587},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":64171582831221031219024877069397717879}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-265653224099619003272599230813828687841},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-152549601655971526825637072982215259059}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1072805351830165844309277848958666238033},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":129503087283316929981317275145594607887}},"cumulative_internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":358084034722210600380617175243911049415},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":170674966787623416476041165564531732877}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":17879317250523093612656667049497545293},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-37155547005205402784316797437444248893}},"form_storage_change":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":51669912292449599934775481299086437997},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":25834956146224799669019895139784322631}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":35213654113537272287359564846576206855},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-35035201744020676326457286084062733647}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":355070282935651511376663415523510971121},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":177535141467825751039327950308238286439}},"phase_storage_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":179409757764429427387573616175157602445},"running_phase_work_upper_bound":{"denominator":85070591730234615865843651857942052864,"numerator":97526371169918044601278296675134826631},"time":{"denominator":64,"numerator":459}},{"channels":{"boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-11427428154228503156177047607133959455},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-30317370263708991620384380584186281749}},"boundary_phase_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":34782579389169827674521552784636478401},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":68137050724334313008877325610142092605}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":51335464508924906270484385407822477913},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":817261310372389375324206221092466660755}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-800384740918723407334907168866611500055},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-802093446989179213381123174844019797905}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-28058643590979661826237879328251583967},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-74706892357980555836008091812163857861}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":74938252204715550447905768679649951575},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":1806577173328810827440468475243020269}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":1496801774545828675911327900565005513},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-5970077579059196634441448933744024505}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":22807842479036270420828468208863308767},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":20334688854176588090205474735581641839}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-10564145349550003454541278698157555789},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-23437940987081137244227619000961122513}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-39449461291513406918801479084522341795},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-40114977018136789424387993135255521987}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":782216387268844267173724350229752729},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":277676735354050109951160749481182111}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":40804456587813947016383147670249684841},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":40141939534782806125108184006457243303}}],"form_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":25377835542236618128070721432614451387},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":19688139184340471673106718775890540421}},"internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":37085644917628171463725215316768524381},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":69098627151815598469235200244895140419}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":645137253198059925512348253682986793409},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":319351373338019007755398186135571997771}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-323948403031455551800521583779241245499},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-654328136076840944240816968400107965093}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":170579062540147441000926960572626156559},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":164460785690202907840931127449628031627}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":68533334333669505185472063399248669},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3734672828099540439002710550094689967}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-76963713828632647267150259107084630607},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-160089338828670119132806902267918548569}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":271076138311080018510433499733384337009},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":266356819709926814339703640770045401741}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-137033850367160982842590897248908501863},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-34838482400922196234393272500647061843}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-123934137781493435957834480684979632407},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-126024917099101927611046828704517442181}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2457405255761349821779982366045846005},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":27260849745658782506456512326769103}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":128190981049999937872235698354891376607},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":31527405585829836547438609318471280135}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":6488306038637561452584768686155496075},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6467906495590072715390159814126944831}},"phase_rates":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-2282866210360545222997097213760188213},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-19381325080240817306520095648058268553}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":1022548233815900846129991163242324855},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":7748543543935082723215830821666763403}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":27148500991246021411366664955696535331},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":3271843373421579822209159614858943261}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":87259351406184054788685917245132469},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-148597910355757542605201338867066559}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-1531144436817118383505610613107398571},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-6369752402724035780266083369265454627}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":3347514387890861600415040375508407959},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-6667699485133860763028913646486542749}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":119346788736523080799030432138131535297},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":25735015569488645714918572157826227299}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":68591117652049844542888989272902632523},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":31781891954636819756730425539761914177}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-266724545489077925443490829026997496539},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-306520330043054412633479663804314250075}},"cumulative_boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":539663542732817593499125320052892788867},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1042412546771941781695120450440707684277}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":719644848655448841835958589423769147991},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":685938865298235022082410062269606391215}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":9013145945554333370911682441256029993},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-9362296032243244599338524612280975003}},"form_storage_change":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":51933889879674742866572141028789532639},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":25966944939837371124694603871727984465}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":35399625591553228941491418146502589549},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-35220896459354005670716825550940255289}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":358167323708046168800653279163441125835},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":179083661854023079622561876142619465615}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":361870121882013503220917462801216341035},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":393388220167400164915840577836179186519},"time":{"denominator":32,"numerator":231}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-17265969624892029907147457708380416629},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-24690271222489238482354157300282547541}},"boundary_phase_input":{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":4351231244764809057750184491907388475},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":136412943155220549348710634600428980697}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":822223535053023249686380442053040306473},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":818269383128599012763977876819854880555}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-799227594864675806900566947986901016359},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-400509754450704552959056798351128014057}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-41499016321443672872306296030623154609},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-30054345943651495926335112477930745347}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":61482863387131039322199679806711634421},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":22200883928912916242640368022172270841}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5996326533163657555666839228238904471},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11956795207585152087974315928411183461}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":24397929473559461745918015895096233409},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":10963580811112117280124374495655934653}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-22576928180355575376935231410921018423},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-6218955380587649545445554065403633891}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-39686686624732613952555988696145440917},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-40342166767044202633796561755409688321}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":788892140280242200689833483446568311},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":292146194970178449739058372638319429}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":40987174304997216879821767988969524869},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":40332822104349346657632229260142740837}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":57153173868790160251445182238264644121},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":45748685596535504951620641965083161685}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":74971450429012686946742415601874761775},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":1091418625389876306601025954407334105}},"internal_form_gradient":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":323275578406613719782358514953077797195},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":319917629983482594116667546831910870981}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-649093778826583643421962751442901629143},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-655800178455040150109823957746124226139}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":167947843278783452776847307369282237685},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":80859152345188037041108613642557018799}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1127353074393430982540687356529567201},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3728608312516415903977521793611904839}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-151140233238162743078106738993680310041},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-78708559495721316562893187802292554337}}],"internal_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":135722042156126281359559751677855450659},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":133383660743335058641072476456224902309}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-137132699261609700837796626734962892467},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-34856357787213543763083111489557924523}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-62339701572790143755544153448731616461},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-63369327372620183352356778194951058503}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4956755504758275017922684814360196587},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1835608679785048044470311831962673367}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":32191251421995899000968200844921550357},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":63354648810783966285114703071815975557}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":6540366853216217008952164565494612369},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6519338865136517208613251336528427685}},"phase_rates":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-4554967422844027803539488365053443093},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-4837999256991753774098462054861522429}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":4029955154042249699280402255386112885},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":15218121530995425464483494098658749389}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":6682432359860334246451499624983730243},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":804320861872331082144244357578432371}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":89711907199779878451082413919217465},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-593426443790518072591183078308564683}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-24054715219915579280928093981294769717},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-12526856307386584384196696106649941923}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":838272594717683049750568031385440141},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13355475668661065972310812745134232091}},"total_storage_rate":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":31283758362053559915591391450578368853},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":6788622158682549623034227080470111405}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":67981859579424079410920383564048831291},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":62869268942385289016926991322438620795}}},"cumulative_boundary_form_input":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-33441735976905592418173545763384728571},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-307677686506608595687340014927764994491}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1085853932332782400584875916843646660447},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1048806903482342744945841261437602792747}},"cumulative_internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":361579567697154405768293570077553513725},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":344606560587202325501106570066414196765}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":36346761222630666720274964100331465123},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-37743051688637355263220121747424888505}},"form_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":208941097945213361017574044652697432081},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":417882195890426716927978652300604310377}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":35586316182424649421743888555092028355},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-17703363443959588286153543879069881161}},"phase_storage_change":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":90308521067614645707749502459396948413},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":361234084270458573010355688952678504595}},"phase_storage_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":182443831548318586865583583667904206079},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":396640811158377749582662776710818266917},"time":{"denominator":64,"numerator":465}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-11629735263894924863973274014518298311},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-2376357567977901061399738748543498729}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":139309349652486712395801359901703395145},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":136512339389205112582229695038226700399}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":102850547749456751756475466421422731987},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":51187899418350195645175763193015440923}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-99732293372538678721750151053422963767},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-799787374633327762325395001601608062191}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-836695743168456954093112637485906411},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-45396304789720804056155556473773283245}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":11994702859577578322491371610132175301},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":30946742605262674372959988728426414307}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":6003652929550518206961924755516428409},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11969838964657325432431661065956510463}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":25999343732051702502283898906081874403},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":23532538688510108600867072522823676675}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-24030419592895442603468998288162663995},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-26317675643532210785740174839998516011}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-19959944093748161565460602767974692221},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-40565198663560836678857241080959634311}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":795587633292901582993429327447353843},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":306482950900565782315705910580315355}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":10291038211546093339598377304500372111},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":20259135986467140997988658971356225315}}],"form_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":31816843592467125425839558008339946625},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":52204785483611072094299684910491160215}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":75804359712163322390704619990965968989},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":8829655233707052866119147061749378283}},"internal_form_gradient":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":81021810635367353877097954197067821009},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":641176005201524912607196487407168514287}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-81311234553199718352481563293450980091},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-328736087448450296491960598901770699285}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":41340537588799940034422915319858631175},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":159021631863612267482638612016044020439}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1161044755445191936189074215065771107},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3719092967321362011057092883406361687}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-148411161517659276123320264525730355577},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-154803011451241985242348406933969442043}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":271812305581699021535820649018607245665},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":267185256782143638753335340866071853481}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-274460180405471970710619556978491904783},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-278984991989102156932770944630440376375}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-125412027461964415345786096097324590399},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-127439330112853223217492868243719898025}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4998824528079740033809755407588637899},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1925689173999477534822902066587801065}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":32330250043205051360465076223200602573},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":15911488195790444751777448321660056207}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":6594671855369259554199825535288566495},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6573054733214568823084088898606818803}},"phase_rates":[{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-1132864258989388003096507152397495449},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-19271369315028627030474342177149115859}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":15840956554009077669618269109817246691},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":7447717742941319695311546124004848807}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":26318203629335257908683711936754084327},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":25309078769633540459922576180372027831}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":184786011980023059872569192047575903},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-591912029567499530539847799312910793}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-23620369965545149104343637660731498125},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-24637664477976440155799042317656748043}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":3358714967990849126593057887337620147},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13375775855364994793764306467592386541}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":130936338717345300597404016599229191155},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":114303838533226792738063779419592710293}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":67302651532411049745724900582549297905},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":31049526524807860321882047254550775039}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-268079031655739813948387113326508373801},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-308568820594600308585364916958468806515}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1092384058097742715228429105589039007095},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":65950369961950733412383329899532479333}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":726712464755816467273651419217183557247},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":346262120943522397913503910140492205193}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":36640995828755129090347365810133344981},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-38037015978877042276574930752672095327}},"form_storage_change":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":105149104280299904082997567283162237213},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":420596417121199611048689375138003088119}},"phase_integral_residual":{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":1117925163090264438699736755737451561},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-35592756356414200132084857257161978329}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":364267059854283729362873435358934562033},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":91066764963570929817334107012723154595}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":367869712559700426439762995256676200571},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":399859816210697919401421285308054596709},"time":{"denominator":16,"numerator":117}},{"channels":{"boundary_form_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-1488313399122470679633700406366285365},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13285800987850413134525793126627535715}},"boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":69671228552028503550120833998769135447},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":136569439331871975313107071001390204027}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":823106040283540031353476311133925896983},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":819468094100466815673189024484994444537}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-796272562977683849202070892566027029697},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-798456626043283693860026968288758332157}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-2994250099331608305044410903279866519},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-30603592502442531714915506563030039385}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":17226281714032269058522866210946726705},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":17474156410781574636489065830897417237}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12017340853661890385172431849368258403},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-5989129943481168386821881176489965611}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":27607967287186113306653554144452616157},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":6286695688039380931988796960072403377}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-3185695913575567724766835337532341517},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-27759933733782806722145462668826677799}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-40149583744660260142570393475158357523},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-20392248955200237237132463947078140521}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":802287623187953701930311628734023565},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":160334839914626610522402845602956105}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":20667958352352199608704421037828223151},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":2543676028313946819488139140137002069}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":70187291315299631044065145580014726705},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":58735669558827993815425192177457527931}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":76667183042280213307603756155902600613},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":71455751449488153793418506857274004017}},"internal_form_gradient":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":325004117538670198712120879474555766427},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":321363308480051705529876112041376461393}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-652086290973783480188526895949821818919},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-329672361717343049152158502084150974811}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":40705599128543006226027344724611831885},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":156371320144467122260676920415013231537}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":149712571498964664983284222591636889},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3706089090915913229143326445481725893}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-145741270209240463812931985186911872783},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-38061973889862179358431836093885185653}}],"internal_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":136087981013620057172321659981854356177},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":133803218184616164175550831614886190963}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-274648376515905220534398358407986045643},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-279105368057356208773591083266695664637}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-252267274673825708529316319954357846827},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-256256558031324807995425485726785369675}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5040921806146583207093878175283566635},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2014827020761146045308441586516773753}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":64930306124449477648140126882311975999},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":127859102778616931646011718435647794059}}],"phase_balance_residual":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":832108987694804235139315471965236395},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1658678612586839044219231116661280673}},"phase_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-8990124739728763807494423651661202463},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-19138851235993635692710087830269257785}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":970648431180331609716298301243609973},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":14528495006774655256114557824834559049}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":25913989251299066114172276133687611955},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":24887268558797211578071490122903977295}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":95309983188236131364596287357894159},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-589842398358216289176367089901342333}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-5798860891573051763175630400028971763},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-24231005153624885217129468978817719847}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":13462781162428264752101706326461552967},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-6700771372258816718167718760498228659}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":136746419506449826930682984201224221279},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":29996915190762372736342857212769168029}},"weighted_phase_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":33279564095575097943308919310604747287},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":61251991204221497129946236673619144185}}},"cumulative_boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-134179045209037638600409216076351026153},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-77297898128976449175261453377819868063}},"cumulative_boundary_phase_input":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":137364466971811923429531616722052951693},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1061607611859893233440935172345709835141}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":730306238960923352272445345286991491651},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":173968432559059888259018578197479782331}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":18467552956378755900974620760143495595},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-38330904909756812400816140187045618357}},"form_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":211808621816545634068488870399463324131},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":105904310908272815667702693236810955247}},"phase_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":17980686369398359941427972955131405939},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-35779259900489243723243812928131769549}},"phase_storage_change":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":45907843204720825131418221621122644421},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":367262745637766590676934808058372714671}},"phase_storage_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":185405979666817095310956741432571966479},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":403042005538255834400178620986504484219},"time":{"denominator":64,"numerator":471}},{"channels":{"boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-118344048500638637516993422020240795},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-3760935045626986667597416857631241943}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":139326847671588878293256556695204741493},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":68291509885616793202939287692999105055}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":823125220241933911890424828069205722005},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":819650882335329349821000262641782324425}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-794484654597382734357993117603318234409},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-398460381773498090730600283373463971043}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2858396843825127218237765950511902807},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-7882420416224909810907504945777993483}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":2616305991899108910734734173342479487},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":4011271146733460726621010816337558287}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":6011119892632943249269558483363665779},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-749267932393440573978086157653369087}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":29219668170277415003545753224198769667},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":26765802786321587386473725926342874753}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-26939179710368567126232572202975521099},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-29199250224665098434745135755151182227}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-10094060363574867004252026306775443109},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-41000494207957553883139066821022970199}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":808976175523529957216811075268299389},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":334689010334590283000099861946683195}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":20751497612722116374976361453772357193},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":20437493620588195722974592698492713623}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":76804409293649709679479621669294455461},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":65332282103994833455672302148315918017}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":77557257119291159914355667514810304999},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":72304039599637796516135338417829607789}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":652052843751688137053805531807368939737},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":644488171495605506305589316408540272707}},{"hi":{"denominator":332306998946228968225951765070086144,"numerator":-638558299579710590092784351146468539},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-330708954397309894733007083789725503351}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":160328804420779562946633146364866843761},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":153767730141232462259540679889259185533}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1237406766723084109951016250268689079},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-461195633137531807963300009852459723}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-143131376006678133413079815545114280835},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-18719050992500866384713516492866897695}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":272530487748400000773531370166407575365},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":268026589035273171623936154808431352237}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-274826235150680184632322828461561149375},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-279207721135147439663031253417691974717}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-253691407064789756376644111273739391883},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-257613702794540639345202902659998075151}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5082947219907777641237769111291085409},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2102913072208774440242799294119285621}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":260771009804455732456775681066080216315},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":256825119264912563081477321366661076179}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":6714876012250119617987214772135863717},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-418264664950430204130258719509201051}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-17782704195395130653509196708627309209},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-18953979551550686950294455127866438907}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":3794175984112412157321446365580280567},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":14118820237108292681341770658163656317}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":6379280435895197168001885967452571969},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":24472894339997771672414513582411664645}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":196939403539338658614166362241372299},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-587212517969876108955219038269325903}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-11390033001503765899950576922701964947},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-5958458990891524586280839533682689503}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":13483898277862642718306002641882498065},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-6713652018924284525756594468810212499}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":142545047957842255788989744312618224289},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":125662855536739031966709380913543834905}},"weighted_phase_storage_rate":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":16435159666048136527377530660830942207},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":7541321679093024813879634845653489611}}},"cumulative_boundary_form_input":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-33546148146577776509135706285752056235},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-309544180176433326701133071341682401185}},"cumulative_boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":552723340879550558053124667435755667901},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1068009940911669807803710730566928501239}},"cumulative_internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":366970867694195062696715383600874112349},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":699262982092472574747768156778254892189}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":37228903903054189845140450409943480963},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-2414052774792155067790909650766474621}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":426947705819093437891775535846515971967},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":213473852909546716117845281251734090441}},"phase_integral_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":9037359245352781419288314475081520285},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-35966057161937743934515300673733497639}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":370217642504690808087433221265506357681},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":185108821252345398711982938709761472987}},"phase_storage_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":186855275901443454390961741162190602871},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":406183699666628541358481178093256443613},"time":{"denominator":32,"numerator":237}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5559193862764333003479693323040635657},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-862976022065009067962513736050605563}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":139260356349442009720212099485240626747},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":136550897447565677912212069859737756869}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":822859288488742656636183467051307596503},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":819551787106488408669262022256488746017}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-792497322328124025942256822834944465607},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-397591033267664692482210992598497420269}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":8848664812690534768235335813226766401},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-914575519276641694342962909376685297}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":929811402596496273962904638895313585},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-9415979501623357797782710652993472239}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":3005468700980617993160871126710155027},"lo":{"denominator":2658455991569831745807614120560689152,"numerator":-94107803959572406626976930563558305}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":30830314891957257416035575348628230495},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":28385477378980829061194806484191520497}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-28388093052367911487435112133236948289},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-30632471936687963193194808538265908765}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-20300145405244295350843808293944763163},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-41213619324209098977596759611666071079}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":815636726048184175167868949803848971},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":348523582758260369817546202340446385}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":41665921170668237982871613304890086325},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":41047318972278219910030827512823892293}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":83475703418943417992821986766823220167},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":17996359957877958500760190243070919489}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":78472044875572769047814114761378505339},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":73179780659150964156103529732083811185}},"internal_form_gradient":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":327154094337246362610744058043968340515},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":646461184374573920524023486000298608579}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-655882261964312106501904384095227483507},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-663691306711626653716872900364844973687}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":19735176162445694592646991186975694795},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":151211032148566055199258963048562854351}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1280243281224916471445765343304114723},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3669495579030160114137075806203334539}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-70291026143002934678715247033590968877},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-36829235309362096116761851410612521889}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":272871542691917690317122308673753601151},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":268441397126612937199810066074481424747}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-274989964968999411142749399881405345395},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-279288266891159875643008685438708865925}},{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":-1992962114747502326381079642942122625},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-129476403696781644393759656149022141117}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":320299793318875769345408569691145413},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":136864890899518138179432948000317651}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":261794703709645548256445267284854401297},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":257907911465732395056280485598597353335}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":6768506800820105463746976619515203301},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6745443745979754078473166751681878705}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-17532890336496185557962224931826496497},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-9358210073936251231626305261895540419}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":14780168312808264479540425673712936293},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":13666742723558280793540581942231873379}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":12563803356170295613576632575937537355},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":12032991608235893309112434390114623113}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":203757046567132937386733092396058387},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-73002295007063332072971362924843597}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-22374328531321118733148579510587268057},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-11723109699559093437377626623153503309}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":13498117388320772544679876097061129255},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13498978436383217235015628834522647591}},"total_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":74161531395878216160483459242348837499},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":131320571775823125488676163973758614813}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":64847359372813014328144931717874454831},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":59335131944311291485635403001474936857}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-268108597960305133963547539661498920083},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-309625084178501921301254557004437145457}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1111974510962981210311884277034881990181},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":67150672764345278059740354458850231787}},"cumulative_internal_conversion":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":92202514061491574867818381728898480267},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":351346642155435138096292754867223160419}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":37522200103831042832404738317377948151},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-9730278573857018277163393922230519475}},"form_storage_change":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":107647600059049849430933922761846780883},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":430590400236199391870345938480766844153}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":36337611605781950342989715054566589905},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-36152963308737144723928187580654695231}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":373128263343373800356288332564982456361},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":11660258229480430918605330616243155441}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":376561992724167294200619196538800345545},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":409281226652110934119298767300435669343},"time":{"denominator":64,"numerator":477}},{"channels":{"boundary_form_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":2847227313874803277722609650763351015},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":4044607859114793847804543924302392673}},"boundary_phase_input":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":17392602386141506446969576776301859437},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":136472338839175055181798047943742180243}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":822306277966705604660449320291654437065},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":409584247241805765236966551882148493295}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-790328972682862736865645629935439975137},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-198310361183496344104021386531032369997}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":32505166545852688624617883743213207093},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":3478156429054873771876743908077563953}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-5997797900917257087040692446404650143},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-11391094276266930086249808200995930737}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":6033250065051229053384256849653085179},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12112015441660820596672298641818833149}},"form_rates":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":8108944870451744108045239094812973299},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":15000842346939858790188383619095792101}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-14914603419294883131344874378485097187},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-32056511671004265516155041759099153517}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-40822157900594936065684271681545004213},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-20712150956842683942465798796315553395}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":411126073410373632505238511171772927},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":181078055507758266384674343629481533}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":41825229273318860661924872783306667311},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":10304086940930793241802919692128732169}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":90191752737731443229296354221673541197},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":39342948315287434241995046959559111015}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":79409002816736475969771953957883651119},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":37040322374257095637361648299032489083}},"internal_form_gradient":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":164193397838443604095017830412668323077},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":162161402680172067963330528357748454965}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-658081632452703387708938139408946595059},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-666163990412236141834342795290294481393}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":155480062240145471947673476043187262359},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":148701208859850913302102646541605787903}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1326283416096099347548498123507600605},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3645861829881825463717130121444276725}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-138093627911593867437958484471884431201},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-144941643984139950385761506497397978657}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":273194853054657354613738944678590743127},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":268846590972610101685988106125223074447}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-137567926649327418067415558001894141607},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-139671658071746771177956784027240875033}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-64123295682095794091091852022440989007},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-130138282572119565077630025229976374837}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5166362607700991344466056063087917799},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2275493955637992667786195344136172321}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":262795666039534598008774361175425045293},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":258969950684629646689618479221523785995}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":6815933218748275507100058965399072021},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6792516327734525572179440263896480225}},"phase_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-8615317188681027214388267649414973365},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-18425969075226973937567678798449893879}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":14340901487959127474440264609077972205},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":13174313791525179361991877547545577115}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":24745420457754697424465185040225707165},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":23666532433785614612509001304635541001}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":211084561612499234028271634585233055},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-145064233013938831359448934624400665}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-10989141745811545657858527895537961111},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-2883522387492693468560656587711889903}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":6777037640314224459409957652443284713},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13576173701173061473803081545896640421}},"total_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":77035510989459148974211253586465571171},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":136953554643458203212843971267571639135}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":63879269241186854719126152951257601145},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":58267658012883334728853877348453417105}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-267574742838953608348974550351980791767},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-309435493185105915339638719007985470801}},"cumulative_boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":559248368428892137614748934162997593735},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":540403952556305389833746227419483311645}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":741342409498967121253630114172963638283},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":706165814533456878908588164262480616689}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":37817164823861786899931202492071365195},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-9805045121950192123547543501322551793}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":434547486172212750468880647746566511083},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":27159217885763296525654086863480789959}},"phase_integral_residual":{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":1141426382387572698013348497199441235},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-36339782474281422837596664649696710737}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":375991139850045984750289492576385104527},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":93997784962511493370828259853454465011}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":379362809156611016432971457518307621183},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":412330922324327396320909704063514570781},"time":{"denominator":2,"numerator":15}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":17235932833125057086936563230418133311},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":9808282308164296048711557627484792081}},"boundary_phase_input":{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":2171352144508711333004005837838438067},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":136344030589364055280188695025923117881}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":821464894629603880287143904578507092681},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":818499353295042762636592500092919100739}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-787966612790932807238179009953582894283},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-791103653947683930750473914051049610917}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":738241138661675260575933376251400783},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":28682322727140920474053115192474109811}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-9676765527911669640466349063376771997},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-36062578176775128832382940620915176001}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":3032618434480724861281528095559519537},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12177171676943110915229434597830881371}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":34031958475880951973064820192704960401},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":1975645215340789996374778201295204909}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-31259495378006897573022827378258341265},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-33468359683832952656902549070542139573}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-5130283048093786981599990385320972079},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-41632966486379817556548327656317346101}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":828804816443866665020277011286560027},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":5868272592180070174084298000066499}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":41981454784082744246974633542385085679},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":41382609755911266148389011217480066283}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":96943052294929877666408603994331193077},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":85424341763936951427720934542540533581}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":80365580607755005256013805909953281641},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":2343884257776333817892841687019010089}},"internal_form_gradient":[{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":20607744472931872142501535893677497315},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":651040848062006100052792655777728770265}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-660480957944201225413475141974174572309},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-668834539200741227092078177416246154049}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":76562217066907836218015285427814841505},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":36559514687113657535163097590202430753}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1375593517566960266295596652584945825},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1809325849324672866741130853368350265}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-67833093580776592551455489883756472039},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-71313210795259144056936900689881332613}}],"internal_sine_current":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":68374054832738567397241809719322678683},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":67309489253588181082718371086505688239}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-275260272047588359350371600773373133019},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-279369280554516128738163918736723461673}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-257876152555643089432108989400107198397},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-261587643321521803067882580340540172487}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":650941780649972144620794796160790853},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1179886212150735437328071433776926381}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":263777259873372857685701442159553806259},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":260014605591088280951362422631036512043}}],"phase_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1714692735560928513652671772222786931},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1708768347228784731209074249371826263}},"phase_rates":[{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-527371608989339539991039416870663093},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-18082552955304363561697320065883999265}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":6929749249648078092557569939878834099},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":6320152797555476066882211575611829879}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":24370510600546109008210433878639389473},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":23274509917979543509000601098567413047}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":218932508005949688043856225653790275},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-575926305167927010077685763547786139}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-10795972148595709394108701865748297437},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-22699700011639610386796213066512936397}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":13627960321254290416293927545784267079},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-6825480353472963378311429834986613815}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":159780273218782641745194180199192177041},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":142551509374736655642570077182104941969}},"weighted_phase_storage_rate":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":15709305230963191019696394051215245991},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":14281791902699926053712285659891102097}}},"cumulative_boundary_form_input":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-33345851060925108912253049868819367721},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-308975729951910713962355364744197121173}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1125010793291310409228509885839510501671},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":33974969735827725617460978122447086545}},"cumulative_internal_conversion":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":93138693261244454640625720165624087295},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":354840820460060689817713713396504565911}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":9528692795711250412289064198048748219},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-9880513862874776194064429579490047695}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":438820682151055667322228318841007003525},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":109705170537763915262680911014119391453}},"phase_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":18356672168568828181404685204148289301},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-4565790322189975272298933698383470827}},"phase_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":189401414896834619498277454500805324841},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":378802829793669227414690989459433603233}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":382109559438544043951362821994206393493},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":415329152371189029593082459046501369849},"time":{"denominator":64,"numerator":483}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":23093074713814165324912796416923677227},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":15578542738298071152214730667467674023}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":138735848106639923648434407673529874405},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":17020494978214675007963971249280328717}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":205083630179210893431541688236125015855},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":408771690100967243939032748201090393675}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-785411005010531628204866529508017762141},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-788772259880048651385968526888543480271}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":61889999868317060008121484131606486903},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":10840100538452480222590959883359340013}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-4075567128625953915147205540335689471},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-49233095855374128415864295520920387261}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":3048269737264617718049136456663224179},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-765056004108158712255673838143197521}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":35614793763652426787196885881842438329},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":16603666876007402141095306403506561251}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-32676018570645393210445404675702667821},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-34865094382841924157493162633485066285}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-20630513252687014826244494143638287187},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-41840032405642755616715549451558691601}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":208819173468875125279637952667387203},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":97186659852765657555412561737788949}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":21067566009327496970597396618605405789},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":41546639655546881748160517213211420425}}],"form_storage_rate":{"hi":{"denominator":1329227995784915872903807060280344576,"numerator":405156304262765499613502595580200701},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":46095699642896278771196074864374731155}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":81339220637708931613570134722116945419},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":75948392203911425876645387974410808717}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":662329113611328027881674649302951248053},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":326822870879770121371585417465054314965}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-663078890152670176618886804736099147113},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-335850524533369138701177097650013934281}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":37703505050486823455025383725951204339},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":2247206251292709501670869035434726829}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":714116346252866425813396751239360663},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3587859899690204014660770456264396807}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-33324892694341226698552626662445941487},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-140370938451591140573397153764990755291}}],"internal_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":136885761736350540482922034935005232595},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":134805672564046180546528512660781356179}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-275359682641302039452055720222709714619},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-279362677284178736940913074304258542019}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-129625337748856791018161063016592119269},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-131444338431526164998054038602970918245}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5248198250388086034610124190907428059},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2442567172963029490853824559104562815}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":264742842415685207747501243578724573971},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":261045235846416923093532710245784589273}}],"phase_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3448599627757889229275023766082310201},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6873299217149665779325888605037025483}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-16468745177518828413748122263748164845},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-17686228752671421591663656849847997719}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":6668240368663160368667241507661256075},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":12065001044810904354981816539617074137}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":6000699200675218765513919420495217549},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":22889854914575528323741676056127052647}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":56827573224433590501950253641496925},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-285512819078443863892725501287788209}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":-331488837519462285085420626221662127},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-22340728721018930758466295894644742675}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":214053902668386618653466353298615319},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13723366849082699438491923267622049117}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":165441952334792214809748347272821684175},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":148105555971371389534855280822831502515}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":61721938443524246908691682804290304719},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":55914156685578831992463131094082040205}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-265684320610190832298419111618511644397},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-154122742880526495938547649622079786977}},"cumulative_boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":565757018085654577824765124349603607267},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":273395429290829430721684447284196723177}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":748922322057348243294391861390091930177},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":44577607612792482982712198709644352405}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":38415026396991644471510728106540162205},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-9956684751634759292792173138058945181}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":443411262440618380317810608216690226731},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":13856601951269324182025126788104515783}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":36900529587043914751638589846617468777},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-36712389673616045487956038871829227037}},"phase_storage_change":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":95389981173253348585996129398328107827},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":381559924693013382438179030473068349017}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":384798840562105318272632447335007784399},"running_phase_work_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":209136157183314713963067534672448788027},"time":{"denominator":32,"numerator":243}},{"channels":{"boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":14476530601790691051590013879297139161},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":5337116614983425333606963632320824423}},"boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":69223616676619155859759521672704782313},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":33982629165689360439755799352829264737}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":204728803646017286895290371672692538193},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":408150130699999573442616098308933319799}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-195666521548266949432761673182102677993},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-393125397049635895324578672570873257123}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":19099817925479257814403938686944388363},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":57913264344364708259101217565017858435}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-45727451601004604106778104803714827325},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-31135251820990445013796927916629590779}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12253921511627168708504624901747653113},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-6151394891453353874742764778759995645}},"form_rates":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":9295073271185895855289437373161953573},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":4348589707195419849411209978748915845}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-17037965929671914568729825496374742295},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-18121946090473975291143269288525995351}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-20739427064820945920318286483345410541},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-21022956459014544165840926720260833539}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":841649395246296097290029233964715239},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":401671009629020831289169168906547835}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":21143396455857875561670882951335528635},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":20854484644146431879911533752637348107}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":110512968681886122569542830065644373177},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":98977629035860029007501017109428967905}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":82327357615185354653806518908354680873},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":19227645177581313131652587658653355593}},"internal_form_gradient":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":332707580748452722235896933236282445245},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":82057324121393333880430856282444602313}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-665873595027268061962986012041702227825},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-674761145216250149918585633995186393573}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":74274072536850831057105386849692152009},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":141450075535782536256142898331767003679}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1484252553483509100065769715532624729},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3553488102839715124783248268310808785}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-32748344533033161637754361800472734859},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-138174621152529249428287816971715271801}}],"internal_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":137008367569060234666556523040892034197},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":134981337559033498354202132875045893871}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-34428829997452283445684735120364012417},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-139660066298759500989119020262874886947}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-260619326826011249264811170106967252741},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-264182262273512740574284811785937266297}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5288239114008112134362734716116221601},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2523773386021053889455332378452963003}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":265695755910638291778133948998462120201},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":262065183009806335539342575456659231327}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":6931099293596651620373103633271208101},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6907079581885055255841574810496471417}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-16009406325661213766257404425528262287},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-17237182911804167071851213488311197489}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":6386208755955503154158203007786985535},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":11449069826999825227448371051192455887}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":23642171575611600502185145934427579151},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":5628119680560441551034140861883493071}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":118113065341834114514569525085239081},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-282777598392590990591152571902617693}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-2606030455254337287152376721972222505},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-10995586983137495102070957142783480615}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":13768243900363718201681560261277602713},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-6896546229965830439065468047137602103}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":171047227023054861295132612201877959353},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":76803601048444016472284067504864319371}},"weighted_phase_storage_rate":{"hi":{"denominator":664613997892457936451903530140172288,"numerator":118230973322595192823417543234831223},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":54629573061028003937067117900299670837}}},"cumulative_boundary_form_input":{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":-4130111654160514922067696059645742775},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-307244776395743599627043993563099419375}},"cumulative_boundary_phase_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":284500937558685550377845675964005821969},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":549976730065942238984596000757721189923}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":752781416945560056793789041963921055843},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":716846905275476223935580039540307142653}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":38717924763637003977661135482472368199},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-40134217435917480218542035987097880951}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":448320053643369628286197181459680091477},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":112080013410842405390728614539873909323}},"phase_integral_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":9271753666279508954510187570657604885},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-36897787107823532821392093963838651685}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":384259057851442456993443709834151743543},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":192129528925721222377205285175938746769}},"phase_storage_upper_bound":{"denominator":42535295865117307932921825928971026432,"numerator":48428411986810549613405537735985615407},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":421156844959265977575802664315716145223},"time":{"denominator":64,"numerator":489}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":34808541229032040445063495681208530311},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":13555544874138070009576654064532373815}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":138100858434203201649541124178954208661},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":135628890357438710846050441255476090919}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":408612661069115295129686622447455813913},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":407305907755225483957501092922121656787}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-389868025436869679613160420795223681407},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-391771528962566276038289878930825527587}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":90742368081458768493052806164585590925},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":36154003029668146064884150377677653571}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-58699799987136823530788937251596623291},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-18788115004812467019648486184777456801}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":6156291398261869055719742769090878827},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-6181214975220278670475406129104302345}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":38724549969806797606293270237734268467},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":18175279558180839756925512720721456409}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-35456495293009986292036181057746649545},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-37602036454042318809998212123604068393}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-20848074913777856323039538122760212109},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-21125507108919252855941942254668260349}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":423952136540811685635678595787130675},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":207163102813713921380416758965122279}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":21218482792072773153201893478030783357},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":41870126167317791621618504241522301397}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":117312171901201608821417256603011542233},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":3305422797487755139260761004818553481}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":83327418241016681352231668731193785771},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":77888499356401730690824462935765036949}},"internal_form_gradient":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":334351573912934986624297916059970434223},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":329738584540788280341863496395863247305}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-334431382464955166752513579197321476771},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-678011996413963686595887286902315208771}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":146325968367894666917392987869310476211},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":139123957347607835176343013673906735553}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1543696995333703110677442439255055333},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3515545027133123424476150460123375471}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-16093371312670348348819840211838016151},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-136036662745912808820786951442353963161}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":274227917014688886279216397487944868021},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":270287942362193723168096837214566921711}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-34433724427068368198935661722663741387},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-34904798054106871906773535750332982155}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-261984635962456702070637776805663501851},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-265470951746958707177646216346513600433}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2663769835260621859626311210422652657},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1301644163788861360702013582631899155}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":266639318639589073842540737011676004863},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":263077761544246680363446951635853992401}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":6977678808342073658183058896903802199},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1738406615006259670601315385538514483}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-15481390467969170795653505066214683337},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-8368799440861122446631594351954511741}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12167957003610983666639273218385739343},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":10793257399081639407091077160962667343}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":23288501168458752738116411591861390881},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":11071132757188899483899276326289777987}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":122843503721732669135199341115342667},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-69939546091295987839186811099573337}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-20490716763398321837421832740023379369},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-5412726829434277842689075782010937153}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":13851342720250861108215338639656811031},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-1734642190731330670243608500616739225}},"total_storage_rate":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":44147830706491427993354772006049412395},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":39758065534346149183163937963807206293}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":59279150924764103152001831421186107347},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":13314683154444108069077849925258778445}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-262695495496162078116470196457270887741},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-152986972031896577781823091122274754665}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1144477227973845476588704944051911766407},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1106311064367389417540100615949292821607}},"cumulative_internal_conversion":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":94585923709450964216521862679461970569},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":720497928682807555061712436240421128759}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":39023446844895063332844550924472627465},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-40444462715536179747433385603399533157}},"form_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":226773715731954731415455402460172123447},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":226773715731954727934135659687512671827}},"phase_integral_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":9318309499662469082312172123140656541},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-9270596650151588492899991639381451883}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":386896912690431580137174403006159683219},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":96724228172607891888848135313491207529}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":389991623189965333121143580343342021999},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":423979299291037921526992507811490637647},"time":{"denominator":16,"numerator":123}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":40652728095106226489232274017548085773},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":4107416357345600084817192868741090009}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":137702924551029953763626733399756072383},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":135263222622186435659517262441845509927}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":815346741141434545669119685796242423241},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":812545930347326521336571818757696781737}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-388312665835921565409158198111527551813},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-780653104009784607046472890122807303593}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":104890320696082162355158365770006400239},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":43256100122189092919537208739115196703}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-71500071461359296273410317616671292669},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-43928796967290339956055868273382726129}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12369941277532095028178963972865263381},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-6210349576735297173050355869180961045}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":40244223313403885307473216730810870687},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":18944479908562396599012954137974302415}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-36815049706519715377322825806268485563},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-19468492121820764841726103110249799057}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-20956653994006626975204847811347020763},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-10613933637209311923251610335989582465}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":427011248652730938505954635324240305},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":13334258498164454379614466655007653}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":5323273372253227550843889647018556791},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":10507627544900738295433383958938099915}}],"form_storage_rate":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":7756806050119122063838027824440743695},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":28142322315144721161250325315817037963}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":84337260318943252501869738984081988169},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":78879624665609057314691938268257915667}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":672189751401563936357712473064872249069},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":662698716507271513930389068803087653725}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-336021816325047746970924107092640365245},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-681450331010871278614698608441515055549}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":18018311341460126547116972365488566855},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":68420976497302204839313480309459882805}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1606602004394443698480693048208354843},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-434255813175121515633917156759795659}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-63279737704926434673027816883952975541},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-66978014031647351007235590405108227847}}],"internal_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":137201274118184018773979007551351374985},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":33822854149567024097960284214890647723}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-68868399409319234496362393713753812569},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-69778709255929151261152908538872016991}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-263349080925577672660325685909121104921},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-266757247522770944431918579462023554529}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5365981607070496047995892502500951959},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2681011746489646039480378783107577091}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":267576904309134469931384564819843367423},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":264085484013743317771804349454368149463}}],"phase_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3519486193822944084062204014068614399},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-7014970657669116501979620458120191277}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-14892253115139148330200934684174022131},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-16196458449160303098198742758828141979}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5761911411164052377388896318923322559},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":10098381209312050736409970586112418157}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":22941626529297109984727626425529082025},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":5444768310360020336914875865299559233}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":127849325290361333494596479939621987},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-138227918466422395200214286392385667}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-629455190831101892083754660625181999},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-10659882011615001434228814393038937415}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":13951278011843788009125571285178419677},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13978034157805515660902531480658040865}},"total_storage_rate":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":45518457873198756086795094169238162419},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":164377618488330664591956475936646117291}},"weighted_phase_storage_rate":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":14491233672722267831442982871475187639},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":51808329227751779946955174673377965439}}},"cumulative_boundary_form_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-65197474716675993437446858403174580305},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-304433662929788555531839734918771600577}},"cumulative_boundary_phase_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":287733013140543751417843736795006333075},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":278162881981951101677910121906563582471}},"cumulative_internal_conversion":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":190160174688264544673300011362643651937},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":724195411089007979623338620846745718555}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":39331569599810158397828074114855821929},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-40757482127324629665070887277085266437}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":459093317759029582489326960042829939907},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":459093317759029575278341724560791020091}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":37459402144640354113527814971946263573},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-37266410153780456850344219810984632589}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":389470231319386582131968257147625985709},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":97367557829846642299423026630573745289}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":392489710665860813897801427566166598705},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":426736641473167026048036326333279613745},"time":{"denominator":64,"numerator":495}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":46478107371897594470328761350416611917},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":9646538451260147046044240679641038299}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":137256947973362273257381072151019315261},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":134838802684971616355868142088623237533}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":813334246111986530565652069366421706679},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":810180217566950368335148163158988393391}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-193334644892190107188285490424835103237},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-777585217672000127177264947515861695587}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":118811974935622326888118801585747110701},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":50247414623576358936594057485110222319}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-42053892921663951822929666509026596073},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-100365570697559697053111049176478217969}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":6212741703364254550410236584248046173},"lo":{"denominator":2658455991569831745807614120560689152,"numerator":-97477190401925290181773365785579733}},"form_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":20867801168384043686091324356241900451},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":9850055819701547279997883845196632595}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-38149089288101195625141160217065627023},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-20123126098488461961862091129685272565}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-42130713975008438804500157389171901431},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-10665115836346817969798980347241249469}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":859985137389621225460156656768472021},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":438765712086093079250685887869574575}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":42734972576553945852374282744808967867},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":42190643075760927050843629655086587889}}],"form_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":65446605749723154522765333943110983425},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":14919412285260522321230953045926585229}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":85354271281633021242785853837550275739},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":19970393571919302940133307999790430327}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":675871166335177069075136947569791325741},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":333059987881691456666565806793516419169}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-675412987134228010058531581185130860461},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-685072454519948569045320758074791323635}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":17751070035891081068745241833370806095},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":134603011318994043763517985041676724541}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":209124437670580136891568031119885775},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3429015519236333718675049993332143495}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-31107448004569743734671000361530057109},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-131931460014355428055669634415051867553}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":274536810147384566455989006645700434073},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":270843526760332521028968708918769824271}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-275438910102591470590407528389541840185},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-278946420012074644232542309135883558465}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-264715083028758694390562744088752083485},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-268043596489210615212376525446272974727}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1350861494909821529784625350411285367},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1378423137736764371505726156029040325}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":67127937948931577109758438090179358813},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":66272907168519803409936921355389885287}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":7112680843844169932982059575317907387},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1772204030312097951242586590699396737}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-14250632937012889728262030628060695673},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-3904979803274483938981961546911666185}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10840810357874088052363800756598123341},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":4682663369695256315967042640906385323}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":22601364331059948023277683975366849361},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":21422734606472240773184029807657346365}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":266265503812686359049013385174564929},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-272872384912642314510820902776777919}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-9901808233802781365818400016644870463},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-10498772005307701575219477922735288615}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":7032733628308434775774955452712722651},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-14093199498739019465984715344963238341}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":187490423746629074091595015712612836031},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":169641855846520848261725118156472688837}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":56597212247182765046064347826390869181},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":50286557564436669691877493789060007005}}},"cumulative_boundary_form_input":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-32326404697955784251123846615549692817},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-37828117121272159745088304973917363237}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1157365971998426362230314684937104362703},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1118972096803662451228321806786658544143}},"cumulative_internal_conversion":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":191160420054846181640988908087302444231},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":727939859883742848924613616096706424241}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":39642255070800655751854923853549106967},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-41073264651372233307539501658187138451}},"form_storage_change":{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":14529911812011444584867565629966144541},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":464957177984366219247425357766625095937}},"phase_integral_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":9411351673154244720981356621924564679},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-18725144418894411527077489144359111005}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":391975823276894703548291600925147025935},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":97993955819223672562886522637919929113}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":394918325144142023460126250072781191407},"running_phase_work_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":214713056057341756652850534420198969231},"time":{"denominator":32,"numerator":249}},{"channels":{"boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":26138276796376982722538460556877262263},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":44284582017669448735254490077276776785}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":136748639663481054692268977458306607511},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":134356329636103625834796004053990076253}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":405519028823111087395406195588470412261},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":201883613299459735840234128511379970149}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-384940322091409594033814587600460619809},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-48396493631317998705088441912225406187}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":132474718571348917890666789239891834647},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":28556614010655689437547437928370553009}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-96503551623977698497821339677648561823},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-56328574758938492324491225239452417999}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":195156140538899017552202839325773111},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-391557689538510428477925380263160933}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":43194707662275208698445376928113943527},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":40880867240907546067741806257901896373}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-39456263172301515769475476055531878445},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-2595464552070491318949423807020685579}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-42348743325812955719814351463717776741},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-42865580414934367250358699012890157489}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":216443311251507153634485925399679737},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":112629887661387142211517250266660415}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":42883817318843819502920661178649052215},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":10587786799679861471988111341646511351}}],"form_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":68833331020580828450726169837238906301},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":126122143879015936394562992880067602129}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":86375436351494304660779683934734227459},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":80892087029002671042856867880351556713}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":679743121528701300466108868344337740469},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":669737198660885352746691041095421673455}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-339483595397266086082612414979660997435},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-344437134296276689966625021803200000449}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":139910879435703787220874621808647318693},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":132405929069195709606664036519548741735}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1742897218440214942887226258017641923},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3380482204068345443572663053301796531}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-122356597503575637566821671718520362851},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-129961486818196829874356585688428961125}}],"internal_sine_current":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":68656452556484681098076907807930347303},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":33883330068327700353671136995727957811}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-137681483968323079165350088996160813723},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-34841210526889650374031825839289647373}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-266085001842267538825075142217209727093},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-269332385046840658244871403202018235117}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2719906866185535642086590131981610541},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1415348910606630175807448031532217501}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":134723485446766487298954950253991355045},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":133050052910596962468763313046655675383}}],"phase_balance_residual":{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":224416782039854154742618110330813683},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-3578852765487197826371235482550499667}},"phase_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-6779540706479707915389613940492707679},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-14992486780431473086081667020867919323}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10119782949111498366908498245803497929},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":8595043398099636088509222085253987485}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":22267508054526465663486242848814869745},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":21073058106037373527897914102843203027}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":277390707615875083242181852657328319},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-538020452811662434379713751117168383}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-4868414328149880876066352481893178707},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-20684013038688222289615478412421129199}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":7093990348636618228590972596526423107},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-3551050568428773936528316769784869611}},"total_storage_rate":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":48207223087761577756808109831079924813},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":174820990982519924391232631492921653593}},"weighted_phase_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":27581115154942327062890049824920943325},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":6087355887937998499583704826606756433}}},"cumulative_boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-128080387066992965939376396123595149599},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-300549097188099022551241385568966556985}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1163776064482652036669014793255462484931},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1125270049755354808689327869476689328967}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":768690528798361022094929680033650443837},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":731731676463227349129747531778597903461}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":19977719941027993474902934902918560527},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-41391735507190784422768896661469043855}},"form_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":235569009578592156764156008007734233765},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":29446126197324019112087999445311943799}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":37831053420108217298018650563525341099},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-9408453410580674329068079209119614353}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":394410574377102003892416840006564226229},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":197205287188550995111497472320193062029}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":397273303511865858033102860339267360257},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":432044388019424687539267261476864581469},"time":{"denominator":64,"numerator":501}},{"channels":{"boundary_form_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":14510128491142314529236373469773227327},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":49947556714366271251054311900245717071}},"boundary_phase_input":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":17022166291472316377516785854239800115},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":133815089194268247750736694075925672569}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":808460919606859539087528137841305715749},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":804612152435937463773290429083266545959}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-766256554154046939409880782427431295961},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-48183364971373016163447729358490689589}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":145850185398892899486107157209073689509},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":15959829026074536803975680397810713707}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-54334557799753423852858897041202068185},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-124714232556920118754717915396349101247}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":3140092704557396127546179156565467947},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12578511176084559998572242507519381323}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":44618154400375916943214037047057579655},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":42327484803592913982767542619367096993}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-20367160803998285591971576177848240805},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-21389153796461144335404657581612277995}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-42567760992704318662324971253696078711},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-43071455163524812969533439960560959387}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":217841984135504678821122430082115261},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":461943393455556635985710817433578649}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":21516610086781112600601728451096949673},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":21256259776987802983896842091015296989}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":144416673691880906410346211398867871051},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":132860151508796088271351851469042660763}},"internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":43699074360155695076489300048734566389},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":5119296634955315665569198929522517637}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":683800901932326602352991563516571171421},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":168386541870952908129073088237301895623}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-682702198252290582850541207044732670879},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-692851291240091752798636117570245496999}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":137852011970174531963861531191041984557},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":130249357800981161856789066955269329725}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":908159305564831913409423811587141489},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3328483824312070085656419160527805005}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-120338354378344561888587346743518432165},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-128044430103384624893332271716239946125}}],"internal_sine_current":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":34333251605496920146097877113418412589},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":135624256851553519148216583479056089599}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-68810705234607789227390387318981412419},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-139230909021933640811651647632879326065}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-133730565214446051720921785033782249655},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-67656483560575859517239605246092488145}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5474966216028206277823760123250471913},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2902475942508632199301360657788495995}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":67596424178787586909036724166273033145},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":133557019116362197232589317141014086649}}],"phase_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3622386232571654149739941368446106851},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-3610736381923266952192459524234387441}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-12818471799175265582144408504696596805},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-14314899797600570002091711817542366411}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":4680833949454391092148535975292343307},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":3894270147238717637449370214552691999}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":21939829120216402261175432431990964663},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":20729829128571070628193681714679484301}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":144538042595546010299774319901901423},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-66218081705085208416388562913048669}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-19152443942857762663210988574142736361},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-20378903986338349979660576820260027793}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":1789467590293319163224147767255654363},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-14310581378904754399085744330879305619}},"total_storage_rate":{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":6189949582218158509612005878569269517},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":179907262917443034737994036382132004609}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":53661712939100165897237976715348753493},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":23523555704323473233321092456544671923}}},"cumulative_boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-126720062520948373952260486110803909537},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-149103902733556551793174107349321269499}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1170159376841954155310583587950802409975},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":282885658015334033200660913002874586217}},"cumulative_internal_conversion":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":193196829254906404627087637978304827359},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":91946393617430479484865553871967473961}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":40271044984774414841327467601614607911},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-41712803520623731480819593453830428133}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":477634388457105147133903683878711860601},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":477634388457105139123009986237781062229}},"phase_integral_residual":{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":594002196136909657284174593741220903},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-18908386154018800561858965818334687353}},"phase_storage_change":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":49596431949309091545060034262214646653},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":396771455594472718307941225338393243581}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":399551639846334180501110504565843808073},"running_phase_work_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":217294113951255159715829578487531309143},"time":{"denominator":8,"numerator":63}},{"channels":{"boundary_form_input":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":7970303377252429156855502962197961003},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":55568025152857084731163762942316089847}},"boundary_phase_input":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":8471408440762780945439938095945409205},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":33303634536356919695720263005625310673}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":805606196198074705733509228907732770269},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":801417425385058054728952795552409717617}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-762471497744923086557891132819652579337},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-767359912567368849878202322095700877687}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":158911513086508658548598006570309821835},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":70412197784463336996718609026433485497}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-30146850993740902587981528019401223945},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-136519905457343521296823880816673947367}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":6319113193269707070340193872808334639},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12631079639915210070928274404922938913}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":46002728483436769750129511615033462363},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":43736836432508242001825160572241292987}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-20990575165545953285995029905108358791},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-43996795156182889269818116584892994671}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-42788120629516210263385686843212885125},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-43278445865733897691994834885372057777}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":876750474848541867958088893512090599},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":473023485434866833384193032017499541}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":43183669552569138030139731117006793813},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":5334405765354552486563583587921092217}}],"form_storage_rate":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":9445960664901442239437283479567739925},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":2180486588785520280027834710980523655}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":88419794304169074737865672210092764809},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":82929119099026576959152384985151079675}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":688039371394535659462110745425318493711},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":169385553995202559996064876159548467119}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-686613576361568842818959316795102251897},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-696998678139231856209990145755932479393}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":135830390443445750580856543632555440525},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":128131811088687453066622143355368810445}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1893262804881321354994185204611813255},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3273064718796914448145756425550044153}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-29593329671611326618997697756138995855},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-126178413806317504495757112254907667549}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":274653988459444000193672131129056679749},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":271385576513952267510122480559094293025}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-137537808216628769467769178808152593281},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-139070059937566986478861726376488719159}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-8401427839412625333854267100558644513},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-33990811897643293046251506393589314719}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1377196425407770961012305026817946499},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1486047106817616207136673089152689481}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":33916374755350109406035068490618430737},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":67034119854819601934053170709299545855}}],"phase_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1825709391304261369550327654456615627},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-3639985015410043685157610384215708807}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-12029785153820952466132935634742793429},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13588010322400224082808332056280694563}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":535465772654714502943857732663949781},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":6946881918939811322013735481457501773}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":5404519515294133123676866920371302345},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":20392811102081535340303539755721646461}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":150661066984444421586045001600816883},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-260462214528106664448821944264683733}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-588740587473124796611619355198593999},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-1255119891798130198215073299909491535}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":3612597186653490460042102784625361663},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-14420374465592799662530207948412671393}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":203232952044898725354213226103318779191},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":184884587604631128719352825284297563911}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":52097581406475649523216690430234940391},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":45333445922357830797571403781544049991}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-250451261275427086970700158610783583697},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-295603054288072927739574913310721472287}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1176512933172526241019663541522761466879},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1137787063536903055245591201325053090619}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":776931994877633543886688005298067407787},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":739458451397210706673884699021918748547}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":40588975476522405215803298881236041113},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-42036361016546281062382541172972662561}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":484444372585660184150113084592433317373},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":484444372585660175853605305514311161529}},"phase_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":19100231630716943900834710478726774765},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-37998949854612149631538436004115655143}},"phase_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":199527765960351699580286308492219616181},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":399055531920703384714240406496727063189}},"phase_storage_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":200875212485987750674997921313378100189},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":437054481775315534345778842500842718331},"time":{"denominator":64,"numerator":507}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":69434743540228887001061015602565020583},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":30569478352286929225179981415443216147}},"boundary_phase_input":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":8427746869596125604857555470637438219},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":66277157425859307776881079772503572877}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":200619463042996012071600246058846131213},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":797954953904335718052201442651412013457}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-379265472356293712754515185970702107081},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-763627129875050140776549735118761641363}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":171633465026303594610816422262131942985},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":38409598150075793974034548160682510833}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-132242554985444071427197290027467921397},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-37014617350374940389586893543309029415}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":6355475450044312448063250191333263941},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-6344608738881548439160442296638305567}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":47345399595600169618103420683942920077},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":45105863020183997544431390708154996065}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-43194773783871461637968332116543232569},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-11295238632117517685725190994457423373}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-21505081961998854638700409525480232311},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-5435862372512788610775821286099056569}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":881902349608661800861951936616387937},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":483746765637216409228841652253243155}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":43335642086911767160419871079722987499},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":21419900325916045300697993155730550821}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":157800664685559324384752738984685355419},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":73091639290658861808257234181149611131}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":89437752518851933493774337353010812813},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":83950757080896841038266275771132395243}},"internal_form_gradient":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":346226498456259394890667746666928674303},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":681720251991623378055792117442821387647}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-690696525352877338862943928170777485119},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-175327811213647542978181097753790889709}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":66922161872166147115551490360584423579},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":126051671995700904816484265066921153723}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1973724576391715072971809113274252643},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3214276216901732527394453050433460247}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-58229774502364889349422472821199573739},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-124361373791468059955778947799269338097}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":274586413626128387043936995714514725453},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":271474351093809535358109026713948503675}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-274858596993206666451393197500360138333},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-277761995084948463635053689506454174835}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-270240830026647915444512229358370035029},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-273236244726581771530831077322717798725}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":692644485678537345383291058608885529},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":94983455320231406631585848126868735}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":136142934818838663857719456024789492935},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":67292601504523465792257045900232262043}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":7355386528848370374253066829524566783},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-3666526399566060109699302674933039339}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-11194105307410808298281406227621235303},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12812779323079434936808808895893626141}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":483636092182664038129290223293983647},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":6071198716423256347548021079366710373}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":21301985728702421932655021600084899779},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":20061746683114034473390115818488952161}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":157064011317349320386941824021110833},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-511567948382627869204832280613395793}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-18535112894355564018499697406982746737},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-9896363684305511584914599783994507797}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":14579341990981902814871505630312677095},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-7267637419470062321105714180632136121}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":208272613547274376818993628006206255143},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":189743418614826772036570474771499759845}},"weighted_phase_storage_rate":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":12617987215428763108560222255380224931},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":43560140033509048420056006409200537583}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-247196507671978857892525423504413348357},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-146368582846273014062357145026511835387}},"cumulative_boundary_phase_input":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":147854217915590416902913338515717443193},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":35750017095174292667177306329803915643}},"cumulative_internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":390562194763477364134604338680744894819},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":371696821567688873048776715349345289787}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":40909120558653910232888547304674507421},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-21181141926745125381450675811280634241}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":491565598001485628205727687950341416221},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":491565598001485619613781902234515172799}},"phase_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":19191906805181550363374586045984313611},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-38180129060359866169577564838877269553}},"phase_storage_change":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":25078748195561608612950893580262758635},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":401259971128985722956175712588171696417}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":403866854937061729537124504189113094977},"running_phase_work_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":219720050094672794562876638713524482985},"time":{"denominator":32,"numerator":255}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":75049949579442590950408288314360520215},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":33326680497258763749328885264946736011}},"boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":67040634319799399091225904805344660173},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":131835843182768581476801556850697620649}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":799080430316614440819621189522534652895},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":794229966005113110251888853946298238485}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-188614847996840073475106760193819890241},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-189934635774544073358007729754170179405}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":183992537570677619240788695843820722437},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":20762123287664971026930088930454613555}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-71809971582101877542464974727275173933},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-159315464830677651391524303232909179045}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12777871747136773502328948490937226941},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12752158455568242722332288037503427385}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":48643332469950452973902422984134630205},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":46431697328217974002184052181073189077}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-22186678687114877202126847089367070027},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-46328987165705504958072246613161281113}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-10808554994170518570166666057078918465},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-21848574255445658023463226181369317613}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":443402677869106349045356568808017663},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":494100919131087327652958974407658737}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":43489601456407631545298586202273666499},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":43006643497917739604547681580057869883}}],"form_storage_rate":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":20550303481207034200834255204707080953},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":152747188411576152069484341701428474713}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":90449397287701803841408341424571381883},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":84971195108001972605687322616825948661}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":697035874082415922962392884337351978831},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":171518695379467177113113504410619441165}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-86868237616426771743235697183522512679},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-705783489810370080485295027721161851225}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":65946002415614638683895573086860963239},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":62003600376933168391754160848425544135}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":257211296151088153652961352918849781},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3152176526041553267848779336230905097}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-114594916174681433713810632676882822563},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-61295534056040854691265021735648938085}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":274460070230488965530914256314542991025},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":271511451358783485311559397013501269091}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-274589097461780267267884997652850819529},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-277324952353431042547747300846129101983}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-16978038482803685811174535396463476675},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-137278640744638331706346810158277949509}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":348247648843906525789993562286732809},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1552263817674188473677632310055039623}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":273253224885996375836530848633264684243},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":270218710537227238168118821580944698781}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":7400209550214074479650442911694207925},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-7378511976346079058411056296824530563}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-10312613445883543307538711230976707981},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-5995135867875695848843680499491700899}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":6874712851216375485762928338256815363},"lo":{"denominator":2658455991569831745807614120560689152,"numerator":40349012713153863031515763958359429}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":10495632261595140164299521922042939815},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":2467044872370854651429249130569370879}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":327491593612152583247730814128350047},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-501684475617751746239318319504043841}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-9119173681200969962579624418820511715},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-19510974468953029434544982301415801113}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":3674969779412754186564593148721500411},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-7326234126107245272511162763291262363}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":213189083294937125721717699975477094315},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":194478749966826898587837772398467315835}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":48786655445280852115043658337820446691},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":20865780777625373259176715348519420561}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-243678541285442486441725034989677698971},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-289612789395928019023214707059434914273}},"cumulative_boundary_phase_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":297279700698051132222027284175310151859},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1150180352194769642606398875531101751543}},"cumulative_internal_conversion":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":196341051256203937581068673341441643291},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":747376667906065338563445023946354295917}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":1288479800961879998223471671041220929},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-42690431598455793296565442566235431449}},"form_storage_change":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":124748808035229369870845352590059612843},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":62374404017614683823248026976231680343}},"phase_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":19282952606557672259686500183200966737},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-38360082503069968790061991430095897987}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":403382052383069236801497182531737111853},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":100845513095767305383650530331197603383}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":405898239342731570900698324393443896229},"running_phase_work_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":220871067443069595162332056377443155759},"time":{"denominator":64,"numerator":513}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":80600591273238951272159900344138883471},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":36052153964030841223881023562046895643}},"boundary_phase_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":33313675374296103552914010679139903887},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":131057670076071456164132652571402418973}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":795419026436153897539187308892502732923},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":790248208032246689683141502242309431697}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-187561494899035090374902754041450572211},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-755701265563975843407093660059868602839}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":195967051900780001123022763329688009219},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":44544587191204086381207076172124775319}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-154706195461912034605822650960114546653},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-85138843515884854041838939015890190385}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12838325830100731329905002897757109527},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12813125196703408407586366781724977295}},"form_rates":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":12473474119686749831832944204316428633},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":47711673734758873876013590813587087865}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-45515208803737700080370757374082616763},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-47439238166439092470698932639474847449}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-2716287795417890491841671436539928665},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-21954757708343959469248309547823310531}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":55715104328842643352234057839895443},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":504074425347784079182347955235922901}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":21822998638559363583679645051310278193},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":21588110266807399751273745155534687983}}],"form_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":85465292988251933239711026152237640609},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":79619782178771603836313025673945904477}},"internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":45726049140503832404026258892738951389},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":85987952218341452701755002282624380405}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":701781753543357975994747054357234504357},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":345299967019399436275380182562251389521}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-699356237161640997798692296058512535309},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-710409617841873294130073370747165020927}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":64985759288004715481450394409369305519},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":30499135650594770184645217095789677487}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2145138342997601304275916468459925415},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1543415295678038115632821204871966875}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-112777113682587092192625210216628344913},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-120865087826085501198608473720044694901}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":274271844009023678425761809061911921399},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":271493582321958368854974923389274282491}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-274264541351371485127987816161402879601},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-276826599314975049875282510404363193691}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-273071033059854720300301542279022804615},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-275891622111509070055948542265960725027}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2800546599255694978589919216445633773},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1583596511535095120741700129212123695}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":34279486101099078089422754112764484539},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":67821048619088518291184601766533001949}}],"phase_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3719510165369392652787998745492061337},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-7418061426987684899972155934840959931}},"phase_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-4693291176573610633319613565473228245},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11121651123630105362427504844049828799}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5978393192589885815772514875622550265},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":4226769258659020635463343648692278123}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":5171402410632999623074252528639827915},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":19416352795289627504429794224428567555}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":85352342726006473254807664995512059},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-245642173550798969472533393557067999}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-4487258777555089869839981611666281421},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-19236276174757569684904715773589829407}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":3703300024543326132295871221471927457},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-14767040561024881201261007213712414853}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":217975178102306443141078184581383920087},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":99544126104699242141277467923493042083}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":47044592125802576661656132276908638869},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":9962171962963819152482221124773568803}}},"cumulative_boundary_form_input":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-29987548571188676325105317457630773601},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-286232899961800127658475861100493017807}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1195365116924885048304280513703579339415},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":289080920119896373028523148405096559983}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":789651022131737984612152155136960849857},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":187851838291575023539709947419588078437}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":41555532519432519918688535706769415335},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-2688790489893506050331650266047166975}},"form_storage_change":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":126682496430983121604763116071157177819},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":506729985723932477206003211219159989449}},"phase_integral_residual":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":4843314535466937388120098384371204835},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-38538589127001963232680956099052486043}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":405419174631583006606901225558395028755},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":50677396828947873864094970990771817453}},"phase_storage_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":203921004733006704969940957670546713409},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":443957763758584954145440724025227025667},"time":{"denominator":16,"numerator":129}},{"channels":{"boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":43039650603160115264466460920459917675},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":19371237344066708945644953395523134375}},"boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":66182235942183674742004459313929915581},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":130219897887170152559478936991345715159}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":49468703878381555771143361975281523593},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":196503978720108479588013501037608879749}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-745896219521502930241591350302859068831},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-751520705232656160461858344423335872465}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":103768614995412762385608267796024235409},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":189862537910955181551423160064991537071}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-82744599744576789189643728706899662871},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-180933193865611216920342495451636306767}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":6445832572016362380782655072194261101},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-6433505149814815825510001063445384259}},"form_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":25547336733068063055112822403207162265},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":6117917029421856934912531297256237493}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-11654694625291475783643633425519250389},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-24255098284589454034785535828388188179}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-21844810212296042328562036088720173059},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-44124307066119643894819988740682756053}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":223948480035409700076794362901845389},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":256828301288452199322612619610861171}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":21902632025260413942390068473965902463},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":43348962115727652979715449825737870017}}],"form_storage_rate":{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":5542973330603741327880126147543000941},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":165655513288280867521464277097102081073}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":92443222381590268643551357383073014241},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":43499266029510080974009456497447485205}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":706684068206335940061460688692916017797},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":347644744433289670725178181867522976233}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-351960884984472817393306880651623895799},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-715183564159072852852887722324049712095}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":64040424836113679581616480241124350175},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":120017735738048478241339382744150478639}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":559009613901510104294609432646520721},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-377288741080177915941651093129925555}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-111003668602859627220678364624015844299},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-14897608534909702643231847048574309963}}],"internal_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":137009361202761124140716845698895523233},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":135708769383365569405489775453375260211}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-273882436686624202321905501249455300761},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-276264637632176532380424501251085243225}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-137254990564025076398198823508614183367},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-69310299461830838219194792479668874513}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1407109799323687185790123260866077559},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":403424952280873729339693545705643657}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":68809147864838651126185349493173253077},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":68092390461756127550118534437525092521}}],"phase_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3735880835239950945573938809299314199},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-7451643569390170807346854885844150857}},"phase_rates":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-2104342590465171666422742486955179273},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-319005437011349724456856073368281187}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5050403888753772547095752477050344111},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3258713944272368723446156779199816955}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":20384700340744946716858128599675601513},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":19101415901407238609606235184247172925}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":355876573153268897721783852792666909},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-480378944926628401479477356942769731}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-8833391279739866502572999704004969453},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-4742056077157775945598859175045201547}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":14918736491942519957180743374809106769},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-1859245443306211970354301578069609443}},"total_storage_rate":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":55655895938844877074809873487061839857},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":25446226193029735531263428480527848871}},"weighted_phase_storage_rate":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":11312109294014946451768864306717832329},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":37914296255957016728643150747120709895}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-235865421325463149794798808949753071525},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-8831274779993363116598982260588513441}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1201569701544464767811343431764260269001},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":581213869096523296507659084395927785165}},"cumulative_internal_conversion":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":99248037272609378556852328126786549675},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":755485409356566664250153176224988015485}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":10470374959081302501891231984457171189},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-21676380311153816836278349075164442995}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":514766116233104254526550671823984270129},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":514766116233104244987463117914210439885}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":38925424719573594483469466775037173481},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-19357713728076480325120269491517348283}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":407368864731745159043969010552600346411},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":203684432365872571455474858278118778475}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":409695726122017707137632048316181834213},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":446084292187898103561190255539272253515},"time":{"denominator":64,"numerator":519}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":91478825965955154646726042098892116977},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":82788542248419990824894952574204424831}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":131410967318901539746457386904945790633},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":129322782084798784717569621440282417437}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":393663627543222622979914166213335235153},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":781539778508233700734672316007317954847}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-46338480670835495987969186890765675769},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-373601178767345564967440575530842472481}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":218685254350949465628622174630403004973},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":100565779028429356998049991738772858503}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-175958104214599175909024065512980884269},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-23908913246411403329704665294220431107}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":6468631045732384923096833345248826417},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-6456592908003671870247448872556861467}},"form_rates":[{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":408152060910192332493123468243172007},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":25062222334536418164186222372273965089}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-11920664801214001947943326861160027847},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-49540494798946683767102527312657453015}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-1372548598509442935343065147109899407},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-22170908370339076668394294736976828629}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":899845261587599092640137030513363025},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":522837648329509744742968392655089513}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":43967820177648541660327308209098364941},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":43525282120732465923073586297330007295}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":183726228108524132792201539387024242129},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":85992887758726912048475197291391272289}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":93420135367506013190719250229004150535},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":5500026485539960757569557507645135279}},"internal_form_gradient":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":88966995132316970280928497559392818459},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":175034225583022168846965445984167472817}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-708636461089992143837433585800339565563},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-180024754639362191219702971296257617251}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":126217890563794951951379454556601035973},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":118068719330539253437190037563467905193}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2330352576846557689755803605840918541},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1473346215871091395897675171078722521}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-109271953016275816604243991191050025331},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-117535700766346292601330247619144793707}}],"internal_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":136848895916300124856105733329376996533},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":67820050839005794609925316970449436277}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-273440371370204922068441054828477819255},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-275636857575431561534231183550226257795}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-275967270001422883818161558425790971115},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-278607851438678792910528179591276062905}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5653894526342374152589470827434045253},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3285085830024303293949738195220041007}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":138128980864457736346967182739204465147},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":136738706555916291019487833677078178171}}],"phase_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1874599103139800316147443346147876993},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1869805082649213362733722719716384427}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-7406415062535817339763158675521801145},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-9251183753854599822150553160361026045}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2045984351314665262503557864159439587},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2261769164711336245896693854644039575}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":20088201189859858874909698543838678041},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":18791220305984937646740536189280228953}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":92721782938016385342123632143589813},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-117245166570811445836586584768400759}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-8695585731922819238239631530784177433},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-9353193883366941601990239252231098853}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":15015946905157330041177109968407174735},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-14972694547737556121823458517297274571}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":227127271238376105583641683982894017003},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":207917098737119138271359970486540633039}},"weighted_phase_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":21700521564925986395720072297934887437},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":35931323219665314174409575903758088461}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-231577351358309001920733525726367503541},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-278720080041892932661250481436916597699}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1207729590637538277486958621775429602937},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1168489743603271536048954244796868808647}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":798363367026226872823133589868776966957},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":11868912956573775544036411630558154171}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":21104541730015640919670313876502446281},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-10921645757264474195417047335221148341}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":523099432638859983996420490671810161807},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":130774858159714993530182968700381217513}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":39102408673769503409642817853738415635},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-38890376166002492616935429799330167643}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":409228785250814166635463472781830257325},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":204614392625407075025846423810188784175}},"phase_storage_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":205728543607260015877884023425493122511},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":448119161416816642668628277419707735993},"time":{"denominator":32,"numerator":261}},{"channels":{"boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":48396027266764860332271280438459550823},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":22002118161247195833906502526500837445}},"boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":65197366344455390548180784432383541143},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":16045840665640649852656753062961744359}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":195727397186219281368502231582092073549},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":776826915020919384563547042504275173687}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-368405011781598864020733538668379064913},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-742751788934284638464517822909209835867}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":114697655723821281626759157407187716331},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":211969404214619005416168049767972458919}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-186103313503692661238728847965014549859},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-100641299916449478108403979681033362865}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":3243628617888893684932088193100171221},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12951049110528331224181271196553392629}},"form_rates":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":6667286326878887645984398018705480537},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":12813244791144150711775452045323879253}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-24352792371577210987360346074277191117},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-3158056707063438640619662499171179681}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-44156682389519423709635457757339509195},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-44562323184403726951384722640136720963}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":903579435405354372945252131185486415},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":265804337666366004893312925175715251}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":44134067040956277216623602705237346471},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":2731598565586378753910784183526879889}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":189974090278335387538335291138271047701},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":178221209222772500670085616046628523931}},"internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":47190101899885555614862163183131407457},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":88991103161791029462980928259867013037}},"internal_form_gradient":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":358465156667929735096027269168255431283},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":705135335591279870344353514981417534681}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-713494022305972731368421558878141470715},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-362574724857967714572500492231770100769}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":124380449352665531690019784765324347171},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":116147341558257512245576983900457393349}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":607008658179158048447417448544995183},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2872062155778930018202181445132106751}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-26894798953301210127902469668662658045},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-115926744479887085622559888316425707315}}],"internal_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":136653117203007401300336657596612062069},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":135539272119727388175647891268202377695}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-34117001018746810599081158839988782113},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-137470566096281862630667765796059620009}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-277444618003624036866531589014870474719},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-279993334286033739361273484010897041139}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5677357032408548832644393823558944663},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3340195818019824829165831689397806457}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":277302521577815329849178030349790090067},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":274610239558482703818832521745421292065}}],"phase_balance_residual":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":939863381787825172052951571646551445},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-3750386386339875851369674364985453243}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-6355226821722421964428960112547174467},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8252104556450288328560500850673436415}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3104345455149957365504574216342332665},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":618612655693291411956019201798914125}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":19795763338467852750537632679046840955},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":18485423535979404491925908061888985897}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":386433713795166589786533131603588037},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-228551444479690921901183034657491975}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-8560880393761240679975157129291238229},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-9225157210262560433633727302882680689}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":15104320887878094349408567239177294567},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-7531360622614000580088610910064248619}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":231479518857992076506288601848874599219},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":106062032988606250300363453960778843347}},"weighted_phase_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":20752714289828344483976655355301775759},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":33902856754439999930641291874929162763}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-227040223802049796264583093185261920651},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-274594682886659083442393012213197690679}},"cumulative_boundary_phase_input":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":75865115233270685646928160644747847495},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1174506933852886779743700527195479462781}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":802787439079341143662026917667195536407},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":190945471795357647331101893841975783295}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":42538097133459565105476805736370992623},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-22010956924530143316488908397840729203}},"form_storage_change":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":132931325357057767746872842222769108781},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":265862650714115530382233003843126078675}},"phase_integral_residual":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":2454827945298021340634327562578711401},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-39063214652586420541259382143073031833}},"phase_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":205498370949156988765911425264771654395},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":410996741898313960485183612804989394907}},"phase_storage_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":206561967464337861126906648373071090187},"running_phase_work_upper_bound":{"denominator":85070591730234615865843651857942052864,"numerator":112514989137725095256610748737015606685},"time":{"denominator":64,"numerator":525}},{"channels":{"boundary_form_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":25503011782479375740235580646579400817},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":46569140378354125561649713354974959459}},"boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":64658231413824501509153236083794054417},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":63676135447526835817647929390544260031}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":778253278939624728842183242384026387473},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":385942415299082368233760983172821138519}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-732084884771619165759276756732961994445},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-738174621128929836608967997236146198133}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":59913404727660864276209173683435509689},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":222362090219047535111527034447666092951}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-195916472927057458195587768950486849545},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-105479447069633182271205983536129819461}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":13002850089600037636899474479659446127},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12980027473798483513137687832831887961}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":54377402339595255280608516950940883581},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":52327142824543076812140903044970122707}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-49686428066986392247883532388571625993},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-51474348500610229102439070375624336983}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-44395260626272384521306480472991528345},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-22393045099975561134643826636041631327}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":113372604126449242699673039429636287},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":539961742964468518960952840846340847}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":44304388156086127775112913882815228213},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":21945112601255797468003624454684143965}}],"form_storage_rate":{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":6128411407877607224950659878484575849},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":184352816756835095823793956372734609383}},"internal_conversion":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":23830199275179019093997330404812223519},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":89968034205775142438222214921897062123}},"internal_form_gradient":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":180564943215196407988464148548613638081},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":710277682843675873986517814967666446353}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-359243969898626989102548493568108575365},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-730328129427983835091209648061830019821}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":122566257646679966385121530781579069321},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":114251367622905337137105846250780630015}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1264515389298164054852397426321955327},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1397254538862953125290078088956106383}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-105922494791366277997905274759967036185},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-114351038658313140027514514911198189165}}],"internal_sine_current":[{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":4263145690991612664374825558974170097},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":135404806111868822275768066392279661799}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-272367079268029024967000658613790321477},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-274175411154247288851984992766414150641}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-278943649275403053052179264259509075071},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-281399303910352559714816014404183271911}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1424682160967987276733553806452323601},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":424084961229178631061616993258991627}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":278372680705901649644395970475399255333},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":275770418121224043714632839837710126541}}],"phase_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3766647613709499683808158011520672105},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-3758150296222285339762271001187295561}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-5265382160083061127726767338515813013},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-901554344024033562732995719257692099}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2088821764674099686595686894571520171},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":186397531161776058286348060163815773}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":19507025760743931589643105870228952601},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":18183669912194712216212925282868133479}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":50313468705643794109789434467817347},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-444759933235251528941244322962922525}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-8429044315335740045604606884566890579},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-18199533050162951370256384539254435975}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":948961401379881441671792737834309899},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-7571782585651060127447561568927323565}},"total_storage_rate":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":58918483518460006456335992324096849341},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":54046236196566096431088417904012766243}},"weighted_phase_storage_rate":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":9891192255439148656730713296220242549},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":31832128029429289900559715243316455589}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-222258409092834913313288921814028282997},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-135114412988094192085494175793084394115}},"cumulative_boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":609951776463688508683666843099410626261},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":590238285775546210300802510287921493579}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":807255601443437209742151417118097828317},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":767999138784826299126199241692367057967}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":21434170584141228977041082472719369269},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-44358538373681934100821344346902192515}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":540638653976920372909293055051637008275},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":540638653976920362328041150957167352805}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":39449720439428234719121446397488545151},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-1226053862358352818263314067271399119}},"phase_storage_change":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":51583836318385430697321881231904212999},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":412670690547083428056708394353769422747}},"phase_storage_upper_bound":{"denominator":85070591730234615865843651857942052864,"numerator":103673565631121831850595608467020488561},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":451904414142550718241134444506454194555},"time":{"denominator":4,"numerator":33}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":107134186582236463437961148293579458181},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":98162662684366084280537851885002093169}},"boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":64093280315523275054355985564356707969},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":63127736343916573122025480963690747839}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":773365740457007499097818367031534779517},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":766721386543884702034350399689998322437}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-90905745418343909613722400761242635895},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-733476515932121345284701713177132054395}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":249448436834755229050781150854241930623},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":116148830492972749754861219052908157777}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-205350457781647293403551245311416732507},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-13768905194083155182079336105352778813}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":102115888681413670089330883434603769},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-6524245885326915799053994092212254863}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":55361169539453659138003857950541045383},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":6667754208497202878772128555113488835}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-50611943770660304747639139836722303339},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-52379290474295141628647666589666599211}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-44636719017189117315029492393142685339},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-45020389987312733716299095645147452083}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":455017275889969528871393910230197191},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":34243117748907115902455631117832609}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":44479148395184033886323870776922282727},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":44079585929473041277877765049611993805}}],"form_storage_rate":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":12633477346964124295646323096440820551},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":190334580617224607867152909650721727491}},"internal_conversion":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":24062221451410494006824937385391694759},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":90902141115838954678368964578421753215}},"internal_form_gradient":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":363858391174673039684296709901144979497},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":44722287484905826110011660420823396297}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-90451437307965883220499823750669757405},"lo":{"denominator":2658455991569831745807614120560689152,"numerator":-5747094973587915917386394039778445307}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":120772978311539379031916362360630919577},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":14047310962916898857114352059627503395}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2633279599804854773999263361879649049},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2714128835973484659325749064795333179}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-52149414479118932019046085990638650219},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-112805514845327069904735480591923203379}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":272318293723104728898238012270967976907},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":270439162310628238479960445789190094571}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-271655874419771044322382031414203805603},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-273360699357543878040822571888335327767}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-280460777089506293463893539289636916641},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-282871452891778338127877933813600733225}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5717915724769473683999350729483525651},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3442493668991259309144308034464143473}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":279470731672480804832468376523912275267},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":276960206658625048751165583057758767367}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":7578785271939025377500561041502360999},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-7562469957244061766612006394623842877}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-4138517040602464400437732632093944781},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-766717541505284252164780539573642111}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1046710862521896634178379249199273495},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-444689164423439152839141624927192437}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":19221616490211759505827071511986942301},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":2235698976897196508927970162599112151}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":419099464851990585676549635194980789},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-431967020433432081168157028407059769}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-4149918546849918134710738777661857301},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-17953555295659984290338323900598343641}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":7651437166678476900002064578993308805},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-7632108519047436007894604807951663391}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":239721009705556184324592942970370206457},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":220056530175188141530883909806389547337}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":37585372154130195594251773427317077641},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":14860974778981766831865500077833909923}}},"cumulative_boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-108618247048396289544817246493883372947},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-265627451162858723970338139779059315113}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1225912297956957324403679559845479693895},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1186394796833334599331794909416188994767}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":811767267965576677368431092877858771085},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":48266261040601953132921736681686286103}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":43201269799535182216426600882745238581},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-22348389291238200428255881796620987669}},"form_storage_change":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":137458498821576927093209062002666625279},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":549833995286307697422284836296850049853}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":39621214938693393187693872385633383559},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-39403377500874777135570864293512194181}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":414248743806451315151057688923963607241},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":207124371903225648570680454322493461033}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":416199690680132920801916542449673560065},"running_phase_work_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":226826060653663037138465886469249558123},"time":{"denominator":64,"numerator":531}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":112151197184131122099453326498975437139},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":51540874690137923810347291466442333311}},"boundary_phase_input":{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":3968752376376805878065841826241443053},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":31273541981198467559866328789658403511}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":96031846038226641927678915760432211079},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":380672309342053984075176058274473138959}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-722298376865548902808035734085117818589},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-364331612672417882628116137503986371319}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":129385031835542099476543408290738346289},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":241766189387627904165129009864179740935}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-53606907689114956713122201799143509587},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-229303516862041874916888864897560643579}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":3286713524450989056449939363911938965},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13124951671370057215862730049157283893}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":56287094210615234255737468568558709061},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":54298540574511539589476179898943301971}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-51489732283636896467508953833667580987},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-53241067730723020703212486562431844627}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-44881614296692353003515187128129293099},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-22630315170813906683067164684731123315}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":228181611611088151309378697505479467},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":277693563224133835576075956187062499}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":44658693282863278924955792789381375661},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":11068499737519945682265546255707321495}}],"form_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":104018525480290557277709401265102587973},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":24522842049118384857049732096537916265}},"internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":48578245440093006986403630161242588437},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":11476055935312663838615557767709094183}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":733294332746396797626835570678602079171},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":180241112831767141560216750184110538467}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-364428737836092904404334826853739708795},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-370521760267267096254090893551359080495}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":59499348295840777981876920286322589557},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":110525841314294478506730392753104490255}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2740929911793451316875093976601289291},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2631046625502470168073889060552972525}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-51352527416641995537623663991368808893},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-13910894278216048386861155107988377851}}],"internal_sine_current":[{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":16982706332554500464025090032943995559},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":16874093695060649226039450247938820145}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-67712915819069204796769177781306547029},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-68120431223576565752246267361940365351}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-140999749755739331040603252508700860981},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-142190463778101232275552053544870376255}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":716853674721674001158625236340039443},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1744800116348223272177405901523905383}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":280598845472726246421881378237166438177},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":278181739693225728811834556255070508241}}],"phase_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3815579841690502702679781840890738497},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-7615406464842261121462967738862080487}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2976227774751875559861815054343118315},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5017658471699855784580632574941722967}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-10305299931659407230245451744822101},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1988921515924503947708400717284001837}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":9469615392029398746457326516408475335},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":8795366992280196055334428492831157503}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":218116272065180223336883342628046065},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-418744075953968899033138303668181915}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-16346017157241303601459747783587614639},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-17711900697654780985905894428198373495}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":3857492595875064591819130739154202361},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-7696157369263807536721449803603470485}},"total_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":121802943844284988113718210524067545055},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":223758958489661295124117365331494673865}},"weighted_phase_storage_rate":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":8892209181997215418004404629482478541},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":27576222096714216267719508559191343745}}},"cumulative_boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-105989703364393216370611309154063636139},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-130397747080329146806559040602040173183}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1231865426521522533220778322584841858475},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1192258585954809311999269846064249945425}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":816321478475585396773406433205475263751},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":388281848812686749533114310534935743983}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":21768605311859334215912215420507334587},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-45036657658365101478340309333140830293}},"form_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":279652707044216936942467485353402905387},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":139826353522108465638460876391051790295}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":39792069636989521362133345006948480515},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-39572551779935616076928751069647359231}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":415729177116213436587996757865723162189},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":207864588558106709038810475222661505639}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":417617665158535831790521652577154981981},"running_phase_work_upper_bound":{"denominator":85070591730234615865843651857942052864,"numerator":113825432224037258538637425378742592627},"time":{"denominator":32,"numerator":267}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":117067582693342238370624215428499001641},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":53944691266120868150944222802747503363}},"boundary_phase_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":31446384277647988501786108212364358431},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":123864757940062066004750972231918652761}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":381464238857164789189286389685955744807},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":755762922531698770487616099665743138171}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-717247543036230518332430024292949998583},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-361870239835055916427612968995774012225}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":267610817371839475737989140685989208449},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":125379879201046557693923287475556652089}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-223142214783557663797785005176280859653},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-119001575439161758606950215019794258731}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":3319675673257575191931659724345561809},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-6628504365756114032536465952553367835}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":57157661725825552083331113631614186715},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":27597068236951265757331274175413544509}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-52318215465980811775249811992410164639},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-13518257378321646514128949597547170313}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-45121733134577434018625848207256113105},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-22753022719619178673852681094948458419}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":915043175339473881086949367357790639},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":562448510790387402572485767909061921}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":22421674182693361450795351401505486271},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":5559222968801684277402261651673264563}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":213848014674069104408580202116835705847},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":50470584468463988900459184170458772737}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":98071763912025945296285453158442824977},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":92679929448797067338965117613958451885}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":738984886500325649345454226594336970525},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":181623363856888221117554623576970950239}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-367109330539402545798230956981002514837},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-746567540564905043028585362909856874925}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":58620597035861025702327819183120620719},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":108690731884122051476705384011805864409}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2852047745104952134032627189382341781},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1272695859336418151642734102929877731}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-12642240850257264288203126314601449741},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-3431024858262078237409644214847405035}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":271087453150832695852677274130812983651},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":269432722600840827831124131850253886619}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-269945349287001994529318618708041808823},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-271623145950532118272288561754861710611}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-141754105332827620082996815732201470447},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-71480729022917269634288163060034203867}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2874692917363968203424764506702805495},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":441746027380400153898257048950097707}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":281759067574133583654628229533455184723},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":279437024615280186528288243247914828157}}],"phase_balance_residual":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":965713583374298470120454822554204355},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-3855717078231239414752452481406622289}},"phase_rates":[{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-55631403536811636703298557679359215},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-483234491550323581625223406207504425}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-69485598575297137426866916008791643},"lo":{"denominator":2658455991569831745807614120560689152,"numerator":-24304284052764093027130639747700885}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":18659515570510779898316800519678759741},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":8649333623816949504637613648153930587}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":453917496567547071074998530556679161},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-405111674131956924148505816432904063}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-16096600984613835207443152011021582487},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-546064566063579322317852895332481681}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":1951572112099476321421242741666438623},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-3894152106186457234314375330858901789}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":247366717369099612878009359770745168471},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":227276511379188363440511146954520828209}},"weighted_phase_storage_rate":{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":1047459459219703389669661176684670707},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":25394173505332407838674410272685737261}}},"cumulative_boundary_form_input":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-25811482973754501914699951026239547697},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-127869089677229731111983530158161383963}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1237761623573581531064863217874660175681},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1198064746483249721343242547887621132273}},"cumulative_internal_conversion":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":205229648102240403239792453455569317793},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":390454034659142930798871305479012895199}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":2742294021228538454338834113538003805},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-45380134315442594721408795669201417813}},"form_storage_change":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":71130824287935376830399612057288885419},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":569046594303483002920161409943159471783}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":39964280261198523836883262581143092805},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-2483944994988066016894740026257771523}},"phase_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":208555217167743316110477998323243476953},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":417110434335486613196804766496510040915}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":419017244425638490457238533032041404867},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":456853554255295669467120606916634385283},"time":{"denominator":64,"numerator":537}},{"channels":{"boundary_form_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":30466458799548104687058213432856144845},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":56291298518294400121719989541164414961}},"boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":62256661764082484444397463740020207209},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":122580190294223430331006251583979451349}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":757395246087880791842688297917133976683},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":749985217135833114421362231460626576011}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-712099967062507047656468010157490704457},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-718713885847765142924206419282666120477}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":137982501301885988913228861690288582317},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":259272429343279737998856760614751015665}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-115751047286627029412762814738385356923},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-246348363450011178861862633873406070729}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":13404242447724472449927090865694886231},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-6691383455403889207786661312988832583}},"form_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":28983943098007543548872404301524986277},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":28015131748983969598173477187181234727}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-26550523181334135183907245931080141279},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-27429715343496320560452964716771895031}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-2835373254337456401713403012889431189},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-22877908188405636413340736414120103307}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":916972241312917724117381449418527863},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":569070101997811977563865151507962571}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":22516709326566437717409689064058023387},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":22339619526170058209618606461943354357}}],"form_storage_rate":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":27439094996389136996759829637141265759},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":103720870016631457469181928099913798905}},"internal_conversion":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":24739667936469568651426081273595170899},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":93525920486799823280711567149106409919}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":744779403200233994361724908150393202523},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":183033960975791116098057118535352739113}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-739688357285652432606547334903039756565},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-94023931803827232139304583954977396461}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":57748640038116758133287349432146023387},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":106871389064540562596680160956050801741}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2966203536756650587290398940963787507},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-153576834196903284715002844356600823}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-99594181007132675898489672112269194233},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-108318897710375770029584916888277059343}}],"internal_sine_current":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":67592363412204642665744481767667858383},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":134400181604234774154335716069073274449}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-268963476879414890465684484161500431125},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-270689589829112457024943544684332945995}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-285042809152369196424214276736600745329},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-287492273176787690798525263634104190655}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5761506513708858847729881453841832711},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3575572903627840858319191821468403981}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":70738328603357901362633994661299355841},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":140363969174813905292566579043606335309}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":7815626160986116632774325530649614723},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-7804063505849218292748941239873311753}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-552354013778182429002633443945924817},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2680105811495882541088701053446363005}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2225460538719690483451314162427486415},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1063459731756852765022228008843690249}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":18381963037801642269094556882837145153},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":17009109844718758743435530447893609087}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":59010744386435424882527865670458207},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-48885024613683175600351332988099797}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-7925453105237062165169520447511296053},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-8619744000435843831425025919840644939}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":15787117349632137757708658451070227277},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-7877039578789272691664752960288351621}},"total_storage_rate":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":62737476170111092083038722279344627137},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":57656269892194710563424568822722072639}},"weighted_phase_storage_rate":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":7859286177332818089519063005062095619},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":11591669767757963657667209545530346373}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-200779402765120745688776193191255854417},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-31307608764796170276569476412104825503}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1243598185613964263981525480100287070107},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":601905346451645722320004232965310084527}},"cumulative_internal_conversion":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":206389320036762414270328051015269091429},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":392646048420552301657012982834070076681}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":44219601093507330885067981593966512133},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-22863524782843175766266230980381111063}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":579050827816242571986538135965268061471},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":579050827816242559860003548909058289173}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":40137720049596119123128004468331014927},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-39914955967021773536948208326375963367}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":418391132805837906681824266337874818265},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":209195566402918943565275653052885476689}},"phase_storage_upper_bound":{"denominator":42535295865117307932921825928971026432,"numerator":52539561939640249621935884333493316075},"running_phase_work_upper_bound":{"denominator":42535295865117307932921825928971026432,"numerator":57288261096607457583437439304018364593},"time":{"denominator":16,"numerator":135}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":126542656712919285066439411659525015359},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":29287406184680705069456092564762499011}},"boundary_phase_input":{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":3849747723522043821822516273145408297},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":30305685433600499720763198776001462089}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":187915932649848557887015541095594743987},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":372010213595367057753296951894009699759}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-353430651067132609646508181722818934379},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-713589129660312973970226164959331050517}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":283839003726999746243094086860107784039},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":133636061038556798498164587793826205281}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-239504801644715465315083925944725563915},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-15896043387441136338179519384394862357}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":13561927575622474627254914330929912941},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13540523250194054774108418019380461737}},"form_rates":[{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":1835002634850994485768932823695223223},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":56797037870069764948982419094736579663}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-53835184444235852883201480769315513793},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-55601277472267134313195531693396932023}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-22807261601475707486006871921000869243},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-23005057426008240338837375317013922695}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":918502027199193819995073181896221171},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":575248996973909222244461535018177509}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":22617317254341851907821803122285806741},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":44890006816144955379821753076443472365}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":225034592170426900141528329534297139039},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":212824383745451665843403907173614980937}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":99822250282726435551072913533470427315},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":47161519928040802618224522472158615027}},"internal_form_gradient":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":187667444746612052544957933612036785391},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":737883600301620236687915174549188808987}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-745259282696142051372188320999750092771},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-94738487205146198337004964210578525453}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":56882207733696274870831757168291290617},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":26266320481224138564554159579301804699}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3083306930877303463447047087801520643},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2366674613266993950552715265688986757}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-49035222820782430803144110109316042629},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-53431041509545680353002569285113951407}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":269584752781716878348724530147974876797},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":268027348677703756188572618521788754855}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-33484982277409143608234843662672347863},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-134846500156094056166655447113436634341}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-143302250991393330552830681803377148807},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-144545038809917612572508423883934605153}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5771118441912639515151683767879002809},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3614396045756260828279547584495962321}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":284217590920600140371209249972283364093},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":282052231266393472197930224908453598631}}],"phase_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3965788413061595228548372360159382129},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-3960272484726479555967911799305877079}},"phase_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":352759068881622932642782497017209523},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1462117235560748586334597729067014967}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1680153801376331039577107185378654021},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-677026500244697061203717454260213863}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":18106169069595598770685953186875881733},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":16721658965690850734003679413139897799}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":490723539118623698410113645092991753},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-11770873855985682006982054795684127}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-15608396195080070510987356332512320663},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-17007628741584880424958420128080929033}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":7997146987550417384863895231047739969},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-7980928896501091785710186514419509317}},"total_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":127183330224112826965302477912575662169},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":233772726072622503793339559371339062229}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":29332068277798753789076626290854185299},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":5237085581792709487483913049431020323}}},"cumulative_boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-97423857865851327100643422884857809661},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-61242370364685432503008198485236408865}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1249372807199247329714259254510005182553},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1209493008922091538337651565701120443195}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":830236448129052458747768746882957791997},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":24678546541698700892483891082809531985}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":5570877580653622086780525969134006635},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-46077703876504141846538268715922918203}},"form_storage_change":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":147327757130211418810423982115507860285},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":73663878565105707837492954049664906809}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":40313507080211977917908268453441891491},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-40089249991637863738976364474517506823}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":419570067873251057507791087271604542689},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":209785033936625518707899187692791326105}},"phase_storage_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":210770115084078180694285830459981319107},"running_phase_work_upper_bound":{"denominator":42535295865117307932921825928971026432,"numerator":57457414733111112644346842482512519879},"time":{"denominator":64,"numerator":543}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":131093119770229973243964307310725679417},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":60792893043959488055176176333533964937}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":121822304493257440843372226175528888827},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":119794631486002776014763603307161379183}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":372871423776057224942912413829026572667},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":737877310672137629439150615448795403389}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-350768544065651340418676673367171343361},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-708371881255866325716875351963387060785}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":36404014577347819154040420151271795361},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":274758867610657013327780205383695869107}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-247148916295475676249912345422917888589},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-130983364673702184998046856871866582939}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":6875717143568620499457092508494623747},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-6864976931117227043921339833921691273}},"form_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":29706940516973969903824091927826271391},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":57494362680926115446173852315720420039}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-27260175355961537458705258587011697723},"lo":{"denominator":1329227995784915872903807060280344576,"numerator":-219914756474426839390046271781272953}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-45867562289833918774453534227301721089},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-46269096093968468528906742219235846625}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":459810912899061417646935350364075213},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":145245831780899715923368852111355911}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":45447114566258199401968624131463949271},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":22553178461226030690821582478564406725}}],"form_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":115203032556829463047259145668541037391},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":109011571276269996954664079476151917387}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":100659976644544474753206531309421537903},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":47534422369301354492625876826512448707}},"internal_form_gradient":[{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":47290524159363441724050603919655591891},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":743728434408520153153453215942096665797}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-750924028176479175779627980856911470767},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-763709826714210752501770720232186176379}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":112040104960288985898516639363048999685},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":103269833388867801192644501562487457857}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3203274493617681154741147945021286619},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2273961294973977679823461404504220877}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-96563037219452283231072400206453035519},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-3294349387374796868495956400846530521}}],"internal_sine_current":[{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":2099457186826123722923414753536248515},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":133556367326508474156798025808758235775}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-133346641753837040680358313706912302965},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-134315547335020161531446703009528538619}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-144097196727814473915330152855141167263},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-145358652377051538370076045959879259103}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2889077172008215295349157043514148985},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":114075809521853365693474967458041033}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":285552642496420883642099638240974516365},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":283411599075549022211640139706106127039}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":8071862939264383197757438704796188135},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8060853772303231859290734884134297615}},"phase_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":995836504361800653660251342907537903},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-106867936410772094591180226205240113}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-4514923014392071670507688133580940453},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6596732447353346405158422631911011341}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":1114483533060298367444559695553161981},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":16435904456114767747417357665637781693}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":509816969739441893125899500350502559},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-361912180494756040842654663309497131}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-15368484693442499357005971227738148261},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-16777983656718593866716029450344721421}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":4058041330114964607179211516347198785},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-2024959466074490022397329611947629959}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":257612582894381610553832802039618104197},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":59178937133722873477039474147668382143}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":27206517780722684459314510702536029415},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":9346302991175749999414868819184846899}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-188702725742473124205476018864525353099},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-29908768466983816000857503426209603281}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1255083227722368772253792327611983099217},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":303777095568249479615835902401535908211}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":834954884534265481001825303038086926587},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":397084920715740215271584095301195282793}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":701875841742621972095048365357135395},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-11608102806163665253701635732590554155}},"form_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":299909873783568854375195629287785202309},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":149954936891784423945385685310799839217}},"phase_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":20246359559842493546157442504580833099},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-40267169432470937803355326399991926417}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":420646216858417424553833191577218372455},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":210323108429208701953634405304800303607}},"phase_storage_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":211343369770245134293802710320350761847},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":460913386290888341710624137009592533631},"time":{"denominator":32,"numerator":273}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":135521055097141379574992142355601926869},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":31472043281609503142954320268836371089}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":120429945475105854796708837750257159795},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":7393961637580697836387919727265591381}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":739641794374787404735373891670034207383},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":11430686041372854584220412089650480509}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-174033156797964755520563544190272783123},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-351533898737599491157705164034363861919}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":74544961607991465642646258500846718781},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":281740874555752164677640279037747844887}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-127217010626020308624736594746306865315},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-269238055481718151279354759669386786275}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":3500589208180887848693265707731857201},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-6990267278469833686814956940276869251}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":60061227995041635561099939063660016417},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":58125545774423066958025797780044261305}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-55156309268280566647239481666436518533},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-14238188938990350412899610979743188163}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-23062624304984975910788841825409798885},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-23266449392344246538799981262649255891}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":920321864351796416679334730058671011},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":293136128141372961842152384268696549}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":11416764852200077135744618486534432775},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":45320180522624644081473836721432309597}}],"form_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":117828945101889787272142011903042500399},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":223038060280709073007315038774190327547}},"internal_conversion":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":25374384935126840201488202574785534795},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":47883680122309005288846839949906043819}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":762708923835953882880711961366071049969},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":749661546257341466176553658860312361533}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-378337507289503949236922063226894427849},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-769591114346898308760041605806909850727}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":55161009336155315086377898499965329243},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":101482414722026947838151141290343577849}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3326048771200476128145674041411829135},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2179613854804066271272873116871021863}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-11883448656919769571407530508619730601},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-25996905055691243279974845777885475969}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":267883891472447424048696621197873353029},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":266079488216722104368659230218339075977}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-265401946737029939910418928385116062689},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-267529021772148300631417737176277071493}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-144906742178084422946001135865250052153},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-36546853243053696953876307505920587717}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2891276407985665842795548245619975955},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1841828613341387097166112094280564077}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":286934596699471391445073142053227959183},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":284755092378481636322497083190016471971}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":8257761532790393378238767859690571267},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-4123413560954531102844721707904548899}},"phase_rates":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":826147239694459225701137871525799885},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1063128693775201871105116244791193047}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-2843951195823862116492426369439367613},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-7794187561851334784100325252492165315}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":17558294603574612972032078507849034431},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":16151427939912320303162697315666339111}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":33084818931330011772564778129629875},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-173448159511823895303193695551642471}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-15130476757820207889043463727471675059},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-16550143778815783875472273097003076135}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":16529938869624594544752700291287948529},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-8248591091479689675530113448516392379}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":260721498197353772498776697002882894981},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":119726909194643927510320376604413150953}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":25063607993574197954492673196797894183},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":16415758108578782013325714434635974359}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-182350176284794622037898262191606512777},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-233369139620568746167556092359270006669}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1260728381416514359197388054381526403583},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1220653853501183441840634549401592826379}},"cumulative_internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":419856290854800881769802170510429607181},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":399329468221473449894498790923847128597}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":11319848226293798320365403346147944483},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-46793215697253808006777670033521477309}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":610569189727553346902903102873016028457},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":152642297431888333373732102198932806069}},"phase_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":20338735338937368266746700397955296047},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-40450702504111065789111139973205987597}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":421618742469456414834523609176644204111},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":52702342808682049202409916570078269849}},"phase_storage_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":211906555681044350191989041032029517203},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":462069444973567459408390472533832146389},"time":{"denominator":64,"numerator":549}},{"channels":{"boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":69906506366719156058918442593720985051},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":130055387427448362323460916531409964527}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":118991540725986659250737580318684745417},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":116760042232482943533187926787812126237}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":733369617691549193290039874770870146371},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":90636384314915798796969804130171891695}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-690653769100482375321081505163936209349},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-87210302998217836349934942676009051485}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":304647346620985549590673744127327095637},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":144116091554354903938396929561477050955}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-261360652712311437106609240666770107733},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-69037802678593614030522322387885479143}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":7131764307302269553836156732981164553},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-3560325786121856113632903936504651915}},"form_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":30325105384249460778231869955303448973},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":58694279470770729914115015196602808855}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-27872413958285375543496401444605028081},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-57561556177528785350805991840806850571}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-11596931219607655082011344545835085783},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-11700411253839707021813070909391672985}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":230148330890667439269789279363756555},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":591115974133548335908519914135088687}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":1434183038966290138358337696596111155},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":11384670477750823910177408500405430995}}],"form_storage_rate":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":60186225642440718531898917815023254599},"lo":{"denominator":664613997892457936451903530140172288,"numerator":445071783430748732641594907661207119}},"internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":51152521763796231724595661640557341243},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":96425986527709972696462441262720724763}},"internal_form_gradient":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":192210186759515107045809197078189187357},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":755675459646630100173870383153420903969}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-381252477163223611395957026086649092689},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-775542598548037825665377880954365190797}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":108607204428379529744437272178453233059},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":24925110107615434953636004036561561625}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3451466291842353480305550864022476571},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2083256043589844926452414814256381537}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-5848856905685396449573044920776679827},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-102562798426332914819480943980552974583}}],"internal_sine_current":[{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":8342731973311899702429383872419172269},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":132474184235324409832495622324238147167}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-264021972862666236355526918377124785877},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-266353675335187381026911339976020081379}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-291462671389644242947567071706821847213},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-294063408312337320513178663151338790067}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2892129222248294811516289841419313565},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1857045601757529697601807853999687017}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":288359609543653201435713978614947935721},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":286127977091540720246502290639629760709}}],"phase_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":4225836691886506886815637357622042067},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8440844721437162570692286288476491653}},"phase_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2320992213336057688432277879896891967},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2366723337985142087702777854062953207}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-214933877655156011669693524483859945},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-4503492273287765557998811919473746413}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":8642686720084293578354227541952598971},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":15867817922947039113527459093757869559}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":549317921261764786927718802233318219},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-82890124265847199566654605238404951}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-14893991807631973073221029745834951659},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-8161688173444273777951275696864606457}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":16836144998495062128574706162812455517},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-8401545433021048136247510008050570795}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":263651574658426367985223549482034546281},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":242001462593382875096079445490025573929}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":22906672088663493857627878221941527885},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":14124709476839523983582852767487529001}}},"cumulative_boundary_form_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-43949110328228675289343664549611292607},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-113636396667453552091821930948430082291}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1266306109888044983849766378458964751025},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":306531745120207769954688183367442879949}},"cumulative_internal_conversion":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":52781758164059853766486574018728841569},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":803178904561433304759144258781884291167}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":45645119564159420376245195399536006487},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-47160458521357352013936213936601013797}},"form_storage_change":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":38846951924417851309484099517785008317},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":621551230790685607092474312164615280879}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":40868145799555343230011155811174683939},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-20320104835591469051967189135903660693}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":422486995655428762784978704981284738631},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":52810874456928592623335967675659142309}},"phase_storage_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":212426960999632484810945482026502212251},"running_phase_work_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":231563602663305839545311059838540229929},"time":{"denominator":8,"numerator":69}},{"channels":{"boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":71981342695868576860740871193512931925},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":134084225778777881401505522035579387975}},"boundary_phase_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":29375626810783381889981627662774493617},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":115168525726622139436505711202088767741}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":181733911961944839502852632106467955219},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":718468243329575701261758001302969119461}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-685105966137990292079011015305638167159},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-692221290587375615485088963177170631747}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":310629091089217881897527988524629141267},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":147119658968527732522421824756902479111}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-133965124639935130891594507516282487259},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-282707633739473521007998391964340347839}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":3630518039764086431336105965332696339},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-14499433488158005509773701870528033971}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":61178019871004258528854538645787530933},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":59201636280222914112706946892538451085}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-56286352357782770788188543918303162149},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-58123709259743269253791297969384443007}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-23327558595463632065661646127556249005},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-47075440275648441220628317305051879191}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":920428351240792483364135764643025549},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":595515685280774038998006378306223409}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":46127485503428425776750625681239059037},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":45763792406550438937292921478887929787}}],"form_storage_rate":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":30706371405458564936139598817945252273},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":232536460592581116514562857803232532225}},"internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":51536604344500984151427408643367351173},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":97044673305834292362266844646651844853}},"internal_form_gradient":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":387517805123300046789786382157313999477},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":380880955510174088801445663339049521451}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-768406350210548367854961774039639327639},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-390778393692924925008885438468087668275}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":26723257779316573822848102041167938137},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":24480317630868127414624094891306876983}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1789707066547196430298131876941389213},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-248127060697365116983586795503338141}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-92101871654782208003335673044086772485},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-6321325706501382636313257755786308685}}],"internal_sine_current":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":66490040568633556116928170739063948279},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":32965369864784297230418425615907204725}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-262556123913860408566317861338095301055},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-265095420289921961201031556291259236143}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-293142746838775927822493637430879866809},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-295783714668964428243715442689937919603}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2891610946413839517685532044830875857},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1870867701975571087646320370775251463}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":289827539172280855577602542297857029365},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":287542388049654446734232162737589608689}}],"phase_balance_residual":{"hi":{"denominator":1329227995784915872903807060280344576,"numerator":33767079257393425538750998807504691},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-4316836412176518928801474653524659941}},"phase_rates":[{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":375124002605724169389710424422152981},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1847590644444520264492710836889243279}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-8083485885852475011482740885194632479},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-1279218747239138118292097149971183831}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":17012554284388714528797653645831488045},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":15584654237649355470435147388074011875}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":71210181581870496620550316453833047},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-315925185798787239998733261119661803}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-7329234070936955206421940950642865275},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-4024280932334250524828188809247476497}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":17137909065781386722676706915969128759},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-2138071366167920928348584817186812045}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":266390660571181407560687940153637284475},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":122180310852763656927309787250314670979}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":20739689327512888071571149610075266291},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":11824161112946197340056716697396809733}}},"cumulative_boundary_form_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-42262047608794255519170050381013333265},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-220987595251526890992948290551442380771}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1271814039915066867954137933645734968579},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1231525505124266492604838938682369430783}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":849339687282254627527981503859977154277},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":403863936811322143606812758562348048197}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":46017157505843730614617921774346025269},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-47534060970116492938881190258676561695}},"form_storage_change":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":158189358969240281708823787086899935223},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":316378717938480556256210056038623629761}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":41064700060845214643051174941837917459},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-40835648389565523416569155936833955807}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":423250517902857079719908609764230193965},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":211625258951428528661971630292102458189}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":425792457701245226072318362714236465331},"running_phase_work_upper_bound":{"denominator":42535295865117307932921825928971026432,"numerator":58010770786552822592564052065129859023},"time":{"denominator":64,"numerator":555}},{"channels":{"boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":73983113790909726256281897829844690787},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":137971075222429574415685355039353602561}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":115964345662958113539236827409870918419},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":14191319364517477422630027999233674841}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":720349298492336389294434887796890508993},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":711704885616837020843887570855334532543}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-679494600557148387195865173974136979099},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-343344932995834499194810007111705481635}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":79032462133822830220036290643908041135},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":299766995362412439977769399300804673325}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-274145099270167109394243323773967099773},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-72227402815692047470850278926076792649}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":7388809222833059405040658892134156829},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-14754557808632168053013695713660377113}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":61644910955439283755680641277554480355},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":59647901645616540847474994294932549287}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-56780954375174737310046598712564293107},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-14659813832929188176911795138551217361}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-46927535003290734105462074715411238947},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-11838593368593748268538530202019083565}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":459910035355033104291764317679200229},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":599473594191326616612054845673642627}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":23184050358169632285018092481866854245},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":45995696483702636205496757215516639979}}],"form_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":125184842977903829633031418369203475685},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":59252787541552061405666371017422048931}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":103799480393020961163115384123659191263},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":97620992287711966040296163914785035151}},"internal_form_gradient":[{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":6103791319423473701331045246547744493},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":383956317097208578116945784978251120495}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-774371699777712178707219755182590459617},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-393813101700986555222515951982812713037}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":105176859909602511657255739314534721087},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":96142253815188405614863197130852890239}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1854887261214969690413852896871542185},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-942513237940902677923536212413294415}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-45312265654594371896648823931382228761},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-99719350363086808355815624317937299747}}],"internal_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":132429874815561863412294971757602165471},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":131200616736666975202272176600327088997}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-261002788116431440470900532950711803035},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-263752350023524203576078755805289981621}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-294854398434832087862712154764840494851},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-297536303644887702591019189738051924729}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":722424994191797038084151668883406563},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":941650919766270323781361131465986013}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":291339369142726125823001263950334295933},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":288999484339892173848776414715770202811}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":8835723394620272751405646827870119595},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8825175681959570062937342686431776157}},"phase_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3691355040882443534244617332331403201},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":5046626657950252098850907685471034201}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-9303331510940485410390802259826914931},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-5736559699067835541454886801129037575}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":16739417153497035751977145119611463819},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":7650757467341433962909208323394963987}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":73803619125137524876829812240526117},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-75002820373921186770332425725834785}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-7211671061621810814109754901812952217},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-7935413766098926736096291341500846251}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":17434853734977396438667744403264277141},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-8700622692641371496565909095608998579}},"total_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":134468241936773395117696661718243639215},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":246529327859494823058668804878342302835}},"weighted_phase_storage_rate":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":4641699479434782742332621674520081765},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":9518177693286577436003320808654107111}}},"cumulative_boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-81056136758639617620076886801252696649},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-214520201100475504692213039533972680651}},"cumulative_boundary_phase_input":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":159656233577252253690786207491321583485},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":38651476558936267082447662474440064339}},"cumulative_internal_conversion":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":213551321981419371270625634372693419717},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":203075964409032696405441099952050411229}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":46395422027479123773854753341748152563},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-47913935845263859937864570467179497745}},"form_storage_change":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":161044769640783601175851528403994279207},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":644179078563134389904484193421088787825}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":41267081020598543932463293694528115953},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-2564810500062853839048142380115917735}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":423909042980881605488285955385836495933},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":105977260745220395619938745510129084801}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":426628108830029503867156379721775320053},"running_phase_work_upper_bound":{"denominator":85070591730234615865843651857942052864,"numerator":116236502745471810976131315030592755741},"time":{"denominator":32,"numerator":279}},{"channels":{"boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":75910102526468270429946761776018589005},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":70856352108591804197735054606898035787}},"boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":57189307973764231095453532480584570023},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":55923946457793957584106635932496798159}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":713620034595172861519971704824569305799},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":704810487090637593058760923006521521273}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-673824978247990647172605229691072467415},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-170273387637302261642879110912583669145}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":40144480610398848457423338961068404659},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":304821387457267210771022754705308679777}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-280008286845287927759836302027268415809},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-73690056065271333134615765418298851359}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":7514912614394810465022393769046473429},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-7503167561991562918337575520469371819}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":62051298813391486855554103233905194161},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":60033519876957330348125478133209652369}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-57228791304760295737289286265200521073},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-7388540033504867317477563382512325903}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-23602535571618452211773974276936945279},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-5954814623721339657611847359983513863}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":459381292070721390961169455579401115},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":301496443111798540520696270688554073}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":46615836973885094135476859065172349609},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":46234556126252602082834749446195723195}}],"form_storage_rate":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":15930941979771150238868461858154303239},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":30161899952495301465314378085983709427}},"internal_conversion":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":26120332422752249174824163044192810261},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":6134533889397823406023780811161239587}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":787581599523281194512085264896100021105},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":774119381793257939282307333421238515727}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-390196756399736768030073527553787758835},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-396871699866790775890867827956611005235}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":51728024873393916909564185211283977007},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":11795091720680208670135269817794700771}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":480303150618056069824463235667297073},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1783419615026682856314443008467163071}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-89146146026223915197263965207015469763},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-6143356991212962477358607120707644539}}],"internal_sine_current":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":32957983576297057641120981755579082141},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":130490603793245360295549228585315185887}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-64840091041321805438525360343181979687},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-16395160618701630653644641081487429035}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-296598209431553202713821209705579619721},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-299321630005952473424643700841008906317}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5772755569463861832772379117144065923},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3788716043053917264335271960580060145}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":292895941956193740109403613465527105151},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":290500283736440287424303033464601049225}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":9025594215865037853788810639386485323},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-4507609932720419709401603141467249857}},"phase_rates":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":1097785974072521908131697159237385847},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":6419180106938698723320933233924651851}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-10536053227312133288208427928283981495},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-6361869849069713117225830442164506577}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":16465541709962310553380258139984110843},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":3754494303137088892440346770546611863}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":611540964827797982884923838963305771},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-141920023669270798907746403691594571}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-1773506224708182343754896232167431721},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-7821965058637571179206260745596701097}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":17726631984010836580917438979288024529},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-4423191882195035763140549531420458925}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":271287229116782360144600820058077692421},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":62126513367921214999559597596881120589}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":16392157440443956322705430327608840597},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":1802713462930612068930841424913701735}}},"cumulative_boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-77497850702711417443673132343001825289},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-51969354522573755762168844541143997449}},"cumulative_boundary_phase_input":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":160326420780069803273936053575078433915},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1242090119866378730161835196300753633675}},"cumulative_internal_conversion":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":107387856281867941475347758507694978849},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":408452379026589576588141117708286287303}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":46779820732868121993099383096278955557},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-24149994076884230041135827096735768539}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":655807160695752252120706240348275540367},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":10246986885871128700518189830970072549}},"phase_integral_residual":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":5184403566524735373816175207396746769},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-5155513755468276912734475282580489561}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":424462498143633081349582529898367777035},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":212231249071816528856665195461705490113}},"phase_storage_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":213680229681038634906535743828699344471},"running_phase_work_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":232853304093689636507603096592027448357},"time":{"denominator":64,"numerator":561}},{"channels":{"boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":77760801540406768582495283915913247845},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":36326567848500462244505237363727174829}},"boundary_phase_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":28186732437785143831689277927211437989},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":110122339740493901272045724245621835377}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":706757341771660135878589282952445656247},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":174448629443684373810325679016967261649}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-334051161564236690073500159905136512701},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-84429708716478110137856696070824313545}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":325714659839283428943818020858922297195},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":77352504717701847900717079341966114667}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-285523637407892959038382397502447208803},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-150131646750409340624267599401114430853}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":15278376508013965222622578664468005487},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-7627225356633527209026439704753182807}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":62397746099375757955548554142851429517},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":15089770704776598175663064871274773557}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-14407524953308966953961494718791189103},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-59531109343515717832282509776349277519}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-47487801852714249423893078494090947951},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-47927926747638124475172863385454709047}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":458625485507455147560945459875841837},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":606077704993324139179339077711057213}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":23435402971550030227375449278249835211},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":46480510782259019150823791612569003451}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":259221600478189290980645709239473599141},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":122691704651304288806368933619052013103}},"internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":52558128467531047432900089407891948065},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":49318476288086738390001090560048447169}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":793916418321874793575059983825914924923},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":97546743173223799995860490454514485333}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-393232163828474294699067544408153700667},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-399950487560679872962604727034728150805}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":50863981268706640798631264364575566011},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":46287027013407473739132829546584599113}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1988619908124791571646055686755800603},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1680331442733858354161040878966190133}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-87663180057157491868159698137868751647},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-96860805809943320215098924755264094317}}],"internal_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":131185121199898372264358350632077766551},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":129730467307480129598317056192937002179}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-257627257188831994025961541418521230231},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-260804193820100353054181848082896968355}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-37296832358903714635174157906173081249},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-150570022572169684083192384987275957635}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2881628912038546557286882434745524999},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":952024632755794531040690174165693197}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":147248979618675970395036358502403797855},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":73011415604323054143440341626090951973}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":9213854099584697654416108623647497417},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-4601836865327010820514867311943237141}},"phase_rates":[{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":79678518809710728411487327512732129},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":1952741059804253113805467181797073509}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-11780294282504262714006933463116992793},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-6992135652505449109893526385645178187}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":16190508088496471474515288937738165323},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":920851143776486075983269396508834237}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":632997376618022667292045822317059165},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-33429131892978701582451883326635875}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-13952028433251474726220522926563619627},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-963492252282290889675887859087978611}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":2251615781088755598905086199053562639},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-2247352510629057246660577042213229763}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":273441537383205795041307363292959035805},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":125144856373460827259231531601483204771}},"weighted_phase_storage_rate":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":1777492113127063007582706756685679583},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":613287930539134613215649495607797917}}},"cumulative_boundary_form_input":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-18463203282626212541592166477360847949},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-50266546654675296594457661539719286129}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1287896378572643140659930168211979615943},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":155906513067714297722995292453095894651}},"cumulative_internal_conversion":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":216007543699693641874904112860887425231},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":51345522825324205306271552353536069783}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":47170254182847361043735405694104335759},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-24346057884215711694750298425700901283}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":667632432769333459566249597191804307771},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":333816216384666721888689261386630557383}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":41689075057949263026891572190948369977},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-41457008566566802727743308090500512135}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":424911004800889077311237460372165826261},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":26556937800055565814490126404056374205}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":427989288384218874756678396241034418959},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":466368013367455855759585330555402499415},"time":{"denominator":16,"numerator":141}},{"channels":{"boundary_form_input":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":19883478980686895531093583789758494707},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":148749331659344406088502771839021272895}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":111070943092979469907924467836434115535},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":54177862368644220885684249237786198617}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":43735668565266774203181335155963006385},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":690666404721689411224415735190463314473}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-41395735764599418966117451008576055557},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-669727468346444719828450870769238625243}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":2576680625744694158114636096892609181},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":313541660296664095252281010500109559053}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-290695662656688053700069425423876434295},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-38177915589616331044358408661908861851}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":970186360675027885497586080064335717},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-15498615352680046390152814555887191725}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":62684951736391673906502390503732119649},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":60625318206044402093156709210924849349}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-28992594849403418678154781482989324713},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-29953950553013789478457875348951549071}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-47775786859141606736094224472864433411},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-3013915145357126590410752314578811353}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":915281281941802509869943628706206589},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":304366563169616286860907734152858249}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":47133096952342908136079768649365637031},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":11683419344363502507310316744805557411}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":263344200584596045535561948582410345799},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":249271011784634629109842795263125070007}},"internal_conversion":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":26425448822954877812811734875236076019},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":12383985894306399159887224932794962679}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":800281698118169111888254326596313157951},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":196667043568270162327756883734468346619}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-198144181653280375670929074083895609007},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-806091587790390061493847065725215667857}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":6249373003742005949182853161577578357},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":45389781846996669139992672946329880539}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4114088258673228686152470570772830817},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1575899072546746745732043053387434675}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-2692878577143345820902846119878704303},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-47708582229571523080079423816278156889}}],"internal_sine_current":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":65244157875428914062222143555727413719},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":128919251298146907221674675716300168091}},{"hi":{"denominator":664613997892457936451903530140172288,"numerator":-499613037632145105586259285641860665},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-129597670651554812426437925995882258625}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-300184122032302107320966110656882027269},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-302991797734302807413028735410660853067}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5750881902633230099930140696500511213},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3824783035408161042411683520450696391}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":296145982252831906454516392650349198237},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":293636355048490065357939309785129661167}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":9400373709238503381564900637770974651},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-1173800864810212883564190379207162389}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":11630543855012091567923001599646083825},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":9220108695453924248860718227518906819}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-13034711138876330674751818917795653397},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-7626695087947923870438643864187051119}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":15913897676329375585147635449858373665},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":14448016293624597682943073645741595237}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":327388741342086244542080005910732461},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-250812127209748117561974610389626709}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-13714717974356265215568076949727387753},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-15186113379484929706554202805393475253}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":18293447342670631577377137880215743479},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-18259114133793431486517197550959888193}},"total_storage_rate":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":34424812967412934929656051024351176701},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":125939830402340601335077970301771092499}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12054303154707433901686459612399067809},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2608649020046573560313145340417114991}}},"cumulative_boundary_form_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-35062330410813028627144309474431837019},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-97046780848584708671216039364461511175}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1293102829030126553311864127641812465109},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":78270704946173423593249702374425600833}},"cumulative_internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":434492473226539303544759325866328232589},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":206543089978888046146325636751593806883}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":11891654131086538987645973160906677969},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-24545105033548792845264818601725342733}},"form_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":339822707371364461596727180460539458529},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":169911353685682226722602944157869607909}},"phase_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":20954272992199344931064094102287343927},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-10418897611119883350046598055325071351}},"phase_storage_change":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":106313719667523715066151193615681959001},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":425254878670094835326375188414136952173}},"phase_storage_upper_bound":{"denominator":10633823966279326983230456482242756608,"numerator":13391080344599984252195544611298389145},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":466930469114574368726561580635437237577},"time":{"denominator":64,"numerator":567}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":162456728910907266517525616371326741569},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":152039839626977739356340065501845770937}},"boundary_phase_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":27338087342779376086089231601234038097},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":106549899453997062963362130385568603911}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":346334770575799761594632156599568112153},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":683435506383485598679683427343671891007}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-328259185736848561580609145081549073405},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-663968105454357864882953157564357384085}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":333467190344503537422510585145110442417},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":79306554936985140799658852818163285961}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-73882376418998411936431979067372686699},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-310245453824192444478978984148031383035}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":7881687519491864822574228927319747833},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-3934641089000729545324655052282418621}},"form_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":31456869565339047706459652467558220261},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":30416538914760432067398846915067583961}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-58294437757837670323650108311674533315},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-15059760327578808798788331738111029097}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-3004316842116918126314569065963093425},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-24261343541302727561044246097026967817}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":114106316013042436946719101459110089},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":610965129164604925589758733091200103}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":47402777124694805059828014091621632753},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":46994150384230250285782077512529503403}}],"form_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":133629131305777024018951510497300907393},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":252953678907969173695342216460922204175}},"internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":53117757176532412679557610149362568545},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":99455047945592579036414497638116548183}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":806669484098050064752801661859757449829},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":792993992894748701928468828959369833961}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-798723349957628170776384292714499396227},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-101538496025127484914765666451045854373}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":98239448571966169862316716215174720703},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":88974622253901513512942911146420345501}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2126418539480760857065334681105949291},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1470260828873178625405218027767747637}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-84669455724352496490732307826843997807},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-93959350185754246560013637365456271921}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":259480831643905490786299976319293677027},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":256112031465496050565808928628560829425}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-63470656634879300677295061770503916853},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-64373533773785700324772623267570407769}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-302026871048019094793996011810280079203},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-304877034542299309325267540126634341609}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5735609025836312091830441004972035157},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3838807122766123927996274552797492779}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":148920216374695501875719574537646768843},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":147636477608791713502079761254147073613}}],"phase_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":4792512278510430162621631815616670145},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-9575289896577632439598202602342635403}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":13075531140099603751938404664061638349},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":665297183662771140062532346705558649}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-14297975513501618192205099515155519591},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-8264894800482125699770586331224309577}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":7817646923425227137318077267495868713},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":14160750941442579697698035830269172185}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":676860043281223378947256845206599007},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-58499819637388402723080982162900555}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-13475562407431073354048210563584606687},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-14954095031765182557212934024285595417}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":18567933188532343647690998825264247049},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-4633346961277076074549025037715930245}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":277157672269507145967393194712678621897},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":253275690436916466563686442625399172977}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":9899409657953097929490173718076807111},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":161005764473646434172113082238484401}}},"cumulative_boundary_form_input":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-16579270309444167048821028078790175883},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-93483347107327417905051819079262000919}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1298228720406897686328005858567043847253},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":314331451418920222454600709463158285409}},"cumulative_internal_conversion":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":218491184047094630194556794421039801495},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":103854289411000229590954309572895242591}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":47968796093546529966457206182096465231},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-6186769568241458791732703531730732389}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":691836417166893530883988044606734404121},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":172959104291723378513449331199997984951}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":42133559937081837791169603056016445497},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-41899775694511668382052150290432168017}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":425494629424384206831345263224490381153},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":106373657356096045304579807923362434627}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":428936478850072565735278129806855658069},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":467394405118895849600371381983881906525},"time":{"denominator":32,"numerator":285}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":165686558856650102899041773850655093741},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":19397018799722821274977667083899360811}},"boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":53796437112939343755295141473222911393},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":26176679463228526891701002420277026319}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":685463252494318356262544452742780052315},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":338055544351458839178609366333665597409}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-325333452481653269474356234053446553105},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-329082334265113399615309809256252655397}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":336681863216674453920843854878731484219},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":20029664546502530330566726077019655677}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-300030886401133272338510488207741094653},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-78683848125410003289305534910926553237}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":15999313751030303834025225906222296503},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-15974056451271559346304280043193798611}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":63085044316550280289189528824935041067},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":60983325642878373915248335213015342519}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-29279140878181871496913353552064415597},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-60524936951660856861127139706953545679}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-6045959589530861392912413902826615823},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-12207017077429255027750139204715304711}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":909956666590364841681295185148310509},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":612780563440274282732956660992922493}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":47679891559137247820438121144742758845},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":47262001943199737609282753760436838181}}],"form_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":135479821528422608378754018436340226079},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":32053440781339896550170151928741121345}},"internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":53357511922670314424311860811233837815},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":99784178908032342723661474295263269167}},"internal_form_gradient":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":406535964037673980933406386920652487803},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":799343416835486970851430553000712349673}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-100612113627358099926910037301889220111},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-204635732669022767093996199115132528929}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":12059225391283345908897247527900370375},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":87156604237274079034222041940359980291}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1098337461443026613467417500328837983},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1363555887901402198005195561093296713}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-41575871849448610453070374941845277339},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-92483962842393394582101978686467892507}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":257880672112108244422034457779656055421},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":254279670749381777874531026166873987387}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-125933958458383688262064618001791585857},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-31962337419666184343498119264165537719}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-303903075685934655274538666098269876633},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-306795801381575166852071529315663509295}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5717426357690694072928936503263760879},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3850213832733159847834208138083807071}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":74895398523071785211769938426595755455},"lo":{"denominator":1329227995784915872903807060280344576,"numerator":1159984047646115845055921887642891511}}],"phase_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":4883848435215762578863784460349356059},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2439552986345800463007215196392385499}},"phase_rates":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":1816499549678113322063409654564600403},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":12083060716676252898553659454195475009}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-7784387128238493858282549993308386583},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-17812199545874519935134299072802458437}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":15354282647056321451395651020689499631},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":13871404387466199934929122982752038645}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":699223344686646752882960877951482899},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-217016659741566482601929397843460881}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-13234011036389853763153564269649687543},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-14719279843094083516929659836804672209}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":9418082842076771433395273749858301079},"lo":{"denominator":2658455991569831745807614120560689152,"numerator":-146886120776144336510710105480929173}},"total_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":139359516967425110316707946926009796961},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":254478009623182315336261163295541982383}},"weighted_phase_storage_rate":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1939847719501250968976964244834785441},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1949516627536857065100052134386988377}}},"cumulative_boundary_form_input":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-15608450628643482852146955185133993693},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-89846406082379388915993506501030870767}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1303272136386235749805064778080158495197},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":631116966537518119305298387903217542035}},"cumulative_internal_conversion":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":219741750732782215688876603658803094569},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":417755849337157926396403054095376203235}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":24188337994720032233471859427907669105},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-12475958850745969470254606297113518153}},"form_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":352097781249498569713881407022253001573},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":88024445312374640257164043495710794515}},"phase_integral_residual":{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":1323875928388737316568021353137811451},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-21064738929786476665525287903271544485}},"phase_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":212815479926173484992633522235816336113},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":425630959852346943681208094082862999757}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":429255379690342948575718635461371333283},"running_phase_work_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":233880218855959948506129334944703044363},"time":{"denominator":64,"numerator":573}},{"channels":{"boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":84378005074437787478484696256589732059},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":158157017743330477977672344170103654779}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":105794267607430993494876360034168060671},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":12853505661976640011754661476680315133}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":10596267543555267296547383217247792843},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":334351151485596356079525940852935456099}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-644782079819410840502609600674652784243},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-652322148837657280974106917284647364545}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":339471049167253445096667607947085469511},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":161649376221255911054511989569350568455}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-76051511942489828345039280339238288741},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-318899374459910241321487701790610238461}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":4057644377892573790627686121586829199},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-4051218131302900480473660658604222079}},"form_rates":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":15799976036028783434996065843385764581},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":30538562956357594556077320552671594719}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-58777214541568169327934991006956164265},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-30383025217272172614684923586951597089}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-48671619461691758698851816791797247523},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-49138777404654278512848029767282646337}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":453299290959028476940006947316886137},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":307093557830230359400962947235745123}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":5995557944551185101163853265356291495},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":23768641017131987609080918619539387787}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":274444665125124895499210888557957943799},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":129844557532904226773585302853430554873}},"internal_conversion":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":13392247180268060064011981978512316743},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":1563391716722251911859809373461046441}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":819481301380611951422172983198374526573},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":402854283713227764431817717969136305035}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-811090198047733968047644133992272231359},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-824789383919471726186305151573476374309}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":94690451623750007672187774728834278533},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":5332681473393022087932966341342463881}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4535487525347889885477045437438680145},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-627961961880478081571793203566252913}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-20403889778428957980549848869272459615},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-90987646525771248931108433314428567463}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":256174014532940255341332217051180338105},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":252339597766782677743880636144953096819}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-62439037109206467333649905403251145801},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-63451789609645973206871679020040554375}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-19113300267396104517811788648396539445},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-38593505525211502010141287461443642737}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5696326889417384175920204783263309147},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3859051460976816089501285186783834653}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":301369612684382784524267140756506140851},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":298685552020939532653303771836373854145}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":9948278524297631215958755205211331675},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-9939060012845812036667396370398929815}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":15998148607536064249169981861492610781},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":13533204195349154845500300255624806943}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-8422906612280331116116103415916624915},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-9549684080056896069548247817983740765}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":7535226719761900381694179841732322523},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":13579561862801136024778716759033430717}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":11278832171730384670481308502993213},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-199886500613924874444803234986042071}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-6494759833078331478247661466095320063},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-3620283426218652870743908191503215147}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":19097948463947568225401443764967086751},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-19063024966137055805493983078224256411}},"total_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":140041505751545583148555539874256631297},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":127743626395084756323175884734561634189}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5638346377966270797900191190555318795},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-525232784454867612602354529717230171}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-116957167053419320241067701207016662163},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-172279201958040161676783621869088132717}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1308231242680334077625137107456760123041},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":316763499424569369653751193465047550561}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":883989095623729385279510907877154497055},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":840201873824482608528385536311135545793}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":48790134614834045247117388654341364249},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-50319122089033590863683582415232795419}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":716712806481276492098719303096388777325},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":716712806481276474174759624254905039473}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":42599862471435347770357229458829405749},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-42364604309868055002506243165649284053}},"phase_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":212832382272991720552925547720932555469},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":425664764545983414094245327979975293195}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":429471836995990480457854234764484164681},"running_phase_work_upper_bound":{"denominator":10633823966279326983230456482242756608,"numerator":14625917776745358409273486598300768039},"time":{"denominator":1,"numerator":9}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":171258504465421422515689859281723316873},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":80490935131857940080206638192770291825}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":103958108155166360206354891746542528987},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":100917433663429546607806916938415586797}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":670769990687617135306708122154433697293},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":661239259519898944628544663861996642163}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-638868972081344607085170474187094590351},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-646445388468253018376522828715237951205}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":81427810167386031975646063864477367333}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-77015425709826489185927737184972331459},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-322744102669684087325706460357869493307}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":1003048182471579233013691567937599427},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-16022630472163021868219720608023488555}},"form_rates":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":15773345577131163011078465731462048361},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":30557815761023733378810496015530592129}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-58951778324396193745235768434414745817},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-30481446953732844840197031241754465671}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-24490446306144786575119579192701860031},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-24727395032330147979140795352087989839}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":225694016014521839043714604062575301},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":76899159005700610467390393166741317}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":48256494886471803781241393951080944123},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":47820018694117842630061481316870158651}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":277303616935450450191704288630387721893},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":32841977251658808211929429795614219675}},"internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":53749972010006032523982649845606964541},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":100272975752189302303071947157845547411}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":825873131148925768950549703835872084583},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":203020889993660258540160284406896388123}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-51081065156187512036912530843043590687},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-831031902832318256403915649501084978545}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":92886838527800194321518633060248484815},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":83470937658679786155187332351556837101}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2339554426932927159083628481333546845},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-573752380600488924228508849913791753}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-40029233953541325276059539731488265305},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-22364664541077640127742955921335877257}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":254358752130841365763938195307319602855},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":250290016357951218054661224554044984811}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-61886429565156330700778317473467579039},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-3934650566470631846781585579972822537}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-153878012397039499793890636992604739339},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-77683402575981140756534598289778775499}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2836154650681595821818507518311977865},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1932686663996339415895955726842404659}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":75801124911666621123376889031760443299},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":37557754855991798102939813959717551661}}],"phase_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5060092777058043675658343514076241859},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-10111249570311143221603915800180695959}},"phase_rates":[{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":1091762269588173595113352180188551455},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":937114711582870715002748154610224525}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-2265990439534979739439772928239898603},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-10194560102681011798506786555147414653}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":14783399499878111057652509363412890579},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":13284812332894324663868972320431632945}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":23271978229931364152480412461838797},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-182631054966620576342395930957673289}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-12741700903776068334375195760552789913},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-14237787649218165321864885231070834069}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":18941988205838592334642399581785692879},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-18906911774651402344930283874835802843}},"total_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":140420646066492009551431296452870931663},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":256309700845936380377114467153430043017}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3537675197533568911158304275354141433},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6426117167334085318320971211483714383}}},"cumulative_boundary_form_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-27232356164150672765161184763296470421},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-164733176789428479794264249538515917859}},"cumulative_boundary_phase_input":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":164138034875013437594976249125922413011},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1271784502401250738612245723091678432875}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":889028155499667450828634281300180149981},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":844902169562866482073842033834159555827}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":24604483347333737112867572814660082643},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-12680192843739825438381810846567682143}},"form_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":364688979734052738252656464962481901627},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":729377959468105458014462298860723539725}},"phase_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":21420390616004075518894062566833279715},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-21302490651824803800256986349350111779}},"phase_storage_change":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":106399282033397859705349891731291210581},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":425597128133591411085453986474519524703}},"phase_storage_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":214793304328153677581333654102972786181},"running_phase_work_upper_bound":{"denominator":85070591730234615865843651857942052864,"numerator":117050527359310254671491989793304937065},"time":{"denominator":64,"numerator":579}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":173485243357924710634846712479936193111},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":81825027644354158370846463301494436827}},"boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":51043154047940317911990740441600785543},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":24743898183972883321458049712067279991}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":165825131447220857545399688767513537601},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":653716265985075663170880817077880185787}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-632932233285031427256729458543410270459},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-320269582862602324042483428318435447147}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":327725460716999875398043927083177521395}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-311604983113897705683708909057568269069},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-163138348899144753727690155608130372303}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":15747166399201794417664960142943041203},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-7860298131349016351450740864808539531}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":62889033446314985203311193994933762115},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":15275018129745718404735188592434520973}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-29541279580298933117365361403349426463},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-61116023791281474337667712031909886787}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-12323868822106745038894356084339841153},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-12444016624680208393809565939497736735}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":224622445817364432419117958670835569},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":307904139893052625576628298511747387}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":48555966094556025559480606348932381687},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":48110218277123457231033796756179099257}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":279826047896777261917689890605068586075},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":33195603741669843354157062295565908229}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":107800182838132068901311267614208151783},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":50214413104433575379166001929568335609}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":832251605056035553595864914989833707111},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":818459471747989925557422506943419021259}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-25734680837056558291861213643480899169},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-837269434165762786954360327662989776355}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":45530218193029574754327669506453746095},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":81598151126360710874410825685166935627}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2412035352532202674914962611188357495},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1038438035958807676823392611939467405}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-78476505594102315018495023427752403139},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-43949785219937984948472965779816725435}}],"internal_sine_current":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":63108202369494849738116674009237149817},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":124064578080660374954025634464379044909}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-7663594322773690218118147667724217163},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-3902004004369331266074281990988916455}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-309732606042678789591310782582480625031},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-312752249673956784232433406500586293829}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":705672225611203480461439009216620725},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":241827345974474528514368411466381217}},{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":2383485412040817088814609317520596613},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":151142708302012452651784798803997200187}}],"phase_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5143861524058214133658839555514111585},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-10279082824744472403161504459504115053}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":18943187819820572830941307454078753507},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":2057859434526671503243931232553265489}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-19413785854926246370575143005307547069},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-21680850385153323357331731709579071955}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":1811589821368299913954563048001816993},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":12986749098919814232533373499423200421}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":383887349267902420997903086572530167},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-165272546517483598142404294999274897}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-12489923781880159914475336619845293707},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-6994825565580252727765598871112189113}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":145808850141041441734401371085154561},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-9314161229088793481541861217024856775}},"total_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":140644590421326577284764250475078888713},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":256943228995627759495744470929088050647}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1463132945875892651838610345089191351},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8621600937730987337512027435439215185}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-100797303874199970249636299405688872631},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-157062080447770277446997393604000814407}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1317889574692101905564059124923779377733},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1276423983310745654235019107412691047873}},"cumulative_internal_conversion":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":111760161133775611444797905871199519637},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":424804885395703564882819423257528293645}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":49633017247603248335466413083850134201},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-51103277604764839725905277056251484459}},"form_storage_change":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":185545176897810025163526966498726476771},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":371090353795620040791420835253827900003}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":43086628833745620245709231329106421799},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-10712620206602105338359294562425890563}},"phase_storage_change":{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":6647333173035724733161642058940645509},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":425429323074286354444983100159019228191}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":429600645348889814742611372466280256727},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":468279803900694775798420278408722790443},"time":{"denominator":32,"numerator":291}},{"channels":{"boundary_form_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":43910925403418908709130306894020843631},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":83080663569636813226636862565170855259}},"boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":50090380780324584282368096795271084401},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":97003464170186496234422209449331006879}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":163940739181054731739007273651534808423},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":646130086663222291794858071080878931743}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-626976411517721884799591796355556997471},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-79326019659589103028258025727009404721}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":41169421585491432643012827378343045085}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-314843388304587916559258882216728233781},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-20594040504434239564914049945058336217}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":15534581860923296537052150864410254133},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-15507582185500976542621864593044650013}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":62672724188406868634041345999663671567},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":30515872497418625278019379085731630285}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-59170181653695920476705740231317901003},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-30613017762322523339279594344782203461}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-49615331040107044868060012932568933237},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-12525637914264023234735646149521878157}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":446870631035146385452364770868391959},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":616042106617890866633525683379181387}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":12215709210715858953151516531999801573},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":48407865756532392625994486462051017597}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":282217680643716888504133410310353392027},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":33521728578368808771567626358368617361}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":108037709198775811878641647883910214377},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":6282610727719997844612970894725089211}},"internal_form_gradient":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":419309479661375026886693060748138395017},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":51551734673117054677025128779503085375}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-829721004047750088425109584603791883471},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-843499993435684217129626333882335849425}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":22302187257200310443436497695741642927},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":39851009677987359888061513593357426107}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4970228451863782939951263924121695249},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-464431431945579772625134597320821083}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-19216471034141898880505523894178913455},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-86311966445369612473600180604644246323}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":250394142751336602250016298253493499939},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":245855272450707558277205828178374034887}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-60705608919971521202920691287200645509},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-61884285541752477376728438405189874189}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-311742319002051854525159074932631205853},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-314803616423821086765848387947654130275}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2807770983130101891937438529492922933},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1935353356452746094063202017801586997}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":307014258518192912426488986568586480423},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":304155590873366166683891587554804379811}}],"phase_balance_residual":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":1306799255716239458838678824144017089},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-10446061520748704851585787447876295473}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":20423703715966819299620941689580842327},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":4484583051966471975848833906409703943}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-10351058008114043467107415171355700787},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-1435866598258609705848594232455645121}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":7099006687489017469176767749887393253},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":12684970354909297065585202869057829213}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":395518213205049715002198748572911143},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-73916558121386210194368799401336971}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-12233585415463636112856477076773196901},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13736976107762380424537795070601496493}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":4618259587849341460731866972313400961},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-18437706150993835029373538472612158485}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":281637829660857488530623402468926321241},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":257386757023330968371883882694013384841}},"weighted_phase_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-289925491429699986755003920713535393},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-10787071603619501800657128172935554047}}},"cumulative_boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-46282002680529462433337183431529982225},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-149273268238116826207000187738516046727}},"cumulative_boundary_phase_input":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":165323193486282166917566391749792005237},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":320242755173430786561501912120157109705}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":899145556688897507740194574214154448395},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":427160864418598564074549287343050202099}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":12515543265446409155948934287124227883},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-51470917666972663972984709409639452133}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":755110633660865938565894124096081269003},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":188777658415216479725133874485363757953}},"phase_integral_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":10834335756417836419897245972601108451},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-21550506011281626121086889983100215887}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":425162807030496984185402058156878424229},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":106290701757624238737314694836508801481}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":429515088420172146115602824516046202729},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":468279803900694775798420278408722790443},"time":{"denominator":64,"numerator":585}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":177732679818027227880714260468377648427},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":168515968228677635063923522579530808857}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":98243258677302241242753693442007036601},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":47501467028973824249240694077834484373}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":324082998969723944670956009605124401781},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":319244715898069282924064045546173696163}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-621005950495487311005127815275820224401},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-628656936646624031456847414919916014869}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":330615432048315475761491242757748714321}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-317784737703048720119616303552153042261},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-166217880371737523567744655815305496511}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":240770899675723453737993521729979243},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-7690954823877854296546974783375831835}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":62444241113932918953836299104507574305},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":60912000365318570256052218353017317763}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-59215303899703354885336749059492173989},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-61293558546498943393978356343894956067}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-6242551009579469256303634925558921871},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-50434175476802019435610191322035512871}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":888532844666455571770161246127675619},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":153976349753831716245266292167289247}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":49177046285070248186604518819890345427},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":48712925063101094665381200246849387425}}],"form_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":142237570664715751629755106353075756875},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":270561133720372598802475972880106353533}},"internal_conversion":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":13526295443762634939356957747310046097},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":100549835521507567156355104735902033341}},"internal_form_gradient":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":211241970737552199733824509553543345733},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":207795272451012927482101338683606663913}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-835923926138306059847787006308328784923},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-849716869597898836457544384526922344963}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":2729041079298034902382500733843529545},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":77780051700045342931920031045747117957}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5117436320805868795137059090904285187},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-204729379959933541960943853839481211}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-18805854876392685180669498213007989059},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-42346321275516733135573673732801688101}}],"internal_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":124120370253312846233530498671031570577},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":60866661635278847767809890070341665291}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-7509573544723017600085230426330266307},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-122621209491347925178492144311847653853}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-313784838261670521783215880475097691179},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-316887270335559463756264956265196826565}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5582816514554755447520612957057890443},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3869847753705682306579827037822727287}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":308988494668843849356844434299252910243},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":306072335026217028449947067088995016983}}],"phase_balance_residual":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":663750435664425782759789794994145329},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-10611993530555758047925475012910582105}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":21908044095419159175218397484820132115},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":19418504353779345400464299138086083319}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-10995855305792373931942731666528965181},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-6066745552373230700141421155762402677}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":3474723021368986969678938609098550317},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":12379079702005393618841990592002383279}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":407232643207128145565926898428039931},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-32583692816762240267755602836775581}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-11972179050586880815333618227820824395},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13479252705511964739858151344289342925}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":18368816521283601204887664868046661381},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-4583343787429488570629716834270977585}},"total_storage_rate":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":35235964850988610595911571950405804873},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":8051330104550359838779658955415649209}},"weighted_phase_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1293711260761309246108818551452537383},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12918570374761083961526886306805578845}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-84232785994588898559765885903604762179},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-70687041113698781031689386308800270031}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1327190700640755877898785213378430121737},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1285424283227689442269373963550425421729}},"cumulative_internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":452108958740154247921226716684697857841},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":429517501188633897679776360110297906005}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":50496317558851078460855871953233233767},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-3239243361062394112434019580845735679}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":768157237708721311757029819556228505715},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":768157237708721291483743234172259182639}},"phase_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":21796427043385504840717919714121152117},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-43356478429336156443458228475042264127}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":424799219834151956108356369609272010281},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":13274975619817247690492945771337251425}},"phase_storage_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":214665633658309709143907763404531817919},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":468279803900694775798420278408722790443},"time":{"denominator":16,"numerator":147}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":179751124057127692245329519137228811797},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":85357308149416944427790525493284428395}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":96275589015508430511356333882464438349},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":92975874975852231778664479441431409449}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":640518181576144136543724885584295220971},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":630802818692708454485633232145676743339}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-615025189071528611796581883256141667137},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-155672493294973562191163032017852163565}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":165760246030973918345952254813696720293}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-20027320208214240651299705967050671709},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-335078115344719983989483451100825685915}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":15369540510810782474396099094384040537},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-15341686727036597303247015533532694937}},"form_rates":[{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":971927724609685397540798606868589865},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":15185558779513319306815076991168816059}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-14804653172472957898135996779920271385},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-30659625766036252569284666677572014653}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-25135319756729196100230353775337246015},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-50770853142770383314657808247813504135}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":882867664159270155075879868824654057},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":153852359819833527762265808769429197}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":24749256735458386564410302285939696295},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":24512669729115774290276313996499761017}}],"form_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":143297632526611865117243907833288895083},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":68181371818129572293950467461886488639}},"internal_conversion":{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":846219140175212454950932548780076857},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":100511108243579058904510665585624892839}},"internal_form_gradient":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":425645612343950843527205672201070227733},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":418756158207907993202135126230153393417}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-842111911291242776170575544072252221113},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-855913480752862902595923426329930471435}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":85419707966401173524133917577573425241},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":75829794456424322625252164657804568051}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":658193467281380170122663343396189457},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-708739127103923460527233367579940631}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-9193249671474431760032427640317543711},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-83038462721789154661763360952691768381}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":245970624974235553395133886395651163807},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":240961586766552532192502918219688304471}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-237685152415602598133662020728801266987},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-242842215065630983854038391634299211479}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-315859743573483325672781221029389856975},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-319002678499627404363817155072049963009}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5547221135629487839614000458047637813},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3866731546779539968354122277564756917}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":311008332567695104390138832139367981925},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":308035292563452094238555028974220453517}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10784366724874926140864000205752985025},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-10776683220697773716324762149116130367}},"phase_rates":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":5848636618097948884257311652342814853},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":10450863439948376522950687834969888891}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-11640695357741685070075094968416050393},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-3194880196170553638580304323812838791}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":13594968760318897432219073889206493399},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":12068686621382333474094172393954887873}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":838037950629002684911288220581604665},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-112799335441224513494335210081408353}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-11705209026344789424741391638364600851},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13215981808924825181761883881121127133}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":18348965536837573286051398641912080705},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-18313428248886235690363077024423880447}},"total_storage_rate":{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":4406866512680057717504639516717380421},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":257713284823749887066322775995269369699}},"weighted_phase_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-2277904120850018157095443298332721611},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-15012202448768402109479093852276584857}}},"cumulative_boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-37903476027205518992883032347023580813},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-33342958647097430880818352713151281225}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1331703618875857835579005041529170642285},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":644891263683591257816999430512121259523}},"cumulative_internal_conversion":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":113661904040169971321519878582759522103},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":863746460576185563745701657669921978861}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":25467665550586770582840778233452248313},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-52178323177979372093495292961875153251}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":781309957088969381388109803284221350587},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":781309957088969360492897671006153861947}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":43853085015597675746902653502616220443},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-21808389119125940915767992820227910707}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":424340380061420420808742485864782562665},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":212170190030710195000883699109396421005}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":429050696583147730254368600329338217891},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":468279803900694775798420278408722790443},"time":{"denominator":64,"numerator":591}},{"channels":{"boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":90849061939162403770436431667415317747},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":172758249707056694375612835168065702641}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":94279537815913097330466966745003170123},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":90924142437438153227612994894123722579}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":158206960989983148115109669620503186735},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":623078558901534497675593157082154737449}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-609038361140391374568388058472556921535},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-616711631447570256737318350139148720945}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":166042855234816720189912851491894881211}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-161404432499115375966434303439661863189},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-337440018819835797737883098132814876647}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":7706548710628629870582170688581793123},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-7692410648512573538955651570508413481}},"form_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":30974958944888879201481475539553534443},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":60523881079505497794656510829261045129}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-59180818984559936602138065260130768331},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-15325949473877373356575547958783568151}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-50605943635003909641807267622674296869},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-51112485362262849101493803201539334013}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":876749607849184518246832920849685761},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":153641525447272588690345811999184269}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":12456784444571488122661279868459668545},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":49345031938873545498983275399323342299}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":288575098603779709046161615312219810123},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":274666043347920764968103759560592020307}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":108352740766621104505142199366778211775},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":25100937868866438732346109691747630309}},"internal_form_gradient":[{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":53598874961749235827091391999332823765},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":843814439541255960127913889144770345859}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-212069612424938825835232777522366606691},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-862083379225689186944557307443281499409}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":41738771915783277286168312860617729887},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":73848833590618438920523290077464607093}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5414415667379456417683924013344124153},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-598463358296027952057808360992915139}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-71830577131373489541943852323737545935},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-5084147662730885968276870170541333117}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":243581853878111673425418266698033591873},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":238338430028716829333204456540497660203}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-234957213467731840520724856861015452443},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-240334664497222357454140969110047972463}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-317966521503414879077849049186098617961},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-321149217041601616919568090794961245941}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5508780254113460410199635804400994195},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3861432701051846690990150628027422443}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":313073139987339200462594704359141399907},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":310043979660637683649875751922022220187}}],"phase_balance_residual":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":1368409381324975750651828657682237373},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-5469965908722944340252897548488416927}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":24881587816983423830691351165850333919},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":11193186537632752163121486117932533823}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-12285001260299260411288986144511397087},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-13424455151017733122781872743151146149}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":13285863737964173513230145209005134093},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":11753406907517726340095169156055129189}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":430865508708821945636804566389449919},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-95248401732188897092154499389670507}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-5716095707800873121859720113675454571},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12946675710923629394973527193193679859}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":18411383180701716170621210038833794691},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-18375763823315686182659337638205970277}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":282093775325196563773847040101023219911},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":64400474467730554672170123110406958835}},"weighted_phase_storage_rate":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-1620330819645786318078643802799147553},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-17064145476998546279423267118964184967}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-67289852497614562632287649225226975587},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-125273791633371440974416559204102045089}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1336122972210978762016370680595342665885},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1294044596543937429066543220159904568541}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":914374267044795134845837569257393905501},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":868452886426598021008016553237124659543}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":51379091269203928917033995077748089403},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-52526228484750084794219734363865659355}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":794558186062430508950633989110770703857},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":794558186062430487419330185668301270559}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":44117951730693025875147258941124093167},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-10970451138636363133031150942842399129}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":423788281229835320095852909843634756207},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":211894140614917644238114761793424204913}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":428675072444561694204829059944358929811},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":468279803900694775798420278408722790443},"time":{"denominator":32,"numerator":297}},{"channels":{"boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":91786454777250234397220960446093622073},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":174648171213235148115584206170592270017}},"boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":46128441296758735480961185550191962561},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":88849571762469336096094274904284385289}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":78137889224386350115492814440900748707},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":153831186774180123215351594388535961323}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-75381199487968571025954803001238822545},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-305363085528135542182546239750809691659}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":83081615241081764944469272522005801765}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-40613558420742121232249861349870380709},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-339529962679797847753878329930382275371}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":15537728833650332468648648941132184803},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-15509034974939213220330809881257381623}},"form_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":30841834795216270762826402796502869951},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":60258396244384984668258840540922277247}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-59102653667586826497677465693934773453},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-30623950784553628145252899980246908703}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-25473112086238019517442459119479893241},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-51458958652998748685399543321945479107}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":870183280945200572180858421880498301},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":306693904337275369275339993639874907}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":50162799370315821827235594877517165741},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":49671905671542703527746668209923766909}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":290411902635073210006226458197666619205},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":69095589051504478825164845835073287979}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":108318481626456659726548272329363289393},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":100226002588187729421993603085942164385}},"internal_form_gradient":[{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":53989587077320450537686545557598561035},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":425040317454957803198455305996914195593}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-854417168199801660823068731749209483863},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-868220255786768594613577948620210243505}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":20375119595116440622104928766907630775},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":71834797220282594866168277914428457987}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2781946467575652195138685717205277109},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-244112074129950199457248892825838861}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-70074195431704883979922880624130860853},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-19903338279101859232319161638168159277}}],"internal_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":120536261387175272463976420022947496173},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":29449442988882613153838097544459050007}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-232120920343320901761095037663547490137},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-237717910172096531286299792071668042343}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-320104567176778935185328233792582482485},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-323326172931283582320224021596305124705}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5467522805388210456998998177217389763},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3854029267067020500836415391089774019}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":157591081985282892033070797020862549553},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":78024446973761871342578114278125871095}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":11108530928501408357221767286598635553},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11101537808511094293775929268192617781}},"phase_rates":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":3295948286193365526600958374690357485},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":5967714094997603868889047918032972609}},{"hi":{"denominator":20769187434139310514121985316880384,"numerator":-1578150503840569568737190295893803},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-7033870213887064299417066824318575935}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12971203998605274568393531145401500251},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":714553941475744852516540748600446831}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":221380265865851089017023534111457427},"lo":{"denominator":1329227995784915872903807060280344576,"numerator":-303528463017162184413027311161379}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-5576327293071671460288570121715401439},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12670858684596793805574089685277253393}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":4638445180970702630328936746077423837},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-4629523436295344302388017476507218599}},"total_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":141025761849793647366497114029593175327},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":32163962300354570318351527760817786859}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-8360378935485915273232230138480268551},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-4767664450795338188461790313437714261}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-58684872362247353157548184183405698517},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-7317947412984440212906159346240970777}},"cumulative_boundary_phase_input":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":167555939197818736683463848967584145297},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1298209420220303179196047639296042899101}},"cumulative_internal_conversion":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":229862923967758822692629879880708202423},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":436575490148959660412336251690889099249}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":12956868277471594096317940315858197257},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-52875528708733305991264435879999028219}},"form_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":403945647400027326901722857552677727547},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":201972823700013657905426724864857020739}},"phase_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":22193681640596045366252379063767611837},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-22075722827085312967919374047626265649}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":423145087630459979158032877900745313083},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":105786271907614986676799885065910608145}},"phase_storage_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":214103134492416958923107909876383699345},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":468279803900694775798420278408722790443},"time":{"denominator":64,"numerator":597}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":185080180896062755285894039779421127567},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":176386185154678947259487909561124890173}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":90209297278457005438891175932813626299},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":5422174376430733895236226067580511001}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":617351902012667107097235851153202921945},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":18985914113060803231671004953696481559}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-597074319205165448605742105727347507581},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-302368240039335856239039461444165284877}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":332258249703895399317570576558569602513}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-326744579111737954570838058459745642591},"lo":{"denominator":1,"numerator":-1}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":15444716809555125941858862082643474965},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-15415620557845682653628049476604627187}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":61404431725841720605874785307962066149},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":59947256201078940268394044887068511669}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-58984863588594424450052956639470481807},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-30519152640522271832402119898737187847}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-25645685297804631666083459222663756299},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-51810145643298145972876765000561880165}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":431586984490326272875676042643971435},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":611887485154557113750632245330608427}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":25252679837617823239528981801779706325},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":25002922226468144501721738390743497421}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":291808085579289262166042612268105290805},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":8683581313972867755449520100896302953}},"internal_conversion":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":27052510427228673885529663231466298529},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":99977183615055188964695840624336925667}},"internal_form_gradient":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":217508266889991404012024921206841379495},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":856304886759776587387307703532533790547}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-430261550429171258615065477648103015457},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-218576635581114156912256837443052449441}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":39740255641244592378717011303780559653},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":69785991248219152765595216482559212667}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2856916274242197176384192489170596093},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-378153419642729513773734401601344311}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-34136984610592902873321522176822025709},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-77836523575307255171629928604699608279}}],"internal_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":119220383951171335778068803596728152431},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":116365664674314464029209774062507724663}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-28646832907129380240611853826608703025},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-117495053727281695695910832173359766797}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-322273186111435198623699757572719945389},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-325532745868805375322186419563063283333}},{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":42370953120618157928124162900569837},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":961150614092545149735970201464371803}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":158667266922630492664891647641889745477},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":157097993569898558752259223917995357513}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":11263892586113056658348149796182260417},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11257260091957098202605756141887085517}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":27850397859197139266745952300040538197},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":6338424781510790586106432547620238011}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-6784950845642786648468826624788409557},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-29415252462526945353692146966345339071}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":6324858125039655684786389295590133449},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":11106785465721825207636081818777014115}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":227346173522663270043631109477188339},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-7523123247905528949912080874214133}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-1358267460756955078983918909618491783},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-6194033740049497936681356810259064817}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":18475751301808676022784199577297466933},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-18440022555943274278810993316963444255}},"total_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":140808363239689682803025863109855266561},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":256849455618576486445974222395271309611}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-10191359099909896559990886048394757683},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-21025146428555281728410420833410384885}}},"cumulative_boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-25004619441372205751760950534372666581},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-54409528089312733876855026889588901603}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1344676074392477565597658815612523801109},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1302276051002626229617474808846728282351}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":924524041576140667124056331378732740667},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":54864838173742189550462038806940249493}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":52280293150666391724967349622146165663},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-53216154941480321690958805613412895949}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":821298647751915956778649916754012354345},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":205324661937978983482393906174143627889}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":44661120380011458042911146730077898609},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-44425533806105545554884169147893116381}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":422413129806497020536329624198073440293},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":52801641225812123404422753194198336605}},"phase_storage_upper_bound":{"denominator":85070591730234615865843651857942052864,"numerator":106911583484486434219815888138430948395},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":468279803900694775798420278408722790443},"time":{"denominator":8,"numerator":75}},{"channels":{"boundary_form_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":46593103091675997085275039086954231923},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":177974101827926932137499789648396431039}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":88138580469801098345335394475537544383},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":42320591924964340810315340707757083949}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":609581893210377646875921002441236638271},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":149939926649379747456140221391199320735}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-591111235712812193432821471071229758493},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-598747188758806338191794777977950821219}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":331896637133631835813046246257510785533}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-328325954240372635427643714057067483001},"lo":{"denominator":1,"numerator":-1}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":3821299992675219106388632292547683823},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-7627856795276542128465247001293621569}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":61112011217234457519277870933960658313},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":59591946177578428858086867855682046069}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-58828207896788513191470652223608851523},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-30368449936219992979120000982318829141}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-6455157302185583547936534494965082551},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-6520738172967499520795208837442486631}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":106965949903093608093997086894475325},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":305039257385882636370335032337296305}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":50854661886763824140911842979599570779},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":50346713194763617654932911624181200783}}],"form_storage_rate":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":73228637467917740475625280456725999191},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":139571491683373504187913643152303469277}},"internal_conversion":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":6751642786912256518228601497461078375},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":99655248073043153339446803008316830433}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":876177171356509392229873587001666336657},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":862480434568833219968257451702606551441}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-866589578832915719201588774590446555475},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-440170716606312474257140398296105749915}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":77417996847777843048891026994062598801},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":67699844812331216771866854845881367795}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1466021999751789305025958142387587509},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-16773801351391434889601426912284125}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-66427098348592485318048086388605839079},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-38006522184351706623420736355953382173}}],"internal_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":117842384768771982856985793672572408249},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":57436055960041105312399244317243203933}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-113058421508419464164455640102742874611},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-116074714201145233177979165447151162559}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-324471596133003811948110491059278599725},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-327768050242835631784203692516235681895}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5376695078397003762527056574157133729},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3833236360239899871252698617609103153}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":319529264368500167184779761275116415551},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":316337728610123380635055713594302071297}}],"phase_balance_residual":{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":356719144753427276764610729191895385},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11408749603277920382255919193014636289}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":29328803915548734645850415833975888697},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":6708342159654722612856558920343626045}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-28418960233228073786253111492007877387},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-15344138541180115886469492536741858927}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12321456882596615101990127276087638413},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":10774764948436720472977614041834265331}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":116662323970981312450588544531457529},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-10678533598061843591397594109498683}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-330381283044686613684964082668880395},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-6048925875371353477141779407536050933}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":18329176085257598329811251553270964045},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-4573356669069513421743898061135363965}},"total_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":140472230881556606043970861308590781491},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":256217566160227032999459958578813016215}},"weighted_phase_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-5985044054278874907279699604861216891},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-22925417206519975376367327725793922339}}},"cumulative_boundary_form_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-10318258013263790512508207809985353669},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-50238260077720696404882375569704610251}},"cumulative_boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":674403785175999746041298206114282311751},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1306243606495591636568441872038080508971}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":929587773666324859512727782501828549449},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":441254375266649465310089594901029421657}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":52737390960508987580933882963435311101},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-26772560137451597802798369157253192399}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":834769621338366525391348321626084933913},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":834769621338366501857098212947380749975}},"phase_integral_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":11234766714790466667114737979514333773},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-44703920130271951908599778347174521595}},"phase_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":210797449844214321862086520727154647307},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":421594899688428609553817444079331258593}},"phase_storage_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":213498742051403444647757584935983729035},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":468279803900694775798420278408722790443},"time":{"denominator":64,"numerator":603}},{"channels":{"boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":93826713235876596506358194518704153589},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":44853483746147229564284053965749391691}},"boundary_phase_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":21511635633282186273600433832869088275},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":82509872423205438959740350444771472807}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":75225067326875031736345092154886754521},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":591963505600079129543876863862453264639}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-585155231917768042094600656463954779917},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-592763236792720630864058288606306423081}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":331257165282329134395678957313964520831}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-329661415587388430732415317707556917067},"lo":{"denominator":1,"numerator":-1}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":953867466363348450770888750011183661},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-15232008692933713909692989456682590391}},"form_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":30403110032819846668113625286110055087},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":59193953723883292277063936537339676973}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-29316727334005219284177463629423041361},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-60423326239284694222878822472650679155}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-51995749511574221811075152192668159047},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-52526083669588857919626884607384659569}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":105981337670814164165761295036463285},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":607974694741260354679084925883724293}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":51210531483054343515247282399114116317},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":50694358430546380348289708602316967761}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":293933715961286766063802766108863258659},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":70046997152838976287909420165337003419}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":107766570832536426048614281080622296889},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":99257901514884272594332330245686753319}},"internal_form_gradient":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":441131946322132770342686170396475716805},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":868600492207229298378936013778335045601}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-872609666224765374732587487771607938983},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-886327985429571255230910431376960504385}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":18828798696763452724127742851528442125},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":65573628898337181147749005580237125079}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":6014513555840297908935603290878467017},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-79516741104251387099169385628835545}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-8066358467404419841973814684259967009},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-74140169216945637544017159454609989277}}],"internal_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":116401377915697671940488283962790065027},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":56658176296332167884549770179255532271}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-111472937865723429200617564938337737199},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-57298516633862522589631489051507517517}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-326698929366913310393179640777631249589},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-330031117156446329124414529768595910789}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2663601534753991896263711897939353925},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":477502208641910157583693090607495851}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":160882629493592344794022832799956878491},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":159261024023852309108468486932839007033}}],"phase_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":2891212902121602378869593074169661999},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-1444870694896104576724581055925067731}},"phase_rates":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":7700456929928779714643616953159711475},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":28308354287261020091293662758125440321}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-14846314183575728393408783829282742211},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-3994427703833371793527721360606478253}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5993392770144280762311088287690051135},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":10436367175643917505547542331303555751}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":119654945338149459187514041617662895},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-25310964810600208388923642420299799}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-10270406582708628141533754244435570859},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11799774412546473321569790367516601043}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":9159030876323915636765320730961021501},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-18282304934450397069207687069147588669}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":280241869160442188490407207769691082573},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":255417664070431541037910437299737071609}},"weighted_phase_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-6845923400422288786697779169586088043},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-24770324540924364113727243361610942067}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-32476777687191731127561750503812900277},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-11508311494129848408307686377603901195}},"cumulative_boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":676420501016619951004448246786113788777},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":655055628382714695759839850482589585879}},"cumulative_internal_conversion":{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":7301869778703906285029348257245958747},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":887161464666809130898038517782325409875}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":13299662054089747222924913508033053689},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-6733616632097370633818031814084277805}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":848293620930129332523276680793626415071},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":848293620930129308285650571910995596899}},"phase_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":22610560151564510361373414825592701415},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-11246622992993099602916213081444766419}},"phase_storage_change":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":105173261348614601939667488422220463743},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":420693045394458372699193123464123102003}},"phase_storage_upper_bound":{"denominator":85070591730234615865843651857942052864,"numerator":106565525098379302182620523704916775801},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":468279803900694775798420278408722790443},"time":{"denominator":32,"numerator":303}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":188921952803989571250374576654130973409},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":45177025268712528469450456525654922795}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":83934901429814916485475937737426731675},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":80362599755849488040053544108954322831}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":148503762622950956945719193353675374285},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":36510487293435141589877651464722941265}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-289605062981862988646858177929340448721},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-586788457925266390544123491122526722711}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":330355290629178927964058793778243719553}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-330759820532290700154643351579072637581},"lo":{"denominator":1,"numerator":-1}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":7685417304784156184057413046665124425},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-7670293109215164149153655726510638237}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":60486875809109120937537763729326064397},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":3672172627438850965307346607436771941}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-3650086114013000970276849102439477415},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-30048697773315696146550086322137974139}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-26177346220125611423982045640754313429},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-6611314171668991610960406158228404613}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":209887591933416768510159920903465733},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":605590191614790606300620149893125597}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":51572776762325104511954795011966294009},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":51048608842283876659066478198682456825}}],"form_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":147431336203859643162756514857909496925},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":70252659302520006059450560050662104399}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":107429270624520781285734975001538720661},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":24695934180825215019899094379967263455}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":888287085654063222803041224606576287715},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":874658957696014210862789850346018253575}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-878577578209492230987823923710779264641},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-892260371438490606666204195838228573075}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":18292474375490266249897305908433177391},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":15851291560396505307719322418813706893}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":6164964545950435462767118800301747365},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-25117887230025377130042008644982727}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-62582649175951407135971066949316929737},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-18053809260295164953701359136567273221}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":229793007120547722078423297498785788943},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":223395295726441375340063698142743879949}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-219660198063870594463990587058626848053},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-226122242126592951945972881250026111939}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-328954234302492653552962334951769637291},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-332320896516630291019431511093026433279}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1318762633795348935396111650617912713},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1902517697063061375181143867759577235}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":40505164150436737638844254600737299437},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":80186967257448993490292386892007540213}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":11713166542900974872307029755228096273},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-5853832403939175412103835718718947091}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":32268058751622257582241721053576192711},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":29777243386782172642076066870870168065}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-7739946805611694436195063799363317901},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-33215662668960019964419605645200069047}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":11645350872964427987346439292823970061},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":10091245624911786479849506067678813615}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":981184581474293923855258716331612459},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-7995271825366666932986958449505229}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-2490084492034649183206394933169118561},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11493411941656840021056578567875342529}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":9219233625624683017141629183444339141},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-18402717125088757916376385408789503815}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":279509168081948967952138628578462692293},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":254454137108715729819474128982768201269}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-15353504325770318373374401137356301557},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-26556500101364294418328111219880216327}}},"cumulative_boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-11810530574752359987600221111575255449},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-5224737482197199261152470651391931971}},"cumulative_boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":678387725268881238109576589076834727801},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":164234781703623104533944651355660800705}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":939675078734624416106525403880679847147},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":222947988081428464678567399494642317943}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":53663944483336539470471982783370578315},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-27096960245612255542296479652170519743}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":861860097093895210006302050339668938551},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":861860097093895185046732002353188296763}},"phase_integral_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":11376797702343680638381567364647164897},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-22636566254156755377539486777779073045}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":419710365703735142718558076423195218081},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":104927591425933776687451151654885509435}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":425442722534966666078888533070866599867},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":468279803900694775798420278408722790443},"time":{"denominator":64,"numerator":609}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":190176756132241858768259174552666385661},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":181859244967101176711195258791131729837}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":81805355247555685137186650663155613165},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":9775134935405922636472872316169065989}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":586232397920675470660755300743199009547},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":576379478876918891391463978065004914533}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-573279636940683076506957839191547899359},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-290413292434970787245340084520982763919}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":164603161287211680394074662395624678835}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-165815014461979739471964291660422779491},"lo":{"denominator":1,"numerator":-1}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":7804123722043922936283101071901689309},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-7788791644292628827415292777868871283}},"form_rates":[{"hi":{"denominator":1329227995784915872903807060280344576,"numerator":234975789169945390010511348840774565},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":29137921971826698406505582807407488913}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-58132754342425100443869541062535464655},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-59758922411650013090919847910458215157}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-52717894571883248542960782233722610877},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-26629555894488282988009175227295576001}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":415514453179403114543609232094091233},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":602883741968999690158374870689727369}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":25970608463368099329281583156151031393},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":1606536816063670905921288749369317395}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":295698874025895671825621964747662738941},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":281612052385987731405026191276635386859}},"internal_conversion":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":26753219885582782572899400569926685941},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":49115690807353324620930251906363815243}},"internal_form_gradient":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":447120393810711627090613718917610109649},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":55040619507934343809357001392680775953}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-884487678464627469435469537026100605957},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-898132912224342800233718419168918389759}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":70979947587558773284115337535865446801},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":30596165505934752710321880379024158583}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":6315297621703845767596807267101841317},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":14472725779749102521401109256993667}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-60579902713574836530891423265810003731},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-70235673470078769813301590655327215051}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":226653860684384701200765781103879397347},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":220030567070956907601612033500972142935}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-108129136500674531330465384345793287387},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-111466103991853964933301469379123906169}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-331236300599499303521643556705631422807},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-334636868665932660158186922405905284907}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1305377153568792930544234781904180653},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":473503783684633483738299974291730509}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":326356291031096519031601821064860616567},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":323013392580298588781301211969708371293}}],"phase_balance_residual":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":1482470747503627079274094352618259365},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11854689904188708796890062847681868773}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":33726132336231310078712787699150320207},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":31238668479171219904829891991347525361}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-32219442713523291245781359318095116667},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-34468003027324448645961244575207430027}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":11296809518963630187599783879185266243},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":9739061959854513263477175701610036161}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1005110833590657531449569087372362549},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":9213623391442299844463094719515985}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-9641590968891558935018614442789585487},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11178354614151329611632705271616402223}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":4671628874123095364255464624442585065},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-18650775265149485401983549936440498061}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":278746839946840939260000095818254598009},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":253331336114648058503462275279381500765}},"weighted_phase_storage_rate":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-4238008519763683141405467232352035233},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-14140358135669836450781957998626943047}}},"cumulative_boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-7353262852902941422719146707997137035},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-18767786901830580130025563166609152925}},"cumulative_boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":680305038282495824479979401201752437485},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1317543929229762057260234537963849805385}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":944691307463171187838944041487541100761},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":896396548338903232897481809094790879451}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":13533290089427230768393147550109272717},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-54526220668075495243012115686290932083}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":875458561089289835450952146628791358619},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":54716160068080613109405852024078493413}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":45797182442023822174967390932196130105},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-45563724017473761364856366680786033721}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":418649804208614691596257887408504834729},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":209324902104307327348810313313963980899}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":424542834386036257153858838063137683563},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":468279803900694775798420278408722790443},"time":{"denominator":16,"numerator":153}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":191416636470751536474631279645163369251},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":182870219054756164838345229580067199377}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":79659554556704226681898131889814174949},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":38013610294121945679575246780397929893}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":578458930326001582980492852772657637357},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":71076070188548566448825297366834560611}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-70920923289794530859874737205156322289},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-574881250888635363912563011112167868565}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":327825367488777657417189079400312319391}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-166140436602691576228370216159650322775},"lo":{"denominator":1,"numerator":-1}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":249525646049789548543451070244931639},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-7969269054370934499547056868106137729}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":59806828892315995509836879460751856675},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":28879328246384289836816741359014642351}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-28914180874255115387358638550761533813},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-59407725566361408156212402286040831977}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-13271299795959257083360956725298174503},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-6703952084550158118943195188682729259}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":822153302904046057733307656837324799},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":149977557885091130159439672230720601}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":52315607777646889729556954197842935081},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":12943982921013906671974030582054815541}}],"form_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":148219761697881727797132441358359074161},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":281994050035834800995759650922874980047}},"internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":53257975836912566760111242506961943127},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":97599662993820759649138784640975324049}},"internal_form_gradient":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":112514902361797003198394330533930829251},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":886567619633520050342893585328017275307}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-445167239792342172963997316586278264487},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-903940077839767317303468046691231611355}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":17185809801883655831184449826839658993},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":29466525055353772824345310427107196879}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":6465371015327665553947943471255156781},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":82614165902659242661601662065537713}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-58520177755749035715286519940715628897},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-34099496006535264997999298375959701013}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":223383715926866705364619695713964342965},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":216537145267916890364971275296576565421}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-212738596109375101886747754204397908557},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-219622255696340152509951680387111993325}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-333544143540586592205539350277093966723},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-336977385901452114670487499731745093513}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1291435388263967558990554540715196539},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":117792098513785065576532211813632847}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":82177164531170259067998548573899622861},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":81329443305698084234182467588328131257}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12004012913592370658453587013713452055},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-5999696730140903403737912946373637423}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":35174373207082434518121883267901651371},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":2043209204702356775072306044687436019}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-33470627107516213618850629970642897765},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-8927867927562703781828756678669235395}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":2735206581006930298648051035384975019},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":4689743118300737772597588068621555959}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1028995756012464177885593126847553183},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":26296905745644263658243040194195973}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-4656887780221918542845355314442499407},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-678387918297804045414592828997704723}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":9528682790387263947075377568220257373},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-19021642889019301935486239256010988099}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":277954805223774584091646478277303573909},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":252054548138436461221043172278966556101}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-18484718171988871502618404439414574413},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-14969750948699169887358239321954211973}}},"cumulative_boundary_form_input":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-358366929452462785824372011414202571},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-33249553044565312646652410014935480865}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1364344118184837159585672777335839914421},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":82569231574677249354230919834344506957}},"cumulative_internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":474842121348940870486352235236284391465},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":900971532541738581006035189624836597765}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":6825771644897373026377629351581759335},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-54871772214855422936438568414728809041}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":889078599611786939923751404407619710715},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":889078599611786913463075949875212732753}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":46090980654132694057155856368820551935},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-22929071246005836838539852748678842887}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":417514443151086942752146103245763880317},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":208757221575543452451278941106822815441}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":423564703580561977830340845787242297463},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":468279803900694775798420278408722790443},"time":{"denominator":64,"numerator":615}},{"channels":{"boundary_form_input":{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":6020013407115076812412362606218581355},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":91872031131766006874914994121485701911}},"boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":38749541224249367789373016469312606735},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":2307602690825886585516744571208008027}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":285350038295114513434154162420951816185},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":140217713861560517369803187789847282677}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-70184612444265217140499151172900085195},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-284477995775985990962389846410791434263}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":1,"numerator":1},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":81556819566318165229575085066003532521}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-166360565355570213163409565886436234283},"lo":{"denominator":1,"numerator":-1}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":16450471188987261108630867348416142955},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-16418943320992833205566304381334136005}},"form_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":29722896879320636597202612222077692219},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":28602318108623528191986311437163717265}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-3593060993065613381032505073680487973},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-14760907141513145353844981658812342767}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-13364106270780742755292819304492620363},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-54007796353286596286471777076894058365}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":406438073885454960847013840112569711},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":298350339554688907435459589646415225}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":26347850763479313928281281898954980759},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":1629646127653828158585062469644220447}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":297082064553661698777868955610158745901},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":141079325210227492409887654505987895567}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":105937164713765360028146009994315323779},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":24221882775285605979852025004692799781}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":905916782399051568771184338224954392827},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":27887703959732105186473202564461750053}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-896112642991113702201570817380755352345},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-909676487454207929696937613640836302821}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":2076803728863305897297314780400616829},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":3539081519948212759508175736795699611}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":6615044780059527905338667487482768901},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":67915415843617767081362435935370673}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-56401113822849873169510025799695150233},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-66102794928538621509617365459218773021}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":219981039955945755568627564455968129345},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":212913716408867254695937754469842741253}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-6534365694849328713113167707512664551},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-108095361156123640101511963793782176161}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-167938312328312278122054369551842410755},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-21208812032507349551299082668847007967}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5107451468230923585563211780576242653},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3749180939764123905048904711219138787}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":331096857585707350331567758633271503523},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":327659795365652540000794161982328811375}}],"phase_balance_residual":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":1518084305753918722989814536764449847},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12140494465161195600912447148337614875}},"phase_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":18305254956088223620895482425830474317},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":34134114507556658002581866468180667601}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-34712398827954425861732155680206808385},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-36945123731239750479132911164356719801}},{"hi":{"denominator":1329227995784915872903807060280344576,"numerator":41316697410034435108235164925227449},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":563262317904936249280488929549880905}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":526408537760356730785428590919547401},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":21618148287306785152908275392757921}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-8976516060795182954340417898212997459},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-10520586565066791914881449169632958045}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":4886378005598918695952868416746904269},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-19509804173531092697740841554127626225}},"total_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":138566430196178029635088644094307638881},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":250629707302650100878200794783492190605}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-19949204161305639507691667421543468139},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-31528943117804883941574514228483600529}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3296149239433210645428591726700630897},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-7235762896315945268597692416372709647}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1367976887674610537815926497629837971303},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":165571138653884352443246229275790515419}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":954650047293839492224023814691052313733},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":905513135562104632127257444313216497723}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":55082856392599951986788713624723405977},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-55236307749095708144800379981961131805}},"form_storage_change":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":225677472196044255491316154651739556631},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":902709888784176994724652026435791812825}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":46388435010257493499464883480092577153},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-46156255165013123689342162433102926871}},"phase_storage_change":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":104076874236873205205352725748841096693},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":416307496947492781999326890883518546709}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":422511083763103892637484070154178636013},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":468279803900694775798420278408722790443},"time":{"denominator":32,"numerator":309}},{"channels":{"boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":96878595131137604535722369682694287799},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":184484052713070885052897197622686185401}},"boundary_phase_input":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":9415706490554156213636312516918089029},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":71650161490316389409471032569192670047}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":562963230416379788022401237875010367103},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":138290499745966070829162001526305136139}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-555611607850212150103205984795083768357},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-281527123326820311493794477881401046967}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":339968825271582888106979650490930570687},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":162213304626153827752418254510037608943}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-83239874524773751893799783004371092721},"lo":{"denominator":1,"numerator":-1}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":16955797139135318356791823469984886835},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-8461932092362882371188096395688894337}},"form_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":29518636997012984196155201050363284733},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":56615194978019278484123457613722737601}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-57115368973533054528316835226792460879},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-29333230269844492538458863508684528561}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-13457842781370343943188118317244583755},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-54387435390154087022390556625134119521}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":803206142614412931138239052306243049},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":296635194333607310363275486530971995}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":53081243341152677061420625360672150667},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":26263587156393156119900390848350246021}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":297534243640005044486522664635268443023},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":70527043594705444491582320573869151385}},"internal_conversion":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":13159356037659041704657591965183227327},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":96094393787798841076833643542597370787}},"internal_form_gradient":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":455811867870799853579982999488424354923},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":224540435428656732706291436958972207093}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-901817218769574304560437659163239984733},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-457667372782298029036224286934770919079}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":64121388791164553155763310791907245055},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":27133564654208030523003843125205924395}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1691045254458640878886076609834623445},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":188539798119901751384568239772742533}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-6777585177094797122734945733720694619},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-31971305209476439795225193935696615533}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":216444373531216311527327010517569270641},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":209159032621189707406253109032312972145}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-102670086311935277199946525102500534001},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-26579499676233596632146454656200366543}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-169116240060478009922993460199174908179},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-85431583734648804988950789305383793341}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5046693033911270856755458258996159601},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3727627789258565556529483388826408769}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":333519288247954762438485456880420314861},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":330037969869759949473504246996363864051}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12281555506109579445732011830641770035},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-6138909067650907442765788551043377339}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":38033971542866231900342290590094839105},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":35565666660107039838446163179839976903}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-17971933849584250517055206378332696991},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-38167810341180533118041182304510178545}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":159456812250485779907143534833972189},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":8636881876841483685072200542027321901}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1076552844956738625581750851292736567},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":30007040840330398461237060415136949}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-8629489465287966457734241586012728977},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-5088391261187839662646297491982809761}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":20056898131771405242096743121758209041},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-20021227806554087067480677714596095523}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":276191112335158679704464973313637064489},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":249061614380154371713054561786137192307}},"weighted_phase_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-10671565652423182391028845660815689267},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-33046559998667406253274720509339413233}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12378517532977361070652563884453220379},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-12309603299900591102981745798104565559}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1371507777608568346396040114823682254689},"lo":{"denominator":2658455991569831745807614120560689152,"numerator":10374435238679167189840146787953164295}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":959584805807961632863270411677996023981},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":455008780135453851401367010677137874739}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":55563060335183806927644442698051129817},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-13905278983612469164036066710040966987}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":916342207406489145318451480859908617059},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":229085551851622279319444677180571344103}},"phase_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":23344700330916045068479651644778778749},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-46457911932856825836712140677282851313}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":415032305404803857573227680469566563277},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":207516152702401908878296976396061826949}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":421385088988669503331154992424967137299},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":468279803900694775798420278408722790443},"time":{"denominator":64,"numerator":621}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":194359021559141812596079445181119702859},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":185093778383773761657176064040769585579}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":73140737406907275306567007218654176713},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":69450554483924224123653814184527652915}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":138813099362288989707743187910695859273},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":272752819067938771134380439737535144829}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-549774850036282919379610757218227101651},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-139294840563392550987803449797471477215}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":84483237074559959840247094030655120217},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":322437576408221799822429607040328351421}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-333004567867379897736991609963820266261},"lo":{"denominator":1,"numerator":-1}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":4268091789950602391860584146014551459},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-17040062904741339285928439622069692457}},"form_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":29215822799148206084922430892807139441},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":55991716412235783637830344216728320175}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-56708307877445378114442794858306933419},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-14569014244606082323776879990910115883}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-27104912323332969193738955181941122365},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-1711572101118907647001642762266658563}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":793152363366765883257154183659227075},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":589634820896993151768761333370378533}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":26735982040070089365738622012277214823},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":52911174374543822959664922306242052451}}],"form_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":148693403249820975275021389465630749007},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":281845387313887999038565427889688016369}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":104526428659487525728414422330638005967},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":95220660956065779325424378306433706599}},"internal_form_gradient":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":458610354155345513743350865923170052087},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":225957410529801986743550223469029645693}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-453721974624742496235798411258038963347},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-920902700568206227784847219311145575389}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":61732303332323054312918599919129353973},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":51856616524759914376101689395366823053}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":864080511677634804204136832897851115},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":120343634249251843144883262952948317}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-51977486771624941210037409088281416373},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-7713644041010483436206761479555568463}}],"internal_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":106386168674035661232253474483349376437},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":51317979604866794742012527004573917247}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-201458642408491904794755243011295143743},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-208956530529855766936927993689584023055}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-42576296715589155254575099196586555939},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-86032997423430511929393757641665262435}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4983523275860827888392230835580683191},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3704784843261454371830465727423153481}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":335974259054371383149399575089602295269},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":332450713415750794643679732202632110247}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12409136114086269096868618664337542143},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-6202918551241599473796535247172106859}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":39440193893381547639707596520953298247},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":36985194359061200613545950959274414593}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-18582113470147013743252533787906976885},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-39377887954150461511614686036976546867}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":4912500611893748254634436522943922817},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":8253236851936403448594403533409211987}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":275045369325739540779781392039208547},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":76613137041646174261406297926348685}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-517029621824856883435190186111054413},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-9821316627025288502737912263548349243}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":20175735570466932261320911224191448611},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-20140132303802791830531466092209606807}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":274720068438164918042150789449488687105},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":247359626662246296072114986307564272765}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-22666738061477032507891989481772810909},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-8621440162910425741612610395530935901}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":21489096668562133536093787877318206451},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-5070267792232871166780856898813398489}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1374936249674517124926035443287056669223},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":665591602646183674152667530698952381745}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":964484482151375110631789837724744680511},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":457240514376611643104306644543694914737}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":56046563065397394045302442312220501271},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-56008129339179562110605464040793080143}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":929965449480757710919668876209103142833},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":929965449480757682057278161561269806819}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":46993603490065175424877068477818687737},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-5845361786279558306597688071794142991}},"phase_storage_change":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":103423081657764353274605573037744692679},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":413692326631057372264640649625313695821}},"phase_storage_upper_bound":{"denominator":10633823966279326983230456482242756608,"numerator":13130936268259502940827813504744554405},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":468279803900694775798420278408722790443},"time":{"denominator":4,"numerator":39}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":194883879597394573369423254963215671629},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":46394107629231980746729537264743363015}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":70946073766217750309174522918490714393},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":4202790319333753614407057979085590017}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":136893897970978499063587897020728048405},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":268943435410183963345415691395928896907}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-543969874554868265993836850901837881547},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-275667296413153798942289780771635712953}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":167861091413102950074545813749888692555},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":320274022485362377563326502229297167009}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-166432403449429248780542160585032009617},"lo":{"denominator":1,"numerator":-1}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":17236617941884570806550043421143418887},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-8601981299306984923743482181874219323}},"form_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":28896480305312237360811702731422736611},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":27667776473598890276861696063664740475}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-28134276347927448391802144681785894755},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-57872260558111366723566850087180453569}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-13647890461706863901655612146877766923},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-27578087300202485698316200957725111681}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":782724222569959431438265951002717627},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":585809553954888420367055211515270215}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":53867580901287581951539027394899749731},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":3331275618546124025895555241030126683}}],"form_storage_rate":{"hi":{"denominator":1329227995784915872903807060280344576,"numerator":1160457792579347542868718183955765379},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":281372719755319183686957164451088219535}},"internal_conversion":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":12961600344567322520627609231452623319},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":94264146441500477180923662612559066077}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":922719147712684495319444711296823846149},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":454701689018665635806146567167426065575}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-28530844393285335439860613005895576891},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-231595916970385591943214312244402876155}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":7411071799778210585818615794508724951},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":49391913960753325224942978382766238769}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3530150417486565967248597060128377367},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":584442747410574572341956187165287357}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-49668524725034991714513069601766056333},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-29704272249835194893579482954949018151}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":208963638624420522629869895929230130803},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":201251277378374360337671087626054648419}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-98726904216712600030765932416206352173},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-102575419463526294107715756417176954821}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-343008899291971959893645585136509173765},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-346556465849496415606238692433050189075}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4918001334825133564734409543662788431},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3680749982214782137618652954235741235}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":84614998213069460343504625856112682835},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":41862044041229190466616888219836492075}}],"phase_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":3133341653792580938262095093351217367},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12530508704729146526286391610320407321}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":40831972752480767945177347861068612585},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":38391120476209067742592428810166309741}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-19186257186333761756027505202130889903},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-40575363676308427325748951765977558681}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":2359017421087302899751765537271335169},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":982620906952935778865938282873115825}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1123681777601809935425567015525463803},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":93016952204600956169317085449448839}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-7904991226071340536080995527297195825},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2363790879754343137425237620447593647}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":2542666030252098946937651569435795985},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-5076453747076253347419036183751731373}},"total_storage_rate":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":68290600967071193098233072319957315053},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":122762069187653655144460816573349730265}},"weighted_phase_storage_rate":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-5978697758007049645364891453211669203},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-35848581380011873398035531304388759005}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":30624278524690004162785502953718941059},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-31863247157381972944235066953367807347}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1378261846882308581971777999048860921461},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":667167649015933831758070177441109478001}},"cumulative_internal_conversion":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":60584067642536741036064074449158713391},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":57431228788604288817279317860772095981}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":28266611286203836547262158503474692177},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-56399724772583569222165305847361240789}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":943569636032694321226758335825935112703},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":471784818016347145758822694146448557263}},"phase_integral_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":11825228472692981957484197598696397151},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-23535528311294134000194613960869478761}},"phase_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":206145564821025867384525977045232565175},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":412291129642051692894919685354768428243}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":418929059864604577081107799026940458869},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":468279803900694775798420278408722790443},"time":{"denominator":64,"numerator":627}},{"channels":{"boundary_form_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":48833493839068149790571276358646408315},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":185935584119928801092275414238631877535}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":68743212853560520032346791041695281791},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":65033936006643708390418404215522152777}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":539938311573257932522942064062941507455},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":16572218530663900402623626707163217177}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-538199841528671294261034909223903513799},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-272761551746236275288568534351423784789}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":10417187554062453930130158038301813243},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":317949387025151463428198911846670925075}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-166274268483884520521475105610320607687},"lo":{"denominator":1,"numerator":-1}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":1090437087980441389159126770624162953},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-17414008186712748616392070998366114383}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":57122521286437484271839372028741522283},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":3415501459674166779753389789115170999}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-55796855536092156380433816683994312579},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-14363730497884389351895634835648422259}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-54976348182478143370337771005595316193},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-55544789845569144670680129290357218953}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":192982858148488307937362639123714945},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":290905122780438671340758221926244023}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":13566949467645108398697588053435243297},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":53694600743156735882154566022174535721}}],"form_storage_rate":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":37075852456989927481121218228554341229},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":140346578666037590132508322360726986925}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":102773190162515329719123610285234454973},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":93224242128303556530148303259816245049}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":928114322192606843886221879462519666435},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":28589940353552072946856338327403627421}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-229610418005493665079543015378708732337},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-116471616368611716463968631683300668835}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":7098546241329669281510801392271463489},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":46871226823226323635589836563394259149}},{"hi":{"denominator":664613997892457936451903530140172288,"numerator":14076212345741923194635968808275355},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":343092238462872181801246473269613317}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-47291789369427347465983592256858885439},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-57038823117786725616652355379278753895}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":205017077953997232088513558187251413839},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":197096099088652270781962572035503264955}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-193324437369025267772135837519696119303},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-201217515602628665633328941072320661759}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-345426583142535833957454884571376103625},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-348998207448057941967295947955180611069}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2425094117712208144590375590480145815},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":913905396618662936451255506699796659}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":170487315116711315277273526069259842769},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":168686563232138253935103327774769826579}}],"phase_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":6327032574261100744367454129273063449},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12651651106870175543073189390455068883}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":42208244148267219669591847142381494229},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":1243198318905676477787705487222123957}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-39567889034815986109122836801540608781},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-20879700883058978760552576585275608209}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":9038149784592088392205122416338419819},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":3729893718848951870570873637333135915}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":286758243179006763343196991919472999},"lo":{"denominator":664613997892457936451903530140172288,"numerator":213300100343083617828541388610219}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-7526722045805110291804666905109147407},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-9078010647340030403945926057443233863}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":10276055260998745263152814781557262111},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-10258355629685575485244976681701486671}},"total_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":135760815324285000004499724008634277267},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":243560476950461968224141943112877941709}},"weighted_phase_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-12542594503674709919985148905583087649},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-37132680381613212040874701608576032141}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":39780558619515282248517617270965142619},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-2893439581470038799129332113866492261}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1381484184984819231348294254878940387795},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1337383763782179087346941217579821556913}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":974162575569455762657609110418659779333},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":461634773483716425144409893743828711091}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":57022895941478081830460543576135840943},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-56798207931820453761325493636966096233}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":957144926257150621726245674152861325037},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":957144926257150591144801234052658825719}},"phase_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":23805599226699056137605786242719680265},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-5922781418908123379158621873130967891}},"phase_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":205416193333060718482271839823300569055},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":410832386666121394026205492406235222485}},"phase_storage_upper_bound":{"denominator":85070591730234615865843651857942052864,"numerator":104401465133299274337774551496281346513},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":468279803900694775798420278408722790443},"time":{"denominator":32,"numerator":315}},{"channels":{"boundary_form_input":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":12231972686327061360654105026179271313},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":46543724917316067870780886899520612169}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":66533678456155786703378540558111371403},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":62819895196995857131973238955952572529}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":266172905910807763645414456852074688905},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":65347883010818492612118374357472808627}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-532467824890062285442559066458696321995},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-269873986156339561681385167149827581767}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":330829447221454174968261936482245444127},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":19717292557792117554957335745844584387}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-83015979284273369881625119368650848389},"lo":{"denominator":1,"numerator":-1}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":4425474470424509121187217391396278187},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-8847636957124847974987942254055808137}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":56421594845346662260629775581171425761},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":13482602704179942508164236236078933769}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-6911744942164552384460942115962826071},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-57023900905946898435471499522913063075}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-55363938765606520322544845976753333531},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-27967947690555640643396483405338390637}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":95097996234148867452660198171554065},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":577652596482761065260658930779230103}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":54672306579947160746573869594849080319},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":54093453639946871634081468094522763795}}],"form_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":147988637654695343787095292561204216645},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":279783239997912869435330022976806918963}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":101766950930929583614840227066050194229},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":46050238879214189803159083979370435933}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":933401667847288851358920504854675551539},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":920249095960830156616744896076597271975}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-923803285743059740689572356299174652827},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-234266478639995981744894486828214820595}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":6778739379178696137751088598912239151},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":22146409054404278663140736966495894677}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":7352676053957987801469644950034680541},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":786504080832866963750242534004907015}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-44845365355993133638000927093898913797},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-13649527856527796965506060108417316157}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":200931556388428286649131269963692750921},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":192805466355985171345658289270180586221}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-189069374073880155375655224790042898729},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-197155237574526930490942620426170598197}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-347861886599649220145633261961461671401},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-351455596002532898298276817957694180195}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":597518332680623809735590058622167221},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1814749153437311399363261838332252249}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":171758116706370914081655986334427239109},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":21242449570319644054737196817937480681}}],"phase_balance_residual":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":1596381496633878445854429675559102909},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12769084609010227866358298340794061443}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":43567987009342826471924680557453966285},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":41157816741557340624638759019732618153}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-40749534368768169066973805949288769517},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-42929190624337296649971375255867827431}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":8630959041023802415659804842992377829},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":7049420945487097131435617890001612289}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1170214738940825107715897258421160079},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":62588006113249195366993261479301461}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-3568680785584170899807338371835939529},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-1086194914618460824711522074125978209}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":20806476682267860043062247862748613657},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-10398942675379359903906061870798177677}},"total_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":134900635774263994329079517208391817431},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":241447356086630048666032097235383357057}},"weighted_phase_storage_rate":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-6544000940215674729007887676406199607},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-19167941955641410384648962870711780953}}},"cumulative_boundary_form_input":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":6119317266782572283626024505074949513},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-14420568229763547667263240617271823307}},"cumulative_boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":692301475581225766925007561983800929165},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":670164223184769134075001231577940916875}},"cumulative_internal_conversion":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":244733225348585771722388686515595220547},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":463793378431179590291432975805361700275}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":57515439385643528402013180518714017127},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-57205811510364535320945756648513277405}},"form_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":485340814009119580658807945756082797185},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":970681628018239129837617185454467200887}},"phase_integral_residual":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":2995270010846973330543149736007530211},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-47696329151345642745078727771941323849}},"phase_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":204659932574373377274569056434810717469},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":409319865148746710522070444584937133931}},"phase_storage_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":208111970386773602229724779888503332667},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":468279803900694775798420278408722790443},"time":{"denominator":64,"numerator":633}},{"channels":{"boundary_form_input":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":12251182921386062006355067023163781027},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":93149052261179320849338579536187378353}},"boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":32159482771018029766412167944158185427},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":60603955726256098798351253364123660091}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":32800194312254398215387883602868720295},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":515307911021816941551046810060512236225}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-32923550909661431974779766524179588297},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-66751524078102654950452851462306177297}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":328173109737355677025692894760677996585},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":156434232659715320203505565453867457965}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-165709463985122563525726015715072067195},"lo":{"denominator":1,"numerator":-1}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":1124981379986894734567359410160646971},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-18032778749245672731988679202587260761}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":55691412002567297363413359110847701657},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":13295990367277503467081226414833503521}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-54760598104101277222269487990211059947},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-56579066741263190511982391558933616007}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-27877039384761450976491902099194998499},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-28164612034060757893281681951144264167}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":187323010069644028034313913183685445},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":143338078871079772205086130971759785}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":27540393384913074020371511377321797687},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":54496662807129156566114465812848700885}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":295190333168191217082537481892527384991},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":139329869843808493239822551750148259607}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":100673591694685667109952710332263283543},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":90892526566042259630782572257582276749}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":938576785406893210193393311133496373115},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":462755937511676495783556969297350900147}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-464533692428019459113223813677410064733},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-942258182880211448887487936057597927307}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":51611492563482109188062562149855595427},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":650859517138738803744565457257972539}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":7497142120155592080364945982719894331},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":442655062125369825442151024341614493}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-42327427390153048597274774411438647923},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-52084619208610510408260911350110429953}}],"internal_sine_current":[{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":12294130169285493331116164179591368215},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":47094640650261325063194571996202687547}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-184687550159838069504649728188657810789},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-192962774343018663299545930535720301237}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-43789151067499951941427873597305847279},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-88481738257411960494758122164002657447}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1176985184566241083090944658999974623},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":225154927780529288134400067729958507}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":173041395070031704378134711041906574389},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":85603157760018538766307654874267623759}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12884150049696631145864352102485858921},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12882632226568864446970117173063928699}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":44910222410218272612372941685069428825},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":42516520568997178966563969148909284613}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-2619791109904884249964027958847198371},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-11020985588601369189953873104396240149}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":2053556040457193602000077296305118655},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":3314800301153102440566158743094996965}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1193207227485214801120473631310170299},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":140901482443805257971944916454455511}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-6736619297506140363026658444525941801},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-518095287881840278987336740280237605}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":21102787000843539419771964590375203663},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-10567172923585564849894329150485091333}},"total_storage_rate":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":67001211812364569979200094256718405115},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":59800886609260480483679187489491671155}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-27185485918732937165737104865653764531},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-19728096625287532272464176771164917297}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":58142925325300124773774496307972431875},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5687844580277986337637748785754256587}},"cumulative_boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":693808951336117237070308132356183344107},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":335792314198551630695293794539331282579}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":983651976005031477535333779359205723605},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":232961836011285602875764721171324392443}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":58010708273261932150022161488501081611},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-1800771674756414918720748996328370819}},"form_storage_change":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":246042551934531589328860824347011098699},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":123021275967265790613755538473083786159}},"phase_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":24120069334865839988710165687548912723},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-6001642396023172819413924526103349247}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":407757419458906725223261730173217232157},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":203878709729453340041122991909121162233}},"phase_storage_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":207393487516216761006090788106920157383},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":468279803900694775798420278408722790443},"time":{"denominator":16,"numerator":159}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":196258368714749076701030601426141986735},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":186308975086261054403983657694558173525}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":62100539538191349207460428474408306325},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":58387515333880998913756295049046080661}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":517314984738021951916966605886013680137},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":126972533130075581441179122316835441629}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-521129718621662797675468224629733232981},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-264159337703554556407689457661921752583}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":162696555442667710626857368626766000379},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":310136834515696971154920761196213386517}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-41327669684605402886682628486896130387},"lo":{"denominator":1,"numerator":-1}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":9169629043011077916092980951102357669},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-2301574771280008659137756065311036743}},"form_rates":[{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":858330717916673768254647750168795005},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":52409883393473298244254499055964337015}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-27098747170323895292267690248495264199},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-28060149832150232796523863456683620835}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-56146503841018745930646252525736388425},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-56724499628037188607018330400679682961}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":737466045727008780951973088575117663},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":71115635724544445417845843706675257}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":55492906956109310799390160231045819125},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":27451955297731049073879410209377649005}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":294248444063303995258831907135390803499},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":138669271140718675639916763111991553939}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":99492771736928343851904973320329415087},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":22400052722755196255665571884656978659}},"internal_form_gradient":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":471817718430886011267961313666056352705},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":930662077233506157435625336422613708201}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-116778703902172108437409829707832870917},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-118418179668302203853845813323176691837}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":48931443650103487587434040071656664677},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":38956179769339338591342745137239315861}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3820148668406325618645686666534895237},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":491257736065811836225042650033105501}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-39736239594986757282696813199702421571},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-24748321082442012723662125074489736011}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":192339780844099861371309263062281908641},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":183814679417603279154820831118403493329}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-90088996356908629250455047594414935923},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-94319498253466891829462391279767324885}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-44097360997923900144935401588573956137},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-44551317827499647718594288624700979161}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1158408955763942658635388680171152371},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":446832717495193365191945481058117523}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":87168054409827472788803772391428045253},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":172485722180054537915325048569508435675}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12993185625248687783053653823017127363},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-6496060136057970600522002386436360415}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":46234012743351482118681599064038664641},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":21928744327773062113562263601788538193}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-5383561256030000573992261531704872357},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-45222892305673083161328981479960002341}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1946920282384125988740436870330378919},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":6200068574266846801339290251976559291}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1215991087845576998490494984519007961},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":39093048513503810823975727883798033}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-6324218951426035520856568014202733691},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-7877635266992024222853747791647662223}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":10719941432681642392998464971760171125},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-21512157596448451644903367513659514323}},"total_storage_rate":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":66534093321376334525934220671781149109},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":236846750656491974263587662386890778737}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-28112070777798657155095024448266207063},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-40491791624945377016245863837092329141}}},"cumulative_boundary_form_input":{"hi":{"denominator":1329227995784915872903807060280344576,"numerator":263056782651578077125528538085245459},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":761347156722625146887246292169539449}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1390528865463087193634715972297104577573},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":672953085787741097302628752243874582673}},"cumulative_internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":494157849840099996826695912491798082469},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":468023676965329505400498089706835376635}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":29254278576648305675058347809728397665},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-14514234082039473004285742182528163703}},"form_storage_change":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":249400324927711530684665465050451426599},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":498800649855423044690192081001653173815}},"phase_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":24279255202094703292163701281091488261},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-1510391538529894424326089740493541735}},"phase_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":203074491149735803768096541033167988465},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":406148982299471561255284921187640488783}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":413298725499599144713229344365429091765},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":468279803900694775798420278408722790443},"time":{"denominator":64,"numerator":639}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":196432197219797014941824001563715167783},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":186211319809804466719104608020018360393}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":59879835624076011602031065840207396345},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":56171936128392978741413939036301676387}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":127471497674712843042067533913396575061},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":15641690751803836235319730824669037527}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-515529365587140586088087386852304505999},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-522670251650705686993765619671587879277}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":161250545086931051923814732330593382075},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":307293402698949770889789605278963069515}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-329678788709539383348030213753777632549},"lo":{"denominator":1,"numerator":-1}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":9378404157014491435723445000043388493},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-18832979183726194299740832180501919299}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":54148011730060564260967201038806723565},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":25804673010230837174287471976809802201}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-53605360671834109724025840955539482477},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-869492054595832086428938474209780621}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-56540940518419641238001008896142887529},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-57121437057360462071608726646087311549}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":725316552116169565836580249964013947},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":564386533158028504921938326387901511}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":55908325060633817047468892960442916839},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":55314868127652095600979934306902463269}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":293191635864878898239289122549437483607},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":275823527040388628933546276479888382885}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":98224309004317808291463107096675134401},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":22055876935261362162184406132333086557}},"internal_form_gradient":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":118571692747732038113437706832511055587},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":935695513510462205191750103640419945731}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-234821455783349143286973067842412911363},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-952323514465301260089508608115385916091}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":46188168151455325039461789905416181365},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":36194769166007511327878347923318304685}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3891011692878285431796166353000693733},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1078037365523574479075830936223239985}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-37070154763434735798118714449414050233},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-5854070149866115346717558229626986519}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":187831897399094553517994200139989798381},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":179113224244418310487936892416860778891}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-175539833129456403892153286018777857017},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-184182884485070144890755463083154972625}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-177628603359724620498282204818515871773},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-89726143510947702282275904539213971771}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4557298303310473417435109231886618277},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3546145172708549200326626954982352009}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":43910295821249332813551952079709753149},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":173776783344120024888234165757211443761}}],"phase_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":3274497203824112636688222350615088933},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-6548689467954585932996651943043918181}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":47538460830493498216431712633206967055},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":45179793580712687293597079824102618831}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-44204285047016747533617860421045775961},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-23172649302525506996193384906279001563}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":7351075273663764844529664306683197375},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":5760576426840213468547833971420867115}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":619273744549942849832952111257585791},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":171574975560841267049760319144327181}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-5899898371782208179159964405545620699},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-7453633612463238301398436639571784287}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":21853995866053073775474296835204344545},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-342649325880671976922010210925733867}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":264237251804250519235992843891524381325},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":7324452374609688125651450434521112395}},"weighted_phase_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-14477192030314189501648139328956551141},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-41441051052878608912699862575212786245}}},"cumulative_boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":38275147801740986409766652911560992997},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":11774044242975084965007013669616518439}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1393335732757965756678561178508364299277},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":674269615540750307741880641440037903213}},"cumulative_internal_conversion":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":124114995520597173864631769766094101483},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":940182830856020516206405755563483206999}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":59008839780040012912724230312102721471},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-29252272444611891995863275999939517209}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1010965714879035614084136999545202446909},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":63185357179939723734053806996999735215}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":48879288907821209749280027191114659319},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-24327173038700426801829927389525814967}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":404498555824544434315987151942437653881},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":50562319478068048358561946020728682793}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":411763033287503512069817736975786560887},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":468279803900694775798420278408722790443},"time":{"denominator":32,"numerator":321}},{"channels":{"boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":98271358022881738412285535898696312455},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":93004481526455441805625953573590793431}},"boundary_phase_input":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":3603641126530238672523099466926568347},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":53958544252946761001448026653402802313}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":502520453726424958075986628665499234407},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":493243983142984162763058691238474966649}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-31873656659596093856171867492880392397},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-258534837363620313196832824016764307921}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":319508195248930777245777595183420644883},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":152174647070818596105816231484346898985}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-164299294463492254848290185690615746999},"lo":{"denominator":1,"numerator":-1}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":19213454245227204477692965280995757563},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-19292153000363818967138606268895350695}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":53337066038207570934935460026024398377},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":12695869978038927212517003408713608451}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-26492449318513286535457325887800671651},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-6895068329212879520962969674306011491}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-56937106655101967091272062444681441777},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-14379935761915236483487201945224765685}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":712854258658502319378356039553875687},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":559752195465222086945546126106460731}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":56326689044421098355447456898012071935},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":13932298985736847582812718753490599111}}],"form_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":145992485783630639997919253883462945911},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":68529687268252497845117177339813896815}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":96868186027610333523036243830758313045},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":86762554269123191906893635338748547397}},"internal_form_gradient":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":119173396846496663037962141095103713595},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":940608153350508374489187710308968173071}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-944231892975004855115683435665095511215},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-957188383548721161320230853721445191003}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":21690062527925376134524798450859587815},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":16684637841918499030989439082951505315}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3961102667190089357797955879638445069},"lo":{"denominator":664613997892457936451903530140172288,"numerator":2288666961632150028147904357403771}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-34327613518604250938226466398556568561},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-22045420819287500639890098571295209101}}],"internal_sine_current":[{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":5724431538752153496720065579663323537},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":87136864052811223983944261860196760993}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-42693079000215770587429847154674453263},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-89796768648188755332381859775371131821}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-357746391968653730605187211696723002909},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-361407204389808424217485727920091710091}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1119748851040874572154293893134137693},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":439628346276074921365365705351389917}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":176955512502990013575051528541348212301},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":175078432564829631582291133609295409907}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":13198394182588272812427793859395740845},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13198242862129739059804334277340446747}},"phase_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":24411354492611619022010341483552011349},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":46482548601953555879774214259942106435}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-22661659512076897057783734857268956145},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-23725220841100656142407271665069684509}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1726040333645807362897820414336311505},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":5310885172478844241176008112801661763}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1260858139155587003043389139218339557},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":186497361937851311923028763517452979}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-2731704688017018284033870411463853703},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-7017275391861173626617875243317675511}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":2788277083666041959247268831047716595},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-11192382052003208205400166027113015897}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":262273723975185980286678084448966121935},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":57954052491560219793535082803497921667}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-29711247592075299709160423317959769887},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-2643908694173069512895523634078993787}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":85763235418127135795685074813624765287},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":20493214386080282634284446817140655323}},"cumulative_boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":698019231801431717841476751554279612769},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":21110445903802460857901627486397719731}},"cumulative_internal_conversion":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":249365165096205406325236620514579901947},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":472124912793692832913520697359993522579}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":59511409138838869515691002503347649689},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-58969446690643978468659139135941986565}},"form_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":512127224556152408988508422020237675085},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":512127224556152391313986208868001193255}},"phase_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":24601162504483879799168066182206096337},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-48978435547974189294349239412140609219}},"phase_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":201405101233751814601546904717773323835},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":402810202467503580561562868976431571161}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":410183809315732020069492356986379855441},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":468279803900694775798420278408722790443},"time":{"denominator":64,"numerator":645}},{"channels":{"boundary_form_input":{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":1535876675541228142319867101880420137},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":185705729874515220933209006593293001139}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":55437179287875828956688194975312490107},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":12937157381701898773648946019244684347}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":495222481433176364875203418530321443541},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":243011857470093844248807141210571864187}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-252239908712675754354404773897097348305},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-255759811368933938806799126017502291195}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":316425075360229672645322232483395498649},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":150657568316853916922213975705139674425}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-81846975059245368462671892337972535779},"lo":{"denominator":1,"numerator":-1}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":615839911235673920597637357508423395},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-19788340728934568065432508457611467789}},"form_rates":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":13125351825847661114412182361224394651},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":12483344222169576222476489480213313301}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-13084199710599717951829840131193337085},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-13664845750664501619270326096767294069}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-57334711848027548860250977691247554119},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-57919116410479751889100255163210920979}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":350044984337663206795905553967583591},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":277518747026416730043541489545312067}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":56747637542879426387591583660146724865},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":7018318080522848659781481131150904367}}],"form_storage_rate":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":36328782520602282740145399938856339151},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":136114214726130066510371948793219983415}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":95424555711917498869233417003357657083},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":85217653130761475528829797477288163429}},"internal_form_gradient":[{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":59879534993916466451017164176986981219},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":59087257572013971924621962497665261289}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-474531952370021002692260988040467891945},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-961936144417223750561712217689038720329}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":10126458208792734593561760561353209419},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":30478257327529551401405966835858704135}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":8060731743954972156088741470469845925},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1263721997038850697694221730355039713}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-31507143399996470032679649763891893447},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-41270032401319100660748155542665909911}}],"internal_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":89194515551071512158935078789653624429},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":10580990835843659681942969412257029277}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-165874808030079798085481502527724329373},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-174870181351765157937223399187639191533}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-180122309537451025418133652275107716461},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-90979135308787611988345959186990765393}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4398795004884627866314208891080293817},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3487403427566540306255518881815083335}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":356555922426572702651262378700057513261},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":352779144357232004759566268365169407697}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":13294241308287292378813100667698127459},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-3323637929474330817891952189276372819}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":50085938037731837447579796205726540889},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":2985306667123181194395461955221684225}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-11606222550373371314966839790946015875},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-48537623792945927255932882020008986469}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":6446703519771456201196111029497253835},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":4850765310503107774870106815079736765}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":20045395343565434972227076589096899},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":201127602522694608813443608743472923}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-5014517614814623910113383398409498611},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-821041207279077259398070757137267017}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":22794215886672834497533876581898182445},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-22875989865675867996596697688647465411}},"total_storage_rate":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":65062143821998912631334666813042480243},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":28644175486434645397129310790919850279}},"weighted_phase_storage_rate":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-7595421219205652848956133064670198059},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-21537512780391484921854705629540582299}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":94978495471374504649604277424907286109},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":29198170473948183615528619001201264751}},"cumulative_boundary_phase_input":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":87414817586373913447831141390501687407},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1353494254852426600925763336508062441099}},"cumulative_internal_conversion":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":250483421608454439515110449620087999491},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":474122201538945054996227645738367463909}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":7502014684278304166353552035338021185},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-59453490879127572159475062345884092323}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1037458691026064726938812326760640362049},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":518729345513032345275285506779687595875}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":49527467065954266656865760229719930955},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-49304642819529445514465420916068790215}},"phase_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":200544017742281554761093649128715187045},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":401088035484563059658377549855223280479}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":408565024905478757289816336112444256847},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":468279803900694775798420278408722790443},"time":{"denominator":8,"numerator":81}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":196582958080564457512398952560251945167},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":23163178971150853000872931473898352619}},"boundary_phase_input":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":6652242442296542572289736453867805699},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":49543445050867254458591387987811845475}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":243997984040300800935188735819046176589},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":239438519080652133050710254607412211077}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-499035901077919574666594663365119701613},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-506022700831876442114934276056706130681}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":78315469445654387818002590770786301745},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":298201057862364135346201859209812840029}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-326053631633568514347655425665607507971},"lo":{"denominator":1,"numerator":-1}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":5058827369095597364998464891045900481},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-20319758898290718631361536792990147589}},"form_rates":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":12910519032296759512135006621583267955},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":12265022616287261341330604056627754223}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-51661741057423917470992547150862552407},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-54143932966361652779049170657350080779}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-14433364467707362377751764744000218441},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-58319248506724193874946171334384392767}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":687034561899730907459771888779980073},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":550257706628691622587228604856189121}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":57170800502193848812775105624066286565},"lo":{"denominator":1329227995784915872903807060280344576,"numerator":220963107602976999530510967597596359}}],"form_storage_rate":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":72282504732059137052393005153379860535},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":135078473069491772617071511725934147141}},"internal_conversion":{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":1467089796198590724267275120071976511},"lo":{"denominator":2658455991569831745807614120560689152,"numerator":653041231895682302676521166079289213}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":962626069152263199713813070537929728973},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":950055692516697599085794341716361899527}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-953778051594289769561453848772373520859},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-241640756275056810666307009780060235097}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":37563869757012334941373555081740609083},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":27520331918500936341660987307674724973}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":512343422848408749822326350865595665},"lo":{"denominator":332306998946228968225951765070086144,"numerator":1322013278515658988888488556226361}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-28607357891949673595549079573030508893},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-2398047820048872441386876317092957295}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":173453223168118923479866833569310049845},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":164179401506924573966911475736684449989}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-160846806899415013041019831253443132389},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-170012179209801506773423262966464194979}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-362750014226667249370194616321563199645},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-366430645343204494032734068304988923043}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4316765464852953361502495952467476605},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3457371137451730550608498839014314793}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":359214733715079714771395346267934351869},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":355418150686660367087087128481048806955}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":13385375353137895381715529505999835191},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13386150752233226989946476244353783907}},"phase_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":25663683166041860741735816947563996595},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":49026059431789132734453852174738414977}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-23754159123227842657605818480831195471},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-12401542136281311611979324036167880063}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2989237776744333220995241582459067945},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":4379996860359087311025455577965033341}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1304671812911125809444917214081691691},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":107727333431751518773301432251178795}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-4553002417302733218909560867458436271},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-1526644657326087840945720092779702193}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":23316215555457813231198490643725959675},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-2925180047057684251349639326360806757}},"total_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":129082546187765945848386665211362313051},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":226399457242475324079919729580307936703}},"weighted_phase_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-15482463276352328256399345095397408019},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-43757488896508221154223293871560357579}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":104193321631400963595497978326169096039},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":37884362588129753490855968303913146983}},"cumulative_boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":700565836148921909314953456709113712825},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1355816603839186003478509807819991121355}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1006334955822413530233243623840567927497},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":119020331308658025476064302309151332887}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":7565352040213905513333927053871528137},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-7494806009338666235029165573023249711}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1050569829379105201406041803208096035175},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":131321228672388145493563534697818878231}},"phase_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":24927280601586502401491277121085478257},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-49632812608634187888274304299065719337}},"phase_storage_change":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":99834052304986369512062184555398537593},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":399336209219945426933118190645951043217}},"phase_storage_upper_bound":{"denominator":21267647932558653966460912964485513216,"numerator":25431918880662131557612924891325664725},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":468279803900694775798420278408722790443},"time":{"denominator":64,"numerator":651}},{"channels":{"boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":98071973066394004859038455424996055865},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":184812088659275373854423952016458799775}},"boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":25500865602405186470095666237288332527},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":47345179009003887561927100321729901279}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":240421993258886237050207040929447051907},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":235906509493020860899790611033272335151}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-493663674401971356456328696189473387333},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-250289922580282633175211868893899482975}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":310028246924294030513094216954159450833},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":147508342236518285043061292250978306939}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-324602452342134576931953161682869530723},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-169528512472671607861358549482388274269}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":20424672065434690955339435270125629823},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-20509739396546814059215309850491473653}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":50760075992280658139274220374298251529},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":24082318282769428499924529591949314431}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-3185024652575559371779800805010842291},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-26742065717183205229383067273537655625}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-14533259777738962036484903465911729693},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-58719823680110237778959789050506400919}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":336849484162688835428370905900139193},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":545427941868391072555269242307968453}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":14398949954031500006332250886027076871},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":56988861325876421069626419937101289063}}],"form_storage_rate":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":35889524505575240522480520108422344627},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":267909222495327318482760090378228928481}},"internal_conversion":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":23068753939771530705974622344682072601},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":40939717659945929685040386790397163709}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":967037025436092877660181036631203487867},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":477292044860426467051474622545242889841}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-958372251742857347253237332560081214951},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-485525497323034589488198169677916410651}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":34545681705374707546758478264358321363},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":24494976430323056385408098346928881121}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":4166195112001079095016504940553203153},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1441791527889057020421167548460809699}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-25626955409080670139345705237276410823},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-17692876623263797268385829304676619481}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":168374198574731619272242664470416412097},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":158924320718321039262203931120943196067}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-77843975029742972034214119769724809699},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-82509519124083060977059465957274093769}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-365260657203654035483187439086664806529},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-368947533387044600413421484986090895209}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4232975459244058600982717191110245283},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3427024830472676397305993113930848211}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":45235635394992451474312621325632499503},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":22379473509727606036994988689080800687}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":13466270513731708633535855884018763653},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13467497432882726109530936716105656641}},"phase_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":26272449521432766803872396319841845425},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":50265386110423262591433326049849725493}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-1517915092031385580432578551549412243},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-50652367857494535410162995102093387259}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2749058002944820696463204625682305569},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1949248289902691797160421505186328013}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1326141091920528516003729776661131315},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":229468248571559696972977590856380597}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-4078656629750773410481047917526757875},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5631817544214949932451526742649180267}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":11747681069986068067528787678105215245},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-5895414097558819178732132692165791827}},"total_storage_rate":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":31956578726031424693926078461799891443},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":55891005236840776485834928138976402369}},"weighted_phase_storage_rate":{"hi":{"denominator":664613997892457936451903530140172288,"numerator":-61452277805372122321163150728475831},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-44345201547964212539420377822323319005}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":113387569106375401551032833522262476277},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":23273714622016643320141045527342326611}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1403522378448069304861478382127973206825},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1358035909105233060707975140647572210477}},"cumulative_internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":505330173593060346120306932765097908055},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":956000748999884134716486954734810397193}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":15257820460792573467549787417461633715},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-60468456205408417122272635151500157275}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1063579460087087715226968195459341585275},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":132947432510885959583671757987619766889}},"phase_integral_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":12545836795283737736448795761484586247},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-24981360173968951564074968334415341445}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":397558909100247319413156458163314739355},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":198779454550123633508420745362166063371}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":405224903652975280280022255741632384647},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":468279803900694775798420278408722790443},"time":{"denominator":32,"numerator":327}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":195541846287428922736242952676358054537},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":184229259311407742419900592689597420369}},"boundary_phase_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":12197465841640279950940137753958605999},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":22577347306991993739843344273390836591}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":473769305394659937641056648866283234747},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":116210364864871609087256797072631777747}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-488354402162299410453065724614399672509},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-495194766018323016301834026045368542349}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":306733325860686070393060539409932271083},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":145885571775598171043397464397328323835}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-161520393193799556597002990454932433577},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-337486594756837221405325883236399753819}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":320892723410670918026891437704021317},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-20622295154259951305185668134870377023}},"form_rates":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":6232046773628607785847940147118052759},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":47247994480767974904554900115239999299}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-12558354471107555485649341337974382339},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-52773340234608635678279064148461807809}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-58533143010348306978564506286639600439},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-59120519694173348734092111873689857585}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":165023535906892779376790433523325515},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":135140778918146168045004005959944083}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":58022249962437131355258562841253926935},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":14353271667364783048409825505120367653}}],"form_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":142427150850205004763462464985432841613},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":132744830797673560855239080476254167135}},"internal_conversion":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":22642527615544537569855219102755164189},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":80087908090719328353303285268210898569}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":971307683477351836359810583746845427623},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":479488628807833020135733723815032704981}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-481420852547897382889173313283695357185},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-487703864558583012415753942939472480967}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":31455566541514648065943608789178855319},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":2675038334456627399296581716461091713}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":4232658844856454994963841663777809095},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":763905796809464276397189938519475823}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-2820589781502140426499312774916962319},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-8079947782134867103116835614175405397}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":163151930799944507675121163172261253839},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":153530713521698960213750956513145709425}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-150398023383697242483379937635156355347},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-159890419202486214850761886318832763775}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-367774584145661992296634496467350729191},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-371465180695251364122903231246752694911}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4147493824596046507311658804141860767},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3396458225997203260454284088524816373}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":364564548453486297096622036077964683709},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":360737062601373799000419453012054219111}}],"phase_balance_residual":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":846251806581791420472597190905412139},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-3385420655165730649513732595376826221}},"phase_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":26868867687176827477369624650673338245},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":3217635167644554056411543621002438113}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-1550590041166126278330409137365996615},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-51677963022813392401248890003759870429}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":312894306427380674733329354433586149},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3405964591112664125174504502155998305}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1347297155161073087297510254878796869},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":243158767237558496928266849576466417}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-448910806160554658994915498072701919},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-160745453681395088317933297589639397}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":23594960832132779555165015924734200325},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-2960221925433006497140375921695990465}},"total_storage_rate":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":63244728689381127363688074290278323469},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":220649934250525990562880496318624554813}},"weighted_phase_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-15937693471442750036086316404876194675},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-44839727344821131147597664633883779457}}},"cumulative_boundary_form_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":30638398287774658076073555482241690021},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":55183175774255524566214931337009532301}},"cumulative_boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":702904701646688428676139828978420222725},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1360152535415263560121085454173202601407}},"cumulative_internal_conversion":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":253726455278508823258740429777990602349},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":959754869691636603233048046231757783063}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":61541347421565123882444751390758207667},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-15245005344419178336662975377453733425}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1076479392887457251681707728959525523031},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":269119848221864302998151009882778558945}},"phase_integral_residual":{"hi":{"denominator":1329227995784915872903807060280344576,"numerator":197318855726648580214784017080171663},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-50294192234490004206327631543259449317}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":395760341367250303621108443433764137739},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":197880170683625124956451990090911606535}},"phase_storage_upper_bound":{"denominator":21267647932558653966460912964485513216,"numerator":25219482680722705748107735557092504771},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":468279803900694775798420278408722790443},"time":{"denominator":64,"numerator":657}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":194851434918949301958422493097630767421},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":91780302405098625069920416550774914369}},"boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":23291824197857363553301612068119011027},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":42972496781055202916205444034807109731}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":466776331881323266969766727921384271977},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":457955477768604579504922613945842354147}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-120777115446532887731977014329430201291},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-244935043741130568954438977089905702759}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":303385760042435613559528778193645204579},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":144236533136982048940254928946572405595}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-321374808302118365841321808536587068911},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-167905890671882514516474556419244862371}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":10321653934628645403434930916148402815},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-20728527827780460683172590072656092697}},"form_rates":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":12232975748793557381638542579610617369},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":23155554019688541704791616432290987877}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-24740730226390970974998250673802653703},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-26018540060538376834889579964400953767}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-14733362627274046716992611545111079429},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-7440126021541023497038333513089966041}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":323115523086465733988630572422790941},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":33479870567575626239674660091423477}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":58449758638131604893619689010435645705},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":57838848921974919885704398106972096917}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":282419433835707144373768376090873377385},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":8215719334376487836169503415291016037}},"internal_conversion":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":22195027902219692370543551566084459615},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":78215521156252603427057681157026743017}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":975435845082729311162054397125005559141},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":120403973914785354560647815965175925157}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-241795688357681133512562349165870190077},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-979631846666724564741889774899465754729}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":28293292947957533425867887065197592915},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":9117504344967860965153448627716016037}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":4298090269717287883194236257176166019},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1611746160617798216266787290375244987}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-9709755772629942632445445066632679721},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-7292438274062198232259226818889571983}}],"internal_sine_current":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":19723320110623458105267144564872963117},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":73999422057183338544923736143307174563}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-144976969639942533295145131263744522511},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-154626144524149564315507582245905341785}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-370289790340148481928537588359585100629},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-373981524016888562835373742349936727045}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4060389414357055937574607319482697357},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3365763693383447318457487880141018363}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":183625332341650808015437965179889621401},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":181706102865366340577835694927085339693}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":13608181562786002338208851487580817853},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13610258354391584385153640836701036539}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":54906372274035077913278599489773736439},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":26337780131450017839595130753089046321}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-25322223395356180151513829097929177999},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-52682767376310684060311514424873297999}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4503017429014504854274546951362396769},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2902191770326936743792000607095821215}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1368124624561368055330023353303989727},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":128258684235853237249812015808024561}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1545355627429120746719810729316617561},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-145078449813691075234840363412127109}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":2960862372427140886245273526570816005},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-23774195729545879013209705802046033793}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":250220000570669580146008465348923466509},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":108830443792559075025908005715911377841}},"weighted_phase_storage_rate":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-8049858316259391056939977685487477719},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-22621065557464730352804048928744878751}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":131687254162924380833595276292918202307},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":63787579124733520666519970388644680523}},"cumulative_boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":703996505905962992592700842044113301367},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1362166871201875522757782584362334184675}},"cumulative_internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":509533694422850742677219317515301622787},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":963421222245835944018691375035993411641}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":62052856318571193102351689985285218323},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-61492985319485249253222077960190989779}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1089261657689140657787563035409923310487},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":544630828844570308467405916681665229051}},"phase_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":25422620102054205942166892888788885543},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-50627067005807646930693629617257437431}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":393944722560282449287677735109308710187},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":196972361280141197118008339717487876831}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":401775273135880739623492900263567842553},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":468279803900694775798420278408722790443},"time":{"denominator":16,"numerator":165}},{"channels":{"boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":97038217393978138355153903265561780365},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":45702439383526853728728134280627524289}},"boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":22192145750020616814605132444518614185},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":10199914808958846322076092100920480463}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":114967044915616015786438729932197248643},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":451157961995306630233421423352205618325}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-477928118690278407748893631046316706427},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-30288009529677221197573210454913049713}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":149996851468306566256364393921570793141},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":285130593491188065063615877332236324299}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-319610439890636284462864478662955426543},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-83509624539673406972785617281941584685}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":10371541303166012634768296878172613819},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-5207081868242265325021198254458594343}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":47987561008234873273609641504414349239},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":45354886960256401516676401041141647403}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-3044072619879894877942038731117092185},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-51275977713122191027098856889380067007}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-29666818245735571590026608197568295095},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-59920955040414303274485479917801061467}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":79015076953090224856070021243243179},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":33174177989543059147070032750322099}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":7359740924087009011386740492771873003},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":7283219841516111240064541960767048165}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":279816312504873331857638626755002995381},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":260154228051411927812608317347913574861}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":86906120736424712402385303834624391503},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":76263472364433891673189495876147670587}},"internal_form_gradient":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":244854617309018897854453731758634243243},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":120918066407180982152321156501460851485}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-971392075140549305931194858281558225153},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-491860066049164660841266561559258241285}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":25057713951851531094617520744547804781},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":14997937350586249002580205163495163233}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":1090610750687904187843139217408128981},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1693544145687899943354605628870628265}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-2023785270950868398308263941575793649},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-810456016895837105608985355928792377}}],"internal_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":76139202222437467825228546117892023927},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":35582286386255748480150063568165868161}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-17428112091321542079438742554068674409},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-9326637906802643626695525052151842027}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-186402116512373018192036280024395843043},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-47061808037762466842074458055987976837}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1985865482229283473419884972376034037},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1667516061773259061013894500836093767}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":369940928310974458828491231255214547627},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":366094559177382932314890429053588044753}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":13670652104128934973404707612195337659},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-3418287061808884111606022432671482883}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":56050180645066898653201784508086257589},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":53844913239054876370781100011242913545}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-25824689169970418208286165613042533487},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-13416549851715584308259816054871884425}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3988059038019922213032618845914181569},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":37296810398880718207222901830528979}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1388608735689141143466043593926738881},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":8422997566580319349428826705169961}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2576763437027211541851235995523755823},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4127618599921315816929220091354210241}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":23771086338470139513745493410063844381},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-5964706837053444254328268697510896997}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":247380503108412939716962398936255863389},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":26825237367472966665275624578764650139}},"weighted_phase_storage_rate":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-4054476174557549017584528477343391499},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-45552329111628194490403320717796373749}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":140784587043609831304390954724064619217},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":72356786509144805740656495566262341327}},"cumulative_boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":705036762737995209005885457627450111407},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1364079355228555306443171851631256774761}},"cumulative_internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":511570556627610696874150223073925631963},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":966996072512918782690872132655187833699}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":15641412903945525280548119282429986677},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-62007189660985577548202333640877460867}},"form_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":550959255318922844776860552675585060867},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":275479627659461411876122266807759605569}},"phase_integral_residual":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":6397253348488638278641947643609529423},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-50961184201828672824457897969000640085}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":392116268761243018924006986632281746219},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":196058134380621481248220442315355874515}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":400019677016885595833729055869056231507},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":468279803900694775798420278408722790443},"time":{"denominator":64,"numerator":663}},{"channels":{"boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":96610247088975416825900829161087373619},"lo":{"denominator":664613997892457936451903530140172288,"numerator":355430233703698071396430332352461645}},"boundary_phase_input":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":5274120126492770573941483293098258343},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":38637216746143977220397145194861146619}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":453047781066376236074468002467093928935},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":222225813589975090274552130307997099067}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-472815578242254933884032640115675693491},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-479411241454400260744046668947373880883}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":74141205843021458308199573388132449483},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":281751383007443775366604080537345645195}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-317753347974814572023107557615823586923},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-166086202044570663111738528872741243889}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":10418175583930475848295691500857977279},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-5230396751504044518985134254161760209}},"form_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":23512107321693207304698844104545270539},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":22190104179103901581198940278222656229}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-47905153363431384485570510488853406763},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-25245325737001080690545185830497851191}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-7466671279213143486897647969176098477},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-60320020971119188505842410735142826917}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":617773753142305749550722487381726963},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":8217251305473509105576177826707113}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":59306352258482650319830817873852941347},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":58693420695166722529756793953538260735}}],"form_storage_rate":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":69262445834725922770881175697187103821},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":257248346118961510986480310549412709947}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":84949438947026855410619189243885003545},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":37116576257374663415980494811286049243}},"internal_form_gradient":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":491626321988800606131576287349223268991},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":971312451488471161555121123276724293989}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-975466466372156720052420977614011634755},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-123458685602751006221946498860235487849}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":10873871040353630932883063637448890131},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":11688008130053263817948705651585892593}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":2212836303589811998426630071920040819},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1773158994081741388783070807474104861}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-12876057684217858340648080953241481767},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-22613341006891260715837072547671753649}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":146627958421391183819944624095155919473},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":136522226621346145053876723267878238833}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-33435521413032665927288827751336790381},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-71845387573961120207102798338899646219}},{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":-2932154954693239429221947584336379781},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-189500934747250308309967514395695357793}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3881586968904924377542459878537778105},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3304352810749019411318185804291456933}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":372632801132915073465370768786525270635},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":368781638539981821555652465437205117537}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":13727371651190037778511122583073182109},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13730283437089549886757612039076880585}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":57168563444190328558384449335874763561},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":54989589418378939807367259894153111247}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-52633094061481913615221678646949140475},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-54627696134893736487238843755787477395}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1730630326616090861326879139861700159},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":58131383399882413171571142145612615}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1408735343878066236441071119169652009},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":282207018795961929205268276461481907}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1024644113989827444029317951005971129},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-899756250267350442777932231617576523}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":2980929548346682612055538245434528951},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-11967792005414099692019974717205508181}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":244464932789210850671813781322797740467},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":52869467794766199714823393808137449405}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-32584850549692840411710921465950674817},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-45770474939896712127186735316862912327}}},"cumulative_boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":74920898854100638315909578728958280247},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":80887112118033559454170823542721420807}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1412051320523425206976998971489812069693},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":21342038668180168833990280747066654547}},"cumulative_internal_conversion":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":256780779551465819398918305160914593367},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":970475751537047657386120304043745900815}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":63079576269784642364415520613316870667},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-62522475989198738302033439491411065031}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1114442439924865859204706648199784192289},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1114442439924865815925458938610163868931}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":51511828059885074495307456080576945859},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-25648192184412502576343292313826544833}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":390279184617552602275012203249184463399},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":97569796154388136109548020704603269803}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":398249055509908528823112794885109651341},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":468279803900694775798420278408722790443},"time":{"denominator":32,"numerator":333}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":192287178460515593896183600513803253141},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":181075654686234141202123077088149341161}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":40010787348806850122321345972670912381},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":9121541108440836535863127564677662523}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":446317893702942372144198784223274792379},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":109459755482395020544422484986566749501}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-233886493805394285257400902229236223207},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-29642598397900229849851738945775748113}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":146553157186276941247685867903950015437},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":278342618348965930834515799917937709117}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-157904471519195949381950875012899893145},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-330218902105848829950019661880101013399}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":10461504671983876636535575076792476299},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-656506328264377512351890076074230589}},"form_rates":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":11510674938758746649135180263112197311},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":2711744898406965383161413427264943327}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-47082057849265248198258797386796569977},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-24840856183042654696495880975661620341}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-60132315852832990453496170470339502089},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-60717861829622527328631441218213586599}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":150800325791331752483610657071465971},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":521043576532686667175127601156713717}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":29867312188676835846077709039931771197},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":59121433991616426317835608897354600159}}],"form_storage_rate":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":68531203185036472505193060569843458667},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":127095273255654292704051953166769800745}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":82911570555253071907180788254111727197},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":72126148709943995545578015037639540909}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":986935583453270620879187580825423560453},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":975132656477235352074518402154296702625}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-979402838932676073378958820625976587967},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-495738458479304094736659119592584455797}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":18362349523373708737381362670051872695},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":1038024645902273644025875118347633327}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":8975473214517325121393334965465402671},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1850548646819356053665920663723264163}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-2368986322026585990867996789631351877},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-9602553651521972601302277628035481077}}],"internal_sine_current":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":35208976883255394360455350856835707485},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":65289439255395178357491435857104109567}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-127928998127032194916923233335737538627},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-138020205655315547217033799749172845321}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-377822483453202370695647252553262139067},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-381501577331244507959881288018384308849}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3790025565319962057582535861771970091},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3273813344470479252663617162974455377}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":187661857108840072130518523793217126311},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":92867731348878025265349524475956276175}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":13778279205298054207354701687831314097},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-3445420689808834037993862927917697035}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":58260954667505582484956822812202515769},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":28054494491832243756932143490426789355}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-26797515372183763694790648580332808867},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-55566712714902804707017377351453823317}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2922458693426034056752562445521593499},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1321654027572489350055252439839409259}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1428490928679335776940516385570189161},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":294523964573318533274022761183686445}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1508143533070478925422882667091579823},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-764146939972425652326579121643175275}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":23915866703956731118823078624944080407},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-6001115854596585046408290232393495175}},"total_storage_rate":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":60369421455988554616099666492951017915},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":104146751195468051916435892778450092411}},"weighted_phase_storage_rate":{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":-510111358065494868068337129805777547},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-11474261030093120393808030194159854167}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":158855259198537945095702763732001087985},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":89375033431450784823020342781228421173}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1413926826180400528076482784582281018711},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1367600763721363462225852304230642952731}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1031009598075640765341322320093069860681},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":973856664757826282177319273498635254295}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":31797236587406769272000896123315409687},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-7879835738761018679523642511341866267}},"form_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":563413085682045302772170704263247247421},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":563413085682045280500417971867168009265}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":51846486514832956188999267622833651307},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-25816254631009326052989312866609279813}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":388437652160555653073529251760406743357},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":194218826080277796896592442675213602395}},"phase_storage_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":198233758383282716571404457890580893087},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":468279803900694775798420278408722790443},"time":{"denominator":64,"numerator":669}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":191279962609912572195324222791226802465},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":11256204995498115333179328738057865669}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":37838861923670843815130558483935962203},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":34347457025918130480681276290687987369}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":27480069192674165832119401754981809595},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":431322534967837179282458771671671528757}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-462802437532213821970085987826855882939},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-117305328128608015942745306721052802241}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":36203112909234971801572977781515234091},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":274911018812607908680779620969697723317}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-313782378699781233842225723134356414843},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-82045784684434457595750565316689547691}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":5250739091675350292406629541332979085},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-2636009189632839740942551750439098047}},"form_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":22521911678873706940001280154725512687},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":21189416953072317460797553794196265953}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-2889780695457152075786245144207327781},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-48849764554408519431596079425119635513}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-30265066377938186755726767330822666383},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-61114129119756763267857673715430480781}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":588414036765974287793845412363471851},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":64527372515073000922216034677242287}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":60162330622672067076606965871342624527},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":59549393021098984052915162998192591181}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":271046483532706511070478234670892455559},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":250986115339010949370840241097287834991}},"internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":40397113123080547551528216154786908451},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":69944247238035264569982456696634688515}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":990464625130947905777063783990432798085},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":244700594509194225734796766346715581431}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-983198218311787015639250429691218697177},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-995139551571724517576146855300012279839}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":14900568283464955841107492063426506341},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":4845541328265782219166636334244921143}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":9097188994350767503115651417151110421},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":481418874470654109307855996943939647}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-2994565378812419204108772038363212261},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-3927269157638139773314306027984004691}}],"internal_sine_current":[{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":8431445648562940697851893648338538447},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":62250040494565085134849100212580406803}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-121986283860240808673659259637666736781},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-132215045623424822341774420878539739751}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-380322040773352241245056582226919067725},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-383991398146331809517454834872723012605}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1848557215173099323221133210260074639},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1621749755590442235688371119804948439}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":378011071814053633935195301977099990905},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":374159871281631743289602288180041091043}}],"phase_balance_residual":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":1727915249846602208555526971061734885},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-432109299992098075353067721561704093}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":59326818360128865663994659960672112753},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":57202543465541736010753979914118085869}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-54534643461817651500708001008852507367},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-3530170128777588430998848752149378607}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1185749548595882807472586026093019685},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":48199490896847969080304161962492967}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1447862596692112961153481620997917947},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":76620193569741259054566453651349543}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-119149970612462644272469710653507951},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1250088598580907736287618899831020301}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":23976299357348388304996758320886667033},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-24065592108684025805764605480548186965}},"total_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":119211518155618182058273647210250252553},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":205053232424899390204690175794614577703}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-32623447221470146953930940250391950453},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-5741610364263944895768758162834157161}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":167821507445877596917358586675339844351},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":12227148397259296415363104916846477553}},"cumulative_boundary_phase_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":353925130708268149720079257377803879235},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":684605400384726687296067119528384476069}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1034796827430929566674278090357581133349},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":977135301347109185204037201156290005319}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":32055092616646617437998218993864577217},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-63555661118330418031415728635999159441}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1139062673758476791402938478478790980177},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1139062673758476745560220948396921818259}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":52181846100739287573032450476373837011},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-25984701023350189472236474393092747249}},"phase_storage_change":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":48324477429907886936361074896945206975},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":386595819439263034731806879568740017123}},"phase_storage_upper_bound":{"denominator":85070591730234615865843651857942052864,"numerator":98669786188692697463064942230869570885},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":468279803900694775798420278408722790443},"time":{"denominator":2,"numerator":21}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":190202224634870238972457748101169561855},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":179054459826827590478082960448091892329}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":35678236010489160871495334274001931295},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":16111004025765333860216260978114228447}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":433139849185549541866732484419997190203},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":424904401599096192132378580896065414639}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-228952981995261763585371529568538437645},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-232116280173912803498836150168481510877}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":71531715733937724535898824819660252289},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":271462850607312269863861686588269129839}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-77919637985166471315474733037009883203},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-326070004302444992281856116134965333857}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":21076095225649715742208922028338373991},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-21161103379223260372314681944207526549}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":44028365421728901496666876732627181821},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":41353744408833653933340527173362316299}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-22684531195092794622063179154930014681},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-23997703073107054582250336155439016167}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-15231619022150553667460335000967110493},"lo":{"denominator":1329227995784915872903807060280344576,"numerator":-240267462616914222083995157478623403}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":573422636546094446124231962041372447},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":511443646607833515310813531746652771}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":60589054215686216127105325782541232513},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":1874277750944048213419908535397710427}}],"form_storage_rate":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":33477498873821887942170248059601740171},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":247640446952043763148012240707410051829}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":78599325696396784547869174550448016523},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":8461179492262224664633762750047956881}},"internal_form_gradient":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":248459306797947026285196943339699861735},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":122789871553577742443678161105535320707}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-246712435457386933276463953800702656393},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-249663655258424687763615432459891303999}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":11361490326720485944891703666102547971},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":163892282415329230234396057522740029}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":9216415490035168939946156610542945587},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1998506341733478028727159430493948987}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-603719358837955337621092947732136133},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12124509739623505934851333537098989273}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":128830705139660289034367261449025007981},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":118287008292353113136847067500561520501}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-57957393687563106432467231863301234367},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-63138020881284486566733079700801773693}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-382812339378133836573431761089707151747},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-386469117672426495234212597775699239329}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3602920684750600803208599650942231457},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3213495205816688297143185333943616877}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":5948316487873547138735701702163330609},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":94211475410441952413848489780171717851}}],"phase_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":3465613955050314522825588690470009005},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13867299432411436091908621944195954099}},"phase_rates":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":7545705956693007972432877707720699753},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":58269714738005441683830427222475296839}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-55451405185046814595624850398960152241},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-28687607246241793567260347597391430241}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1808237346388318285900444185349321705},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":208674135048100498293396678506781289}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":733419041413904988337412108360479741},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":318072163087383628163664943033071697}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-24021230049832580296554983200976771},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1929675657626909822077229231977054951}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":3003582660943998325339025530019256067},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-24118513053335709233424231338339119173}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":235305129165910244801227686644474397759},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":201761947592023690610528851036832373977}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-32514861824664858736134297832339523609},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-11469624840005018134370847417644419463}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":176737236725637139369192543617582167563},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":26552591245614228656641244526444031969}},"cumulative_boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":708686470073032139148084186652654678735},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":685360603698434437320764756761733580527}},"cumulative_internal_conversion":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":259620292705737041487489864478658346031},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":980308243656707519453274862187557989149}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":32313277717224350194767592762781744263},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-64073243474972218027377635275060479419}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1151145164073613134469375025818897605551},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":287786291018403271822943591564288768067}},"phase_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":26258876208916233216631941561768436309},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-6538363437200455749007092246102268611}},"phase_storage_change":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":96189447247938293781208484683092662387},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":384757788991753112850836773148933219433}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":392887987728297819726479788832333791641},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":468279803900694775798420278408722790443},"time":{"denominator":64,"numerator":675}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":189057239892098688824868171367535187071},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":44486100043256177742209849202867994653}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":33533798879830112742343476102051694355},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":15055048964953846100117524405803558619}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":106674100783330133318018788989451653445},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":418586618403458698173567108751868655981}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-453085488703348551730003853944734734045},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-459317373953022124667381019495233957487}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":17663626491952382753609162621972500225},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":268003938912071333364617972951928107747}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-309502104022453550155501226033197148723},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-40485516728050168707310960913700114041}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":21161211761627355464565934683867289395},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-21252246302619629722281492349323851409}},"form_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":21499051073629093340853828681977836285},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":20156629078504851599618993435357369595}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-44480078858668921741821486393681443545},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-47121154554375204703207308219034364299}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-30657772579801661784717645654350414961},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-15475435052903438669783583107443173559}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":560370734976945074007204593318087323},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":251883478029536611678359331873265255}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":61015007260727651277856178735334509243},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":60400606594837216411092730051463122437}}],"form_storage_rate":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":33058517995307242262061467374548645425},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":244148878681101266434257295863547237321}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":76343885091622207331670616845335901659},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":65362532027805871663086407501049895393}},"internal_form_gradient":[{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":62315685381418399707164295226033420109},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":985679917638175453063495105135326352715}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-495177328458454093355025234787168373411},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1002019465530052706756522257044557623757}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":7744267723296835732990662216146792171},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2299853567345750507871222167485105329}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":1166634948000085849075900280403230959},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2069012311612655009137196832267907805}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1247474767285884409653046750220984015},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-4225371056379633174033994003671565107}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":122629541601151375801855914244827519773},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":111939568092920139940901973478945101513}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-54856381449006664413249056564981819097},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-30055571276420440419646189012135903185}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-385256932448526015335809097596348537653},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-388940104586459329599187406522735323817}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3520913168580567278814638645406740777},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3165261136552953233862088633664640671}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":23960537321128735426948161722351229153},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":189754101950707816176737085368563721611}}],"phase_balance_residual":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":1738990184299693437933833087066982941},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13910997753343155977857081930969293325}},"phase_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":30688486779587404661400170847275097417},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":59309992960218557158244909451152691385}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-28172402849930668895552522361603455501},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-58243703895374595191031558100942705095}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1232538488789709745880983800319008619},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-366033063630605399162968285220177547}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1485405750063759500567709201848425139},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":164646768355571463571747167970136887}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":99270887797980155262932893843561141},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-672488690020242196148418872896125831}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":24091780172208567299452390036117146657},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-6045472748036612507888591234001784617}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":232146278275140970468526835659196242507},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":99204573889891175767828641266789871479}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-32321865687316967627964903337192920893},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-45739730901318914898600013329967494363}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":185599294845579265407858239150435379457},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":114551508740567447953229324831313876873}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1418944836968556314830965723747593030643},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":686066309118666648856707765718255622337}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1042059790436617956918631518079258504515},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":983372112345510919687482037539169702995}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":65143491346180708575334074609934658401},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-8073996606242274332419324670546195769}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1163067112432259076216045436980418238269},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":290766778108064756916783789966331079455}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":52854778378308476949845936723901825971},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-52645118444021641224932687371707440617}},"phase_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":191463803089511908872314975040577283065},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":382927606179023753918550998836715887031}},"phase_storage_upper_bound":{"denominator":42535295865117307932921825928971026432,"numerator":48889446495958345185273552456718522517},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":468279803900694775798420278408722790443},"time":{"denominator":32,"numerator":339}},{"channels":{"boundary_form_input":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":11740511015220716620895106888040362559},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":176772203127742076321346127256535058549}},"boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":15703449842346941013146923965465305137},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":28012481997242129808683565292744080885}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":420352890746624647823294637217494662977},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":206185577460971651078722735758823165219}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-224171478799903683636429611163538115623},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-227238873724232343082283582654363721443}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":279103787131275569697000789234570749141},"lo":{"denominator":83076749736557242056487941267521536,"numerator":64584882980418072401691265320868303}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-307257422025652603102268776605730391685},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-160814954287807812097877805835993263173}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":21261469946324716192388563516144952827},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-10682815577696584950599832223367549235}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":41954936673495537255857065386741664169},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":39257929322652636948802159558814185941}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-43570236971029247752608383730806559487},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-23113452301616288428146982819289178947}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-61698942034825567463418751741095199615},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-31146579574156777581972274835060100203}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":550571947613739267763033406735509355},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":246827753955096997805676073089264939}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":61440506493696192881491506774176257381},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":60816798471055059191598969800278854099}}],"form_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":130499696623232276339634486587419545765},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":240514996154752806090505887390490988299}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":74032451066614510057383841628580285825},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":31482860086198880082767141201079540077}},"internal_form_gradient":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":500051767186581186022999833793568479571},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":494441405415375696065582231933420227397}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-993710319533890785638286686677187936151},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1005231531704681754437995923771723977031}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":253007049095747243020862336724649421},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5988214812268348491462900167608620099}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":2361778023561218278713920198216026689},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2137168809083661870869410491524038997}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":4998510336326483788338119821077981133},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4687183178259850271815629330517398277}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":116312175374560163227332390910568420105},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":105457586377786131382606782320192789371}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-51691193562201533076024702670417388719},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-7128025195219959601271870065574850813}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-387665886061740983424141768438900932045},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-391399462298483372623022199172043943145}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3459345571791895554903475240396701905},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3101729034109607042225225060128324427}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":96510521916715972834133382673074579991},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":47765401822879385909495236222174088733}}],"phase_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":3493530325785297852227086194091297119},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-436258521856244360145434929523745761}},"phase_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":31180171134941002233513545260661217113},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":60322898051352663397254717737723839699}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-57214352882368226841174139872232296877},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-29543856440062673871549867628000011497}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":161069290002728086935762580213998355},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-238263496917153428923129249512522651}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":93972161733893684161500226047601975},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":21258811261717745787188933422686389}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":795537628122292142424335860603356241},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-11656068312456805955871932689105305}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":1510553772203072356840459316630558477},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-24259172960576239534004022965073757151}},"total_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":114476772740116681919738520807684037533},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":194995902967649108426611535174502654067}},"weighted_phase_storage_rate":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-2002865485389449302486995722466938529},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-5689886648387962207986794026998541779}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":194404678106994802873529569316465651377},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":61418852881090178890396212273231978871}},"cumulative_boundary_phase_input":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":177552129423909542568868530983669425375},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1373445703330954022548197573559608623465}},"cumulative_internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":522765030790182756038785692827799102707},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":986323630478592064695241457026770909877}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":65660910699144363867097928563291107811},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-65112492747443578565382426341623791439}},"form_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":587411123469958393171565905068262987715},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":146852780867489592048214816078805008169}},"phase_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":26596802828997080834360576941870330525},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-52984157504101669132699325965424147419}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":381109247408582672139347341787751079101},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":47638655926072825840375933109645043213}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":389368529425984940959817260655330893785},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":468279803900694775798420278408722790443},"time":{"denominator":64,"numerator":681}},{"channels":{"boundary_form_input":{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":5830569683598349752095241422568453269},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":175540671743739807185669231608143940951}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":29294152533659812418260561683693019469},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":25930581242818813239968438473796464459}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":207055648925029757706867355255549684865},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":406259788317000230829363375480492489643}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-110920037806799561076780783209672294451},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-449715635733598195425559691809186835831}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":34448642224293243916565300041301333783},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":261075058093715316557466492274027976785}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-304948271668149197850801918651064381881},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-159655824500374790114552350745905913731}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":21356543527668350535175206941750107579},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-21474472692032978983071762022154522715}},"form_rates":[{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":2556090756528040216054666930829002569},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":19094397869795006981637672409695497925}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-42640269741606482772584109569763771161},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-22656043566217345654556671549565457521}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-62079633841494332921382285057843052689},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-62681631931572613142743507213812908539}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":540728697753351267648903116601694721},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":241755654386989267712104573691147697}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":61863820098460773920173620507353069415},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":30615538310247548683004072364653525591}}],"form_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":128700081965535809175151414203452206725},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":236755380276654616304661292026722218907}},"internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":35825811546770201610342664263343118507},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":7562868582457932578682298732126295615}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1002993139948878425575209859453026300439},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":247981250168882163156663238451358540767}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-249228425235120051956842141948272286489},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1008288827099503902863723341065858451737}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":8518412777577376177176731018991393},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-9755960821025152669636456891216207117}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":9559701903269793771975273435575481115},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2202495364414545170771487124156923213}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":2209860852976298296426464163281718469},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-833881651869823007256720113763661477}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":109860267451282911531940410644556619139},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":98845862341096231276836791404490621767}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-96926802833805034575230255056009292497},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-107744711161482700262015976497094866243}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-48757230403495727783225166636901283091},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-98460077195623961437149945365125229033}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1698749304447104078351667538287667837},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1518995575571917105103511614047049229}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":388701845488649933511706000739244180385},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":384726200964682284164253785015854484177}}],"phase_balance_residual":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":877010037350953028696812072618509765},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-7002313381146030669721994129845609721}},"phase_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":31657687540002514260140308387125425217},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":61307937993936575809593126085444279929}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-29029758975998846608601719758558791903},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-59906841118431457475642371778072114915}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":5422990003394405543926173091443153},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1552709389277018670098469446630483603}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1521473812390387557651894511210478529},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":350538024383560216067345931212679993}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":351710278296450040805519815774694713},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-16589548356089669816265087551566397}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":24240029691406656403097261433970391725},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-24330425020448097731288811612169870063}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":225711282677965276828734931515910797135},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":95770978694179453377009737796856827007}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-31688881253106341521567896890993616315},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-45213422888295709550641816433008564893}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":203150532632392327501672431450318331281},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":65533087375084080621310334889047852487}},"cumulative_boundary_phase_input":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":177723774848911455532256776462284814161},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":42958162478959723575588159191033369773}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1048888731412875218478541010430286622775},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":247289926549253447353061829762829567683}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":16544669350117026871116554900360414329},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-65634705697617539244723937446026011089}},"form_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":593202279173825029069667104215427816511},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1186404558347650006735489504434578942967}},"phase_integral_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":13383535090927077727857294521275550337},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-1666371384897927344997340683658768791}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":379306608277544246851709261767883411309},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":94826652069386044951472997692469910311}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":387630948745978733512334448729980182929},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":468279803900694775798420278408722790443},"time":{"denominator":16,"numerator":171}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":185250252523996262295706763196936598341},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":174252818952205121544891405458279635359}},"boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":13598787010506393250657950040668516823},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":23858094301703792574266650975862723051}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":101993367140432819799047793802225849727},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":400254215721187698890816621088815871697}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-439103705535823123394023390907507808697},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-222516199104259760402741789622931595851}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":272078658924593095723255230117433051157},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":128807326185970424204651867638312460367}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-18911177509038012725348304428714524125},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-316933068254869676716924554597116747675}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":10748158617627167709844275802970404053},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-21616852690255825315858147174474467601}},"form_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":19913382234940928143635395931955691111},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":9275963891511659726846470522118794563}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-41687697400529043241611229031783848167},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-22188879772949861776211677580297119361}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-62455282406777918756252294493355428743},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-31537801270156119389962760891778029165}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":268032178566464422346915778869713077},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":468476638048485520527396880939736393}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":31146101250789215093439394786338238645},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":15410330776391950736893561844261352929}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":253696887866233522728787008190960090167},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":232840874958631382467459962262315117375}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":69207475124890945487611346239852986635},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":28973875839387032882103525563369823351}},"internal_form_gradient":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":502858785625390189386684629713966999363},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":994804369965931986320284807304818963225}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-999962690219681326569049465114683630417},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-505594381776033524289893897259542044125}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-3583153409953924174058108031817382777},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13602977388388457622778669124391185347}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":9670149426606600428186292673408268221},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2265086278449118646450938381982018999}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12770609455659770694277122536222937487},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3109798192662902083105616465610100133}}],"internal_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":51639876549951205964780894487830942247},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":11510118478313224016538129801823753317}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-11289806443890110529881098280662416079},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-50658730930824497099513158672592274967}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-392418112774018740474131222402434591605},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-396315699122789259134457988250191745619}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3368191692440289072159488767577660883},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2943525528943133445128917238675037791}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":391393451509773074045497080182383550111},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":387303855652013177422012000664222055975}}],"phase_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":3526487283403680664793737776017147391},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-14075567696133444507402278985169698059}},"phase_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":32120828631180105377357292321486922907},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":62264692478367470817993708177493763749}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-7359991587083776506063985771082905933},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-60700109901532628987867120927735345837}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-570276577050747520267676937617836871},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-2164981092129304009373745456942222691}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1539052081681697803065057346880778155},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":360499677744802470679709351088617323}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2032505621164351276141882396258657383},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":247469877190271574169740459133460523}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":24342542922752178355459207596896057737},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-24432696940272390099856131046530825727}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":222453456176661092474617264031038416147},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":47003782401184164674291633057935701565}},"weighted_phase_storage_rate":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-7810857922393107563542436039980418505},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-44825745353894723770293430030572311115}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":211834138219454652296783685975174734329},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":139234275638552776315037454408952562881}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1423065085073526618625303394514591186741},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1375779547497103519695739843377561397879}},"cumulative_internal_conversion":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":263033207952338620387068198071319932881},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":991876007056956323744944524572884191671}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":66698021859035616527681667146781405805},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-8269833184283058768295468608259475329}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1197808304554544716587663646128618160357},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1197808304554544663698692729394378663221}},"phase_integral_residual":{"hi":{"denominator":332306998946228968225951765070086144,"numerator":52614039042675782869777547669946375},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-26832793174560661894906460661151551133}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":377523491667449039806119259906306754355},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":94380872916862242772636487154850973201}},"phase_storage_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":192999572878675919226556906093561810451},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":468279803900694775798420278408722790443},"time":{"denominator":64,"numerator":687}},{"channels":{"boundary_form_input":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":22983376958846055794954157434244502665},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":172911473271508737458193855368866147921}},"boundary_phase_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":6279259722119040052514169373003360691},"lo":{"denominator":2658455991569831745807614120560689152,"numerator":170326655185896641432193741120684859}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":401941108149821907826475582800710120727},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":98589021968349009829964709673897765873}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-108653312827305106795043125104276982263},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-220215059050874822575655104598519442241}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":33572068234262635516288897976614046931},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":254162658076122660648275162903088103729}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-37519103800193371176330413365766245997},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-314497767558222673449605193265357591273}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":21639992215952574258152819102242335213},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-10880559594342232643599711338710771631}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":38743248545243775149551674665474267035},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":18002874422318059657397828111212500257}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-1272373983997704094035083207376715353},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-43424055325736890001908187586466290753}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-62827327667966119003336810547010248361},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-63466619953731042070571196178921481787}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":266009101905362625330991584245715601},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":226160729191616092707304922472193743}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":62719665738815430973452150511055946497},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":62048327673277015205840400796760615295}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":249878242464638756498783545074827463027},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":114403109087447774304530802421581338973}},"internal_conversion":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":4168770105800722971039235502914262493},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":55326776977177444782436870603718979893}},"internal_form_gradient":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":126034325151180950196413502021149793817},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":997519155491898537158842124736531481225}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-250713779606643649093280578926816905703},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1013928903364517847342232143583145793431}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-7519820237918059133204992875567593949},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-17529378594484191262039879887545083685}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":1222227740231971586365252357691879963},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2325260208235569494994045605871761859}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":16791798196535191018662658672198134751},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":3572291797761011087935234004095662901}}],"internal_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":48284984571861390132661318999406509669},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":2661985315493793552754896002100961741}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-41793061315032802810498827279912157681},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-23691078010753143881707157981719693075}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-197377871046361115963049980134929422981},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-199386266994816825023729230693746347049}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":835692240333905894713937997517956049},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":355252442679445907464416083279148359}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":394079282241340019281232735532692971075},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":389861140771798679048101581889012850529}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":14178140806984902384552620020128725155},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-14146976978109966998552640972279344005}},"phase_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":32569388684353424717646916112153866753},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":1974774796489799001668775143906266903}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-59675145946771153897566423161180991733},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-30733649878368366705243682317999495361}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-598408281013565772850498739718641291},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-87183976645044365827220738711466033}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":97261793220977636590121193708212629},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":185038328057790380567074175564350227}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":2672497686380149057503305586294923317},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1137095795560596403084755361610561925}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":24444588307303353888514541679461840373},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-3066818931395038691445145775848958409}},"total_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":109578936721303430725014597955887825123},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":46112375777021074259532192689794449203}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-30720369022031895048754349163051812781},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-22178357533405625785466417041992440567}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":220452904579021923219891495013016422829},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":36834875237038687095847572844842040891}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1424242446271423938635149801272029316871},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1376801507428218899544333005824285507033}},"cumulative_internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":527629704694352511888276109456232714197},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":994469449727761516469121252882433518853}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":8402383034067590733288637094496006387},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-33342149509635005345580532842702733645}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1209028014948456990718820641017769733513},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1209028014948456936305282648240076383933}},"phase_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":27110748892942527474059981480761719683},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-13502350179565890469205871513870863977}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":375763595825398930715900749873343518005},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":187881797912699430144602531167056171055}},"phase_storage_upper_bound":{"denominator":85070591730234615865843651857942052864,"numerator":96100183168136110768094077191318731855},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":468279803900694775798420278408722790443},"time":{"denominator":32,"numerator":345}},{"channels":{"boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":91215612086383805866387149654149338251},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":85759644024542435398813914139237942807}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":23053178065079788143835271897708130359},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":9881662878895206044889993279380680851}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":396015807358321349744611344423781309143},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":388566847800924119797493053497574693265}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-430206786267485771881254379621123892073},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-435911006959727769852023677484539424761}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":265086620817100725931185236119634719191},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":125361448766185569429593756602070063533}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-18604602440486266439084529115975510579},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-312009139260046299241489261836105970737}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":10889946558218593896522078879226097869},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-21901557807513640262638405857401738405}},"form_rates":[{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":2352966040906635526363544016062820479},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":8723952935659916308748536087262231339}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-9931463887966437831524399197694437377},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-21225761522586628746729227984391972935}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-15798881864011640862222390200720277863},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-15963445096497655883895930680629889227}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":528084307931613490133328817195125331},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":436034226914061583896849023442883523}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":31571936662395937192638818937226473777},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":31226043967858380637520446788451836077}}],"form_storage_rate":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":30743372836205185679932845293185146581},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":56165633559575275597246647615614933331}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":64132867873047130918850697011562795227},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":1645243797628732089024711759642284103}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1010662367822283555385183463271825095411},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":15626053271026112778884368456476470131}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-502794381268586623866124999692330100795},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-508253554173294759720461042714805199113}},{"hi":{"denominator":664613997892457936451903530140172288,"numerator":-22535071588535135708307060940878637},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-336495336790473934258200524525417371}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":9882665908769993730309518990602770365},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1191504343981819532394802260419271347}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":2612912604903666926145511617673097683},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":5635388243882673505151936323240947693}}],"internal_sine_current":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":11216537367413691797590526768595757113},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":1221287185981507812127287744532633273}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-4795858051884498399358089609832048025},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-22021759884299010770635599206461264101}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-198534604795647958951586383192419200655},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-25075320920570521868526817007138574167}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1659025782274007121194843916321899345},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1369841923986920773132083481161502811}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":396744657112741329720382077939424278493},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":392398041320383065405967106548967743605}}],"phase_balance_residual":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":1780767961270624888130233736657037161},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-14214175510781017444818737760153053415}},"phase_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":33003192362240832148717405256404465561},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":64091865559243253177004944531965300867}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-60444687179764663830992418894097016199},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-62208396263506442261872824203560065767}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-918161417278744818523428868247123483},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-1713756677682433085083964149427184137}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":786437565153251227117944117594908411},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":379267612120345144949748582335408559}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":207928978468769555642022651572486427},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":896899895255882895259685135338338811}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":24540970457674482828026106948698789095},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-24630666969366953637397222914545087889}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":215823584264549765715433921785936036411},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":45213433817120111559803087072865429743}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-30123398425091719724028840559545136237},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-2738049935613791009360890135687375897}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":229004368212120405019865290293092923291},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":77689733787727800851014547914960860351}},"cumulative_boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":712661531996612276852196039821117192741},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":688863956661557662555520721347113722931}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1058265637570254108038373345334882434421},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":996937315424204614602658320521896945007}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":16935427895100278918027107519744099811},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-67211511202313237059732746973638031291}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1220058494580061331976795846430795064953},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1220058494580061275998505888654337326421}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":54568226715526718849185465197094718645},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-13588811525158018840044480043563518679}},"phase_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":187015251234193967960926781278219865043},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":374030502468387863741555838946083365759}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":382825631191605320905808002004846119639},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":468279803900694775798420278408722790443},"time":{"denominator":64,"numerator":693}},{"channels":{"boundary_form_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":45236365601260091304655619483359964699},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":170078799144470657116422337391705879787}},"boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":10503363534883213726934781907465306609},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":8871621564489463707536755202506610933}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":390199037992925109736906079893916213857},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":382887826330255877439740300306524312309}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-53235751411694292514799743286335511969},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-215738406513750484982522050589942626865}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":8175385856729031777538097661187456127},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":247298835431860479106722551494432775117}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-295144423499950939375839243358689784995},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-154735168477276435513442441840212588817}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":21915958250455412871877614919829403737},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-5509526596257576451135646065377419959}},"form_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":18270015871152329207666096788199947899},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":33774693619231762657484945817066718179}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-19358973030225866213701935202367995777},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-41460740288596095073352441649701635647}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-63559517989635239162671172082980169479},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-32118358853907384968318462543268923057}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":524273480314038637848464590785790649},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":419624868467945378850293019847224155}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":31782200069985979045678275159137259567},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":15713045310545069535221298672751740189}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":241909007760521531798884139174403025297},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":220415858100359207995387299952722428931}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":61508502080349148581307406280792249971},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":49914250365595461810584186862867741773}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1012879116630944969672767147086066803049},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1002447292864214443991401068755273309807}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1008161502260462261685850453990954316273},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-509460671023930216850652911732305427603}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-7819023593496938872759179432039579433},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-12811211171367569885927581871854013945}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":624039477068337779001090272655761361},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2438327067769341429510464720638960919}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":12552668650820859357648146770195553855},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":7744304170193917315768690799244997487}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":82769338435357486579092550462965461239},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":71020152622413233883571668902873532249}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-69763621216852178370169639733484852181},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-81287934354590697725524744262088219863}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-399356229563892742907154469315569441345},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-403611200883184527365853085713293224007}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1647053714226536871217361847513253371},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1318290404042480478314552411104700265}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":99846726254788964287659502406053126979},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":24681993856565970878520992594821770545}}],"phase_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":7155104555433938318340861610686761933},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-3569285816174617169317956111903857239}},"phase_rates":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":16711037992699314414787213259427958859},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":64961557441434856856728236681966671879}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-30594072965613100418289557359049334465},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-31461501439228304723739455683814886575}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2488872510114384550955393521772332163},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4077935169834518738884436593094161925}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":794551739679259388799189271985301931},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":24254487856891097310518622256912931}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3995638529545624949480462843072786937},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":616272144746770320677107883556741377}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":24631915646569602737836118723278419405},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-12360498967487543855545594645600300297}},"total_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":106226978960009593634665983259998760529},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":44307797884957926240350213114292467855}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-29455049840502344529552172654405504239},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-43184666560527503033986447495552557511}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":237486186762356672139488218946222916673},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":163351911285352663754361392895157933817}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1426307754324619854991292215446059257977},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":344639906961196553083405753373615610159}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1061148848605270474378122130004294571139},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":499638522955045950937514727140546935201}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":17066467741570510308813363376187959241},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-16935051801475149309234556310778641723}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1230894828161726606864644300681003641183},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":153861853520215818660084015463425365115}},"phase_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":27458442855176887534630158911315127359},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-54703043464658514069020409997863230509}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":372327664949869513024761201312798124215},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":186163832474934719523621175583551078533}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":381277321973606649280550895392414718167},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":468279803900694775798420278408722790443},"time":{"denominator":8,"numerator":87}},{"channels":{"boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":89706096805931733168945860803661353043},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":168592424083616699454717486555846054511}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":18978371776548092805599646318854311995},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":7871061278184569607309513344787771809}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":384492158333500678260519054354284469759},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":377320247254049083334037604035705255781}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-421652583148815636758840290024082463681},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-427129238815421378768179454506323866127}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":64539211381158045761808525512479075191},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":243893593465472592324858455980092304685}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-73142026520065682587609746946564261009},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-306884279579526447744945999175009936859}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":1378007968969018088247696168924076343},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-22170704369322607883263569025314615723}},"form_rates":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":4427700528619907302811826790455704431},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":32643031087377795022437510958644005731}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-37692822940449861696548703650295645107},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-1264133888051086110228531174987212257}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-63918934874905651261025482788096638843},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-32307532572791602354909466178084433139}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":260298089361553789236187818441758133},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":201551569647305243551200393984652295}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":31990410903905764769802194586054592343},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":7906023209753438562111425544010620059}}],"form_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":118885149630151776124395875233477853261},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":27009038116348558628881510471227236377}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":58830815688247610576423931187809800653},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":47129747673182563382111125208324430523}},"internal_form_gradient":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":507461599768268262082252801780624800955},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1004657075177457261187387613208606878007}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-505285659640416798294737795431110095575},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1021169669198747992099792945164247307593}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-9910257710936853051975132525981716379},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-29789955977127804290287281416749960015}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":2520918252146126422561905205767456857},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2491214400720001209994789880512105519}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":14699028491811138143349689933683637567},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":9899120385831265272335537577187601759}}],"internal_sine_current":[{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":2365122167111202914103065139814067621},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":3984982906222210647713399172049696679}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-15669595212017903009583100364656512177},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-9296189882821524818861643570036004369}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-401614512456576047337542486521499836197},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-405988427945180199684500693808886292871}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3271002261126867592075629931731702563},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2532771722093862829473359858913015219}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":402003359524116670607688202233431630257},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":397400070957948792967319067098378553953}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":14370017257748459977183043126567147217},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-1791983243784338891765735629587596087}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":67651774390495830620546508416403474657},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":65801541365259942077105204494036969699}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-1934535231539368768435773436994987035},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-15902684618815983848314396540687166053}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-1577266502010171783989189774423700463},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-4741218748249843002594253102973740645}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1604866403838548030722039225654301875},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":396489086176301935363094869916155111}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1169711521560174908350659685790526349},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1575493941666796023709008271982310957}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":24717076746187702194833375849866998575},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-24805502304532271823076648082530014289}},"total_storage_rate":{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":6532863230817923152005309034227768647},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":10849066442742455457525919990227937737}},"weighted_phase_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-14359337937065005692310930685833554909},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-5310905230863647713829670490771360903}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":245896133337912772124076893396566168521},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":85627340582136098270650637538731608811}},"cumulative_boundary_phase_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":356799341375411386710388674716813888463},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1379297539839616015734308280370536294243}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1063906543090657081123892001778723155545},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":500743126416136167266782956637617039041}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":68791449882911032494251095276625006401},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-68270292549114348910181555257609332233}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1241532383879455563569118283629322302105},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1241532383879455504337787339917679991833}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":55267399780654312877526751757598524683},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-27526358069880020319785482505579370137}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":370658396529613247487943030349411663381},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":46332299566201646458552227572607841937}},"phase_storage_upper_bound":{"denominator":85070591730234615865843651857942052864,"numerator":94939788124652222164891988046675931125},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":468279803900694775798420278408722790443},"time":{"denominator":64,"numerator":699}},{"channels":{"boundary_form_input":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":22229219976342842105884665952080713551},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":10441403860166737113819007935948606381}},"boundary_phase_input":{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":132568338297905874895666468543804113},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":13760473171597224419493629541732878345}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":189448209175580589304193825678521259319},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":185932616149250854020209197226881316277}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-104377028836761370549579234335600512891},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-422869942113487864879587430946110091057}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":127361452931569032816015955361336342577},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":240509964921025597505367492791881913773}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-289947378374724408682992575877097065235},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-152126827887734294846182004165773872181}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":2772042816008885187412545928687242915},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-22299293014793538518901187735708387697}},"form_rates":[{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":2143299601218849128057835642083369505},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":31501449623405275989319004394910247833}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-18325535088305435423473934257675091049},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-19713366582417089664126884676118228065}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-64273413509290208897786656962008233547},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-64988455683578010600027757589087540207}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":517062505738924379698390011848303173},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":386478624038935435290806086546927807}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":32196357607176790691758489619404290799},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":31819840294057130457834080099319613507}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":233536916924155106414569863688300677415},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":211638065715385999449842250095442008265}},"internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":28051799459718400560833055107252343777},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":44298112633416231094165369283625031999}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1016793073767183083561811861973234775919},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1006695131922038382383447779467006298743}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-506408148311300690860344238393809599559},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1023250255262490381854265194316512953473}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-6021430975908974097597273415797630699},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-17019328206249222862694022574119163819}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10179747552372497332287545043360851055},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":317709165555210530362277682092802071}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":16890769752511775217593290465125889131},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":12099883065083453867549410522482441239}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":68479059655153288541752557997848426317},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":56384203221931324132046225881107765513}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-27740410032204812156436077599417081651},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-16833637505398939859071427441110420557}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-201920883701925092218814674341658898709},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-102083627471837261296853391073445836247}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":203049971184516892141301719589087557},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":303539601512552807179865866646798659}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":202295681062112919458370843743797632103},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":99964976506210367262990138031806435429}}],"phase_balance_residual":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":1803194776039267481161132969691930095},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-3597583762153743725208137260761698029}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":68428969271551254096489923645056839211},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":33305756177179353801896041308828555731}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-62595252319446048724412598289433066673},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-64271237204403690107516760899397430643}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-958340504302568567031883101296435217},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-5417420424255768377160941077948923559}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":810078571193852823527809793186753269},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":404519873309704686066848203174821577}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5376498997478637298773696059589748887},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":962878100320972603781515202476756001}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":24796414450364651321088690256153728525},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-12442070888693971696116497923937762129}},"total_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":102809674692314834780843223386532154483},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":84959182667743372720744819871188555307}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-27917567539525436852883416915236368449},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-41719700379899254008352610353064897651}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":254232090829041337913783643128596436103},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":179085734059397249376665531029424672407}},"cumulative_boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":713996387765716491045464348839259189265},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1379942562019534635628972044255305022915}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1066536399290005681176470100695028062775},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":62722670428872732522881557185025250091}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":34659178040844464843044948734907331117},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-68801673115997180582506415027071515295}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1251966817003049899428860343459643336097},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1251966817003049838507747328796552983583}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":55619696060209084236267761061455257727},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-27702094939865650371782177808252386397}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":369025858789738038688769704621732217867},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":46128232348717245122657428387701200535}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":378274325369265491220421905376357332085},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":468279803900694775798420278408722790443},"time":{"denominator":32,"numerator":351}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":176212382208543894159599907342249092777},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":165491092662545652175320016309689642343}},"boundary_phase_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":3744609239262031663157689987949917559},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":11798753836907505296181324819885406123}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":373412964726325545329235844273686106485},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":183261902944842827950069068973417114177}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-206727089477075131852360577491324767659},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-418700536926640012818039775258913798023}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":251313004570911351827550080953105997871},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":59287607293300578642157296068217612895}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-35910588226614241149919813588212640619},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-301580928466279554535297813303245875189}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":22300546928362941320237322293642260541},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-22423815568174732750920289886341154295}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":33154210024368501745156961328646863893},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":7587641271956800462331576422855092163}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-17796636176681664296666121432712424173},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-19192332585083743508918924480827898205}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-32311294737470521216922173071130580175},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-4084782653511303544371376656208924569}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":256841103832470127965224970799022683},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":369760733802028324517399327446567091}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":32399829505511233513291300883326781669},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":64026247083173439802724470272972251947}}],"form_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":114607497024720110755452213828442720227},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":207119402478951116556858039451894087025}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":53330835838581955148178421995986148543},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":20711677229265814007673544526776768785}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1018487300987566453440351670072888015013},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":252139986027928788228203244709807609323}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-63430913633045657295862883210824577445},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-512580683044433122845715726210764733733}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-28433974064007986755024092178314748099},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-2398051033799117833377923966949026267}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5136408156997704865920024411569474751},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2589709937878425774650417717265148973}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":9563948853761341988600180585216114341},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":28693208056189824700252621650834866813}}],"internal_sine_current":[{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":3822378960842258938180442719243362849},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":12224226940862017709626991061534290487}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-24086991507363421876136388665797313627},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-30093008930513504691445464509695450763}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-50754463087605968210648511773309532401},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-205323570812514128913287005767347680075}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1613780249879962886514386422615059321},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":290409401224605830361795797787047547}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":407148265408303658336065218812635199533},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":402288774946845212045542406277964482055}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":14476827820072881861388178620823486361},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-14440547812987759259909908558209055479}},"phase_rates":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":8646934413358033503698498690477688677},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":2105974611647310478353526218475355407}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-31629078355147846969014109873808591645},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-32452074185776364262756014522358671551}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":-70709492563025298084318136340091545},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6106586813052150034614971936762544333}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1634969495847433442599323289272949857},"lo":{"denominator":664613997892457936451903530140172288,"numerator":805010034741321600350724854747703}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3044299471108368021983995820608045469},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":1141666473826701083989675660583489583}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":24869893368385496048794167972033135929},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-24956882001112164877998865502117598801}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":202159739867838653520295509101608184395},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":41558484291119963983557950447982791053}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-27055254181601567990608918555277256059},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-40885465314471260622626237659962922813}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":262492046245066832952514888785264362327},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":186843129027954076822383656793941374391}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1428694889763794613027770764551258988073},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1380495628605639674939730543856237151327}},"cumulative_internal_conversion":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":66814767638746200645252560264130619593},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1005504446602207390429324309759789323529}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":545675762864690349057575195812064493},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-17333563797041068499885837378080047835}},"form_storage_change":{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":19721782394950653623923087369026171141},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1262194073276841769277012503499034084475}},"phase_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":27986851927869759574052095868760443861},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-27878696460073659238674078747196219725}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":367433050241439983763793771367668125561},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":183716525120719952060549148648538612547}},"phase_storage_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":188412943391953998026867322828759212289},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":468279803900694775798420278408722790443},"time":{"denominator":64,"numerator":705}},{"channels":{"boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":87275081045251510972981794913231873067},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":163880379536607430245568796775737419391}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":13007971274393517661348495065714717131},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":9857372396414454137872152133013324433}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":184021422832967007125693848791636141631},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":361296899719007924926171774650928596509}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-409492303317132959750590177628453519311},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-207311297166998022895569376104561956981}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":247929317599938369022559590659001307429},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":116908583002604159615018726602574698667}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-71145583108315289766520764502269159067},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-298868339625441069494099166485486805071}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":5605171608397475588160491608494542773},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-11272108721540711552846506437107906617}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":32006455583449112619935999483498582193},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":14595492574572973336925364593579207413}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-17260007566589131707280656139405738273},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-37326660454664870273623343761617433095}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-64966098920830527439224506292838515969},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-1026857798888957523761625078405285801}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":510464674419085367648229211313116109},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":352958705226835873108761587823151105}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":65201234099440652662094347393050279729},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":64407468527976315936684824795781337413}}],"form_storage_rate":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":28101341559106009000816575028073936067},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":25315330384916708388652754527598358693}},"internal_conversion":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":12629174607978017067237864817134734161},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":38509666502650739408321837014875898053}},"internal_form_gradient":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":510002273269521524895601894735592775197},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":126281262144303818895110990536373569605}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1016804568044895813588930437346110572945},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1026901367659546013120997000178629308961}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-32865506159059170613188092929184343137},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-21390334100904146081073705561081971991}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5181421899232649925372890089438894973},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":658833418417513991665403677825267971}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":10705191718803183103882903488841594441},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":33278522024487600300232218968368822197}}],"internal_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":26862209792648443033370789989231881221},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":1290668358800270739092169117377633927}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-20380572699671401066450237509037341063},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-13231786794201588610999314608822562793}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-51024254775517244883495922804491428617},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-206462010705339795592059794961110802587}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":801836035536052123714946005361427581},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":554426237680596467597321368936647753}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":409671436103582145648061058846021044003},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":404684059927612417097983585733756573963}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":14523827705634924219232720894071499859},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-3621626810267143303215394671476995669}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":69891052029225987955966986648249164635},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":68140305709236121664184180690257361527}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-63893491837948977127135360445984306275},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-65509136333224730177414308606352112789}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-2615353881215698978135142903732038543},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6808754813092055104816299755361195611}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1649297815014945295603816706525079453},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":419426380861113230985794934943947761}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":6815136715175799290346955960865645045},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":2648220639494854792661361591636665353}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":3117185276245437213905633134298329045},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-25023692754888667457924969306460757319}},"total_storage_rate":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":24834404267873172761835751747892172023},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":81267220305003936074693557792858852973}},"weighted_phase_storage_rate":{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-816734322808209059745205820045441011},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-19994101234662897479917460317534581799}}},"cumulative_boundary_form_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":67668521273264790526557983014594962607},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":48631255454683137528786173535701016481}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1429304638417281809168146475257464365439},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1380957692936721602477443300987472150909}},"cumulative_internal_conversion":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":66962765778683443032759253992456417259},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":503654793609759571919544697934930815625}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":70375783032537509975103964691447041269},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-34933972740602555565987724394302415565}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1272210392070789203929338054704112738443},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":636105196035394569749202273574538847721}},"phase_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":28164677345275017361541659198322187567},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-56112256029426198279015517505293311401}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":365882795168336548676378555504813849899},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":91470698792084116762510390470577355697}},"phase_storage_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":187708357613115197354284390153529491065},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":468279803900694775798420278408722790443},"time":{"denominator":16,"numerator":177}},{"channels":{"boundary_form_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":43212270536039213311310156984472511131},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":162232268534773992585319846129625275985}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":11057827130212324390423163768676828059},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":3968342507338404573420628653805424451}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":90696753879900260403999088422717612737},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":356185357109362296148546620761205769281}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-25351498545368578301900594576758601269},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-410637643275292527384427108930289601189}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":244573734881568610824289622101044837395},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":57628017427362880775454629748226016673}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-140921142900371578407983563153317182335},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-296117915194552387908832962625378088591}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":11268354529520434857907557855485390855},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-5665111595581413178577859167808084987}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":30850125786450751965999904481579876933},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":28023310603646129608862968091598672951}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-16715942833315886617977424884093565219},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-18126650413076827154328230040609743319}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-65303578932367723542184219613887675443},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-16518805066761941814796448752955926231}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":63427367543686787833112803804492705},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":168040800271258240171697199879598221}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":65597024097104721466778331691411092549},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":32391465505058021172323251608058860863}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":220330397066450968966547000348904109321},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":197854175525071793170444121837971960507}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":47665539763240592639514930571314255931},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":17780709736318053332706019254154025813}},"internal_form_gradient":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":510671789399070612577169186732065443773},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":252941070001255524496278727433674408741}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1018544530699101627982675204410105583607},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-257117181478560039301732700861792711237}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-18690249612315099383837131536843892741},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-47274382205714945797211357094339734661}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10449797883702163421811991370085691755},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":334819645828931746965459822785915767}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":5934541039827266194063285928483290779},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":37955595871571859664996387446236082065}}],"internal_sine_current":[{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":2886365669845972745472141959191611793},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":16800705227793690805778713788870965297}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-8311453354272425423263249115487683759},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-11390348859230729766087647769888021229}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-410314487654095266952366182567384697797},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-415162853150569363529893262357720663813}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3188207230588577627206853816308145959},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2111662974542138488699812087415821369}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":412158258001633665614771279363330119003},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":407043160278789923969873388274746375949}}],"phase_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":3641641294713688847131140612674083739},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-7264111009154352300800628825116946125}},"phase_rates":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":17643869819997318717840299203911690267},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":34429313199037032061228767599747268817}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-64500924048738374523082267462642095257},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-33042940204052179523016220176130994309}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-5949291226842657008403758869508820207},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-7523951609655071698663981857284599777}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":831568493751213066807476857198847503},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":106576403355904367429293211959620223}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3778046165880903689804465711876415851},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":6040820700958996872312653554479890769}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":24999153947291139130236786098660912361},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-25084548110029871341809802258460027893}},"total_storage_rate":{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":3049501679636592825974967023998391207},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":79411180582169653146926994724053422345}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-25162289569709028104149110813007072073},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-39031814360732486876590132389865115817}}},"cumulative_boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":139388192909283257301051293246484223133},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":202129659406300081017581561930130250735}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1429822974064010511873947561059121091755},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1381329725046784577906201484923766409451}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1073638574635336991304125326249833031891},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1008976528757298961339030585174938571169}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":70906121105888861403765962520652599297},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-70402651184415668398314105154276894441}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1282012309269487903760378109625721421201},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":320503077317371959376978451897131145929}},"phase_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":28343291171026944961332071943903257731},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-56468712553210157669910157748973715741}},"phase_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":182188866376750738262370151280869946511},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":364377732753501392865006818135208804845}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":374049510417953304661466440274298648331},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":468279803900694775798420278408722790443},"time":{"denominator":64,"numerator":711}},{"channels":{"boundary_form_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":42777752045413924119471179209133979893},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":160548590728784885988591892253797769837}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":9128426969276662383726195219469419719},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":3018497808138459474491155853690907571}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":357646339195932019163594425312667260301},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":175594968592389023344497718469965539809}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-401850647011668695543123507082708580435},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-406747171268004367808457416186321815209}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":120623937113088548925367833261759235197},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":227236762922155108809598453322583296331}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-139533191023340759241816442809022213261},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-293331470123858062072768737182538515877}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":22648565254360097085201034001575122033},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-1423278287960836234832939230932637463}},"form_rates":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":7421452670944428327334448470161045291},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":3356017073176753903033521416136911065}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-8082368232480032981691343476552289871},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-4395646276603747506617429757439453605}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-65634667887409607335407527626528057187},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-33212560845539815855819742780716361899}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":126138421478951237664940618010961699},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":39892288562556817507275859215570931}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":65986615782777877378111021381983746665},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":65152223788277355235468018343252337351}}],"form_storage_rate":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":26972538713924987890177485556981756295},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":193120441775897197028711544033626954513}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":44781886201614880308153854892013234349},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":16291576864127460023813479100240579245}},"internal_form_gradient":[{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":63906454290035470039009512811711120965},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1013101284441699490465812384071377194251}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1020112990266332205416907667359426773605},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1029862006646207004055534867068137267567}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-41979071051227148697727467446109156307},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-51850068369147061061342333910662090283}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10533649732674052873852565474662055345},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":679849029702673019814650795279047793}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":52222287088291783421763189887684590675},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":42724250310869879766673388182117320879}}],"internal_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":19267150026931642330627354306862593425},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":12900481527890560916209073549085421795}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-3203965238315000767687685977104479663},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-19046225542362905903664880500957788103}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-206197390455891936935266572106911352951},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-208680674318503794260689457161465734545}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1585102153014744761968283306422350197},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1002602565464101046695330141278678407}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":414606134756854566639446455804956188929},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":409363495236580615590296768943251311925}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":14605053172573121458341337158987663055},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-14565706432997113727180064526247923761}},"phase_rates":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":17807139177446140790734598867211360227},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":34772964836630498387031253042976689927}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-65080134678128427983929250904096075129},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-66634074802465840055265571905738765013}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-6681176664208687760557686434342040433},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8252194680602482904257807196327861945}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":419120605938424350443221507920076811},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":216402667266818372545831171843628047}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":8311435129665699364456682089728643695},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":849971953358798415309122563075109809}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":25054885953573258283015474469030709229},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-12569713283505266611990097764819023655}},"total_storage_rate":{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":2994382379666172862821713725472035847},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":155100008583921825637630716526367291981}},"weighted_phase_storage_rate":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-3017479676595604987603775753205469519},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-9505108297993842847770206876814915633}}},"cumulative_boundary_form_input":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":35849651790885203171812929074335133437},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":52413843649177968137074201719881755299}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1430250869078195355423184726460033720805},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1381612709216297558481935030785049932035}},"cumulative_internal_conversion":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":268934431387759422204642509549474038063},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1010503864088310910716263098840586125473}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":2232419412178427124765519019369003539},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-35469140001693465527710256337205454397}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1291596659874732451257056514339921259917},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":645798329937366191568826479059083155477}},"phase_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":28522661436443213028629800747812413135},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-14206674612934558682629533242324360499}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":362920306538146295720624594082778606053},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":45365038317268276247050436831268769167}},"phase_storage_upper_bound":{"denominator":85070591730234615865843651857942052864,"numerator":93181695645462800925947317509702221359},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":468279803900694775798420278408722790443},"time":{"denominator":32,"numerator":357}},{"channels":{"boundary_form_input":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":21167211403180435404595830997914925725},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":158831064004611333789815664645869449137}},"boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3610069074807295080851179126309896653},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":4158555439605260765787890500424805443}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":176310798190756404476154809071945859161},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":86577829711865946185265149635261115683}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-398173722085931752696665568349585197471},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-201476312529400056547159375460287867117}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":237953094916820493319404821612285955641},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":111996305076904172212225199302873977349}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-17266014437688981152078733567330888439},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-290510613507090380678019877777331033437}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":11378104019295657584695942386525485865},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-22880188954491685935284473860685976359}},"form_rates":[{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":891065499477922860765549996378939049},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":802064176937462008543268026032114545}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-31213367986315310662933803578278068793},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-17031427460556684461984411549689364383}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-65959005797555676704041744242786236275},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-33384120408619573339749330714744891963}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":250938620088146012228988502882145601},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":302137546133683703237305426768760093}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":66369599520484607410780828043190764041},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":16378734929721471638738204473967200669}}],"form_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":105583421357583440997722323145463561539},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":94163965496273518263823866666379501299}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":41870428721595239226165559210125573157},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":29579570671964233036237096872006702211}},"internal_form_gradient":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":255870647249331216483433040719553266869},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":15847812569589205684083637901495007979}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-510754265303534381341482876642409277497},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1031079875455203641604639791159177419199}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-11665319545186574328442016298637941235},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-3531735972945762851247253425627220519}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5307186850288093289928949667963527417},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2757869161596726403958454849614046855}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":1783074501804396934474359152892128113},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":743503741237550978425762949946882625}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":30785928477787078043911416636881540801},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":17904246739722028203739142751563286517}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-4480707918946338822730441991027585229},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-15262115417151853521228480787860189971}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-414432656103374989853954863533867479839},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-419517229689105351860710935675972331755}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1576693850741759251613946016876820735},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":949193095307227959711492673012982005}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":417012492550502213355907444753540725449},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":411642506642460110021835647227905374205}}],"phase_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":7319655064366739088143094507714183001},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-7299490131898979912716143065511686805}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":71850103309445082052400662493357627163},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":35101007728047544801669454615195208845}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-32815409982230161102050728615531531941},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-16788357136999474817452142279699759291}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-7426373073451774472258780244301490023},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-8993491804636519868202725728396852019}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":844665021135656738732753436214507215},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":219464254734410046210091991805498345}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":4540561933812614740798264960440081339},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":3786633460008758444076561549330992357}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":12552330058846893577874805725180233393},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-25188311168658639570788297653590479023}},"total_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":94047139780955190855676583298327360683},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":151369518206399433827680708582348720083}},"weighted_phase_storage_rate":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-1442035197078531267755717480892025107},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-36958412786147602699967024750410282515}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":294734918603274288651226869218899164643},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":27137572590241003602461802019975268953}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1430589313053958539337014524503125273617},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":690903820751264527540165669076128672395}},"cumulative_internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":538850200948681232828648274392935394247},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1011890406463559234139836712756461439639}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":35984796555091012283589579558860225557},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-71474740204967536814310341775689064801}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1300960580295669287526710288033984042377},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":81310036268479326093388317264317555521}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":57405514655328939931901581972077160225},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-28593076164951931861704577973497262325}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":361512754260495529354936371338463716521},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":22594547141280965092110540987479331833}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":371450842063249866821676758498919320793},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":468279803900694775798420278408722790443},"time":{"denominator":64,"numerator":717}},{"channels":{"boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":83765384961941249479665860397416465563},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":78540647644758053154058735978484615567}},"boundary_phase_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":1333318104641080795574138276889514981},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1150781358704478585372444714592346715}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":347713485566209997745083688446700836401},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":170775052283546182527492597356795281207}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-197297285211929999143930710525479971837},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-399255411213121007632836236795591958737}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":234690510965060963292350669203443177685},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":55195182745936412709879840428567712229}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-273413241406077597488860112919767874959},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-143828376892764952492629180463757885977}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":11429796560853927405235121051620707867},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-22983610997284565843581014282705047741}},"form_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":13667782014731545626363244050994268167},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":1529853050766022146979952150480954173}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-7521041042196058602783760289940780223},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-32946943814968712634368885278685169595}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-33138117316815729467868101192723290383},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-16776054245659998765201031260431406801}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":499397584020484466279239848542090005},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":142543930635305444721030883349627877}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":1042899525953587757195798407781246043},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":65870675660067920911452627407504673401}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":206496411645718234968964891662324526133},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":91741586104878678356221579108551233543}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":38936013283159423596692451704974583701},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":26555523234494273850377177602113879265}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1024280614489157606196407429484242366415},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1015239435727038891529972698805689917579}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-511364917583999198517418707262001155505},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-16126892152275083994876987378332825971}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-51427115927416373753014745514301349379},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-15311872950700186573308042054360801017}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10691947237376581292805660503666335311},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2793997715339022298247881048429380629}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":61984294236822756459745254115412224389},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":26267625619043017488016298255803751139}}],"internal_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":11470555222511499126385789984646037223},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":4957837036730411000338338055258067877}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-5061663010023960325270991033977728803},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-5715219039123561548994450317053510741}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-104106465916305006579929777923270681725},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-210814115097557250475669681955564662429}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3137807562358491038246695468346088281},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1791259861190754616076317837653657083}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":209687391306756429171224978335749498185},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":206938830740665384933678516441537300197}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":14669359861858076694889252658720086121},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-14628068640756759741793377744173493625}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":72439956969164651563395815852343842845},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":70826703073473389831706402990349792543}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-66152690975860491343272763711504675763},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-33821832725155347495969515907525208165}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-2046219927202064296925748921168277461},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-9747841072396078840877157531744825165}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":850838127053108673296630648124970063},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":444678547383667677741944079027591817}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":9865106821852821836743751676548186111},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":2090311230279001719483264222137814595}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":25148462934900781759044220659100797419},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-12615594794688087919529558962008918465}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":184531320941825845237906582045254721983},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":18454106594133830787821144497296644265}},"weighted_phase_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-10982545351946194865529154808534902075},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-17925159728343355204937001119364656483}}},"cumulative_boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":151293961721728140394972771815578479145},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":224463766438624096302887422657785084333}},"cumulative_boundary_phase_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":357709827549644685496546168857510514419},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":690957763627453799973855002422125188647}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1079525527520010563638391507459541472105},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1013135196615176153226573142956560527729}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":72502547245550231606084214945000839187},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-36005970332058217642641632599146073009}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1310101510299350481135544780559346451249},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1310101510299350409143053785892406284377}},"phase_integral_residual":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":7220887298598806883404446854893189203},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-57547015459715187455031173836058356373}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":360157098123687491376554072223854418813},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":180078549061843700652290179318711586787}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":370223789358528637585510171889696744537},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":468279803900694775798420278408722790443},"time":{"denominator":4,"numerator":45}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":165691773265040770752126907381775081923},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":155300783082765127821310880244899222999}},"boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1734042766210104495158529864838209221},"lo":{"denominator":332306998946228968225951765070086144,"numerator":455236812385529045549696443340505}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":85730656969850719144387550181814790963},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":168453411993992541064609405316753416893}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-391114521496255226983231890603140145277},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-395656896646764217016155691482142965507}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":231461004002949377724111225475751899989},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":108801006446473767729731137748224449667}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-135269313073575305202990061756412041323},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-284771103998663517223619683013546484713}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":22958679012489462432820006900803976695},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-23082677155459383222121996428404014083}},"form_rates":[{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":1634424666402788575835979884173238275},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":23283506283991083673842680329742784627}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-28942457181729628937071099338910723133},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-31818028414613101018535057150142735115}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-33292999317145418058870366018658030129},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-67432691753564367889775819641081435149}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":15535073565200168140004986361381079},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":267997635733279986952764741520704239}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":67114124920007726890635632711237175549},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":1034672388310888108495502258915126241}}],"form_storage_rate":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":50443866890919659482202061986321076117},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":89296363206975024964754921680639544417}},"internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":17991815152184331199752466203954010497},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":11758002734212023837338680399790552387}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1024896521125282911988156599677622134861},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":254009668803647215759902691289153300749}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-255943921733212434223242237662822852103},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-258246134689294800280378870334094260527}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-7034564803166319071455099733084364853},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-33034572148522285531307533079709945325}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10766350786049928762978189577702321409},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1413902923465874275143954545297551963}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":33499813683099361194314204787895978311},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":14394227018337971729769605733359635045}}],"internal_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":7502214594132090631854162804353004379},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":919931990923494112148094841836591463}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-2237606429726250548212297359374782305},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-15106748958515924828963177129812674221}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-209186084141428096383508868482096183233},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-105923024512391425186348372018560747349}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":780877967766557536812466413046690459},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":52621212724944116755137788173181863}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":210845241800803944586009192272312413577},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":208033227135340284173074762408445106049}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":14695231397073714232727568157377012653},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-14653001880972699669817577291686928151}},"phase_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":36498987031898981169729191473988070763},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":8927478850656087729254899497420625709}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-33322736774310693915068165097531837493},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-34052262023185410662494608160504177167}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-8956686087393483407297519491303702177},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-5257615450363174987534846481593671903}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":214189743332644878489437264131140099},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":225029639321675666602205280871500237}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5331660940322775520820951639284903523},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":9163649527821608681483197998604237239}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":3148285696702320242590000431231759141},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-12634027100243734083556001055882013007}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":180953231152266471504673772852733973247},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":143891804596973511575331964999687474351}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-20822236411412166424134475092550331221},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-34700921816976538354177878361591614483}}},"cumulative_boundary_form_input":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":38794340664406883364868936551834708157},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":231743490645628711669511370169264735411}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1431001876707910939282605787604870639791},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":690968689310951052670948195136765360767}},"cumulative_internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":540606130095263922344184150583081080295},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1014237509371508530461323644244040892015}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":73036194576480417101922291256219513695},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-72549790912165326374692908614407826213}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1319017194593617659232757305669525141121},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1319017194593617585232626884966431999633}},"phase_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":29065008555061512526358989399911443769},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-57909231794905215433108848462918702897}},"phase_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":179427567770748642853123033953595724241},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":358855135541497193388173294897911044879}},"phase_storage_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":184523752799639124689066225685918794581},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":468279803900694775798420278408722790443},"time":{"denominator":64,"numerator":723}},{"channels":{"boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":81911061779263486488781169269506147891},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":76745460130274295393921768638017792477}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1624777030887270414092548806151082051},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1367016384821453163373278787853350127}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":338249570742613597715892547741803590797},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":332381937360538077422368797702470336159}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-193867433077005608610048105188456799629},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-392158409103402242312037368883883024985}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":57066308947605213100123502868860657617},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":214457123714404845746584362211838161173}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-66908351887480358206968847631087649905},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-281854687061191562276431383032337387447}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":23086635796990019372810505843245642027},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-5794337197450178847192942265299305117}},"form_rates":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":6240091488930896091284980263352284831},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":22084208330031228845854719761153651565}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-3473605640067627943444316069994079159},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-30676702913254389754836215434312352269}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-33443972298349507769472837242903481989},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-16938327303994195782226382053969555431}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":123764711825290248047846383889798957},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":250875089149975605260698383168112113}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":33737434365662066663983892679878899909},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":16639904317988975528617439201418131067}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":197010488641348495792836716115302321833},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":173663178014890314667111022545268817825}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":33018403246164057078320453067453742511},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":5108233145952471408045668249005273713}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1025329586052240197427691008167890320579},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1016656920776942177756373708253494441513}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1024644968411018012235774821174284614803},"lo":{"denominator":1329227995784915872903807060280344576,"numerator":-4037770170374498985478370492526781281}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-30604679352447283154349637237020072409},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-70972599600238780633451599503623954753}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10837567676815061440999062255872003439},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2859320125803921834879054334968819027}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":72103928503636340051399175396447461727},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":62708767196585400949046532830131676025}}],"internal_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":3490335580910560315635250623862738695},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-3159181882243486044464689503941711475}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":5729712502612677071241333660042101475},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-7266426464718235114638533672546495579}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-210134675358710732727281547805696571887},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-106426649244655147877697883916285002063}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3110546475551917224435964342369899529},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1576294674084495615791213340165057263}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":423957103816527099137250896172284074767},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":418206409294649954488932635194376460131}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":14736421772067018517274463467443298269},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-7353511992290678242702823178845948721}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":73524029062127021552805793391712074393},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":71981255458558056279397999700450371321}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-67108908235328181376661942531760984651},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-34267878784548601790612287788488509053}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-2435443000342225773063771954578088335},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-11295640050459876788760981515522847769}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1724852466858065445762625241706833589},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":227537465951917095919054832460390657}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":11475696637698331713706302919484459865},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":9980410274535462499860626031810644883}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":25237586906702866443947189239256292637},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-25298902112027900428039635347456470251}},"total_storage_rate":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":22170186347803750508552180965929815933},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":70073999238693171481807625998853453791}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-19648997858918491724419268387863794369},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-33515179537503971703495770547561910243}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":318033887357061018777274727033693866621},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":238938377532841926862691535979078903455}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1431078038131233780083266375830158971763},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":690936649864431799862431633915175047873}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1082759997842691784863914572403699054771},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":253798825771593654712583051760182345209}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":73572003394516436690287856266389855155},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-9136025148252487161754875381196767307}},"form_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":663852842006866491201655799643099069723},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":165963210501716613293393787048477347867}},"phase_integral_residual":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":7311891065517597591929296499616594137},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-58274304634546660257483811700814088237}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":357608430410312595596383067423583794071},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":178804215205156250487725178544307751345}},"phase_storage_upper_bound":{"denominator":170141183460469231731687303715884105728,"numerator":183961821770278682905921383194692580029},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":468279803900694775798420278408722790443},"time":{"denominator":32,"numerator":363}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":161923139656933225921054589425758431781},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":37913249281810145725448022553619535147}},"boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-96812264092737569677604111769550625},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3183984172302434616988314927645907809}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":333694791344717878398906772509097946695},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":163987919401899597987331580944537995277}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-384460128889552783737484495829675745283},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-97190218508816064525862542039622232297}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":112551830161045125723957084972872678129},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":211346523685109601944408693587133223031}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-132349211328323474911971174277785396823},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-278908341048405719691122482423046250755}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":11610132710892760455019494949631198111},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-23272373172225382990039457758668540159}},"form_rates":[{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":1485303426990671108208188345753242575},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":2610041977793057163495932144976871011}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-26623928408368312141061683839355448769},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-14761782055615727423213697603573364011}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-67181722148297463362599764277503384945},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-34032858123619060285370687865353388923}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":493214025983290385825734879500437277},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":233728283311735895744427368199946613}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":8478426196913141876582353829862956343},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":66892039965308368517814243234520142983}}],"form_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":96103985582647213496025398053501837667},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":168701125708411295270278641882694323565}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":30050359223703452339263510215604431943},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":4333677154067080795054928998315784631}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1025579187338684049871767119629780458327},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":63568341929981373843236691381208260017}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-512668330825742420037628168547083785527},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-517087018695979300457309616227949043723}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-66225448800440315402560279988549570477},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-9494707966014624596824619453946152057}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5452792008842201833859193402388558497},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1444284739372063247669854792573229293}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":38648339302714609033994074659800079749},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":16982580312939243393108094432887022939}}],"internal_sine_current":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-281295065494928805290108732579891989},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-3638498703303544586979072487597694897}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":13773808964355491533124739559056254851},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":655304689509684242641817656303621107}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-422115209513204025659643901533564843291},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-427669508247301420680614411394235512677}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3098955121353100949031094423953315291},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1468558115576606719763619813480932041}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":213086091633804609938893366992897945383},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":26268442667330952286686689523120043091}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":14783599722698535001048987814398033541},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-1846212550527829828211380203063709829}},"phase_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":37009007078928408793555933019122240549},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":36255425983488937517844214391205826799}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-67542788834492025562989244994921665117},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-68936786755808860647491803914202147689}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-10540107535069306626757986651781900903},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-3022259412010445782876859250892490101}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":27119962558100696293524866759043649},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":114932527751626806522880574952980731}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":6151074242319805463205317992560204131},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":10811446413037549459091328925398618447}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":3161026817131115844005522936414892043},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-6331605742253223114171676290209231343}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":173757227491987075036847958778151369123},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":136403092159734858325012676041382405159}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-18450743673307351955202837328852306211},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-16149016774338218472632982920655959203}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":325624034528479763742324160913026293111},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":246047111773181329186213040207882566295}},"cumulative_boundary_phase_input":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":178883620247684385742013637555585072049},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1381724050470786923102191940568116693817}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1084168608431302884192317549445055512519},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":508003933776381098249702503113956795227}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":74110356958084945934022198412961610687},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-73627306675754254476331198226375151697}},"form_storage_change":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":334041334071007117904910061212189441859},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1336165336284028393458310512131706653933}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":58862862915604398296657421564638753023},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-29321394736812274606114285366348620985}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":356418304955088437206531812687699934321},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":11138072029846510632014860108877179499}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":366853619101150598884554435248241819295},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":468279803900694775798420278408722790443},"time":{"denominator":64,"numerator":729}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":159996040390115229322438124072719586787},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":149788204686699965761145839429630541735}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1968264301032835303114244637832077647},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-311130574700349205513653939607114983}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":164629349973256544977887173187688163309},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":161844429703278666274081994527044763347}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-381294180711356382153453287651258872407},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-24091577932540949690927823305308021699}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":110988267760836983698838325101435879597},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":208270477087962248507919751474341035429}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-32716791063435003490070882421001630761},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-275932724474129741710818753811689738229}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":23347945878098610531374650874460394513},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-11700392686527026909139799764416472755}},"form_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":11282418778382348514612476521935344013},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":614764648272395305692257523517212667}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-12724154825122058804902820756221533371},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-28359211267639543303873001721485515309}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-67466983998699165666843216926102593521},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-2136548836501824643453076572538861651}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":61449315430633890214112331105910725},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":216565127002313841115684967799529423}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":34085680640274033505588005870144432591},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":16803979337008755754441058848846602665}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":187374419927071412698466689948278254659},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":81856586367552236137466396724883991199}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":27117917718043296770774268905881341121},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":14238269362272836405946199644187318411}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1025644803782056138383324839444590405747},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":508673862166659504631364231993870859929}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-512924924134746057515547766791265171161},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1034498325152996374700548186884076898275}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-17831134972786882551937575148743729147},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-81024082323831405214501376280211358903}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10970388581626278486872761832115386235},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":364448130496772587112208107278173151}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":41288647553071472431624539468698632267},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":36620499395174436730411294140861677253}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-9307951828336873633361337136080608153},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-22861827228832302792264463952107980189}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":684051893032017075506694809220745405},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":4326727567038955431144105460884847847}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-105976890645086715699042309220648654051},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-107394658060639241254088541474655751251}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1544389743400010811028879536095905193},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":680359412014209724842013554802086285}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":107083323892092743537861763727948893507},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":52791258036221391467057239744872637989}}],"phase_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":7431520072708593835108832340029867855},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-14848115232826346287002545432799950199}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":74479838920066773495075632884796422603},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":73008513012293251982846706821837315635}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-33973458261533407025763276807681024215},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-34653556145333131339814756465438100729}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-5675826543715601958331711862304235647},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-12895383211322430089038036121957851441}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":109124473150294296381502251393564899},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":116007442938322972216297798719848617}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":13142584703300827600227757859512665771},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":5828333497235775040829475523865131701}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":25331337667745337836764246292826107513},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-25369252250109939740454075699938872999}},"total_storage_rate":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":10633840822452482269355726418046425595},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":132658523838972454278869803734948636141}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-17232966767831696388775067259535445139},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-31054648896132017996062989714819346257}}},"cumulative_boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":166561924460883207558406723989467511871},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":126534216933935195040633375715573248969}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1430976699592364171781275620227282197753},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1381490702539761661198056700113411357579}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1085439760824336163728447593300018700385},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":254168821607279683926483433584058717751}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":74651096029077003037046708689740526665},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-74168793420036530337396173617601195519}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1344394816326066128824247194457121895607},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":42012338010189564015870777114417266519}},"phase_integral_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":14808722620133591737783141233219103687},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-29507790483642835528791172163035283221}},"phase_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":177642916097979932210370835873134535971},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":355285832195959765017759541564976760307}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":365838603502851410075529016760736985503},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":468279803900694775798420278408722790443},"time":{"denominator":16,"numerator":183}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":158041948187189231145816832195905889827},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":36974409527219542875983903680562114239}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-3721964947049033056964060479869403519},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-843669936847341881012194029853673463}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":162470821510950785641450382255579715957},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":159760635087328204870524050613009045039}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-47279170765013101680463099556547409241},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-191136638650822180913425689074573388999}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":13680245907252422767820732589927932793},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":205229063475648159340524906617790336559}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-258741607399250293123824039417873943379},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-136464160773744701461666725756186866561}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":23469567564282641441098330496633259757},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-11761575180481478289629067647292722655}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":21360890114045958551247922019374450449},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":9230593282691261698254228687313998109}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-6065648351345468141100973883826336315},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-27184245870224813117693271189504933543}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-16935846542704274163328112549142335077},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-34332250986890640548214020383873931291}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":245103325016429776422297685484904607},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":199393381231294452895285490790634385}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":34253171649367686253050365377659190071},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":67530871483575816998289896224478601473}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":182516338014384169648377542098382146369},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":2479779946056044780533130199371851257}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":24187118721360591387561635858478035931},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":1393641542652919587917949609937553707}},"internal_form_gradient":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":512763007361645869819073356083309519651},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1017419180061406429137621430402353028209}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1026183709473491301428150562358710240263},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1034641291999216484223824039948627633931}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-76506322477280740251657393525961012525},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-86171540848140786931087643422150143355}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":689498293164552100371404641542497701},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2940400024870384741720213681526253997}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":43972566249907120937859023700934574363},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":4915010299882105239723172583650099789}}],"internal_sine_current":[{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-1097643009172618259242452819072575319},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-15618239602289595699265085506252460227}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":30072051801098727986495748163597733479},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":16722840189658556655909940889122369925}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-212822124323535384966948947564763468037},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-215715894963233130308007147805143924371}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3080059220968188694872499946690643005},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1252825563301327229879810174012581697}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":430438049663214817051557993028365442735},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":424308979486636496477605614655692139533}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":14935641288602041728876628218338995817},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-14919689859987047488588484603208004551}},"phase_rates":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":18727357490207693285380129611794214803},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":73474148666625493452497407824924067093}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-34160509396196010415496047611772516429},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-69647044058906046402441451052050094629}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-12176359400041809202242550784749735933},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-3428656669956695319988594795494847071}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":877896492884506050540559619444012173},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":467979198625653713536848504793374867}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":13996902558217130656627520560007516813},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":782248184573815887963331006227634075}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":25367222472747448485756919735994649299},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-12702426920406384691814290459407921793}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":166515501086846884941594982219413718551},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":64457564699663714352612095398610321361}},"weighted_phase_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-8000418463768642353391279939484213909},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-14895393574129718624448070981288918863}}},"cumulative_boundary_form_input":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":42566508155380113790846701498514764041},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":260001135654224054370513733371251894357}},"cumulative_boundary_phase_input":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":178850279060683906044591303736536039933},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":690587163156721953996338563676108115015}},"cumulative_internal_conversion":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":67910845750899996340608721561305303645},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":254299475501903395137850741359990363411}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":18798514605886810941429570236883053827},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-9339062646507006951368136003063053519}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1352393096085384878687634979758745563309},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":42262284252668274880174002154515579453}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":59611034781756653795717936566058642941},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-29696250698528574675978838283916710385}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":354211829080800620338655518937390014651},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":177105914540400259226684893942246722525}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":364879516054572222608696819720693484085},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":468279803900694775798420278408722790443},"time":{"denominator":64,"numerator":735}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":156061892862746087649370295505745010125},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":145982300368540687232570202523576845337}},"boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-2727398478902246384041277538611927995},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2124469031194793293097295451886422035}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":160371953121661185833611673216491628013},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":157736642416250069114596436579382879413}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-187639407115347774960758955819760174903},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-379186141207849052697275653926031516459}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":107912878242110356506385142489707173159},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":202222188471867595985615288625401568761}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-127860286056021436111414095256826561013},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-269895447396759783012698846805082125891}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":5896256718248772209173861054732950387},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-5909840706352523679186135215858376459}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":20153588461263363156073653246523193109},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":17247068491809420415117476819941886013}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-23067385879160808285986188489240975419},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-12999635662508414082819884797358265775}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-34005294105195305117341228010934256289},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-34475095272077747759990708855479449391}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":489056399543532502170954574437359301},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":22777583100054775826809413112942995}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":68831980951721280761173748918467603635},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":67836530331196127005668416833337841191}}],"form_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":88820108011292174093998355879445635939},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":153685937906509063696119524037388358485}},"internal_conversion":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":5315851967293267690873442348769213549},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":8072888781048572118731065016382624993}},"internal_form_gradient":[{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":64076406241002554318603734119027887003},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1017307436883722795131643950810714185029}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-513168763040027590792017296020500094637},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1034602303069297435533452308155129176511}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-81770426593586519799055359268321319139},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-22849916199888719015431245046334729817}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":11090330096977664088612262338266506975},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":2963049543713799113596566285710800361}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":46699741462804744623077571804451015571},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":84127121236429396300599570701749888637}}],"internal_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-12941330062044846014779499124188562963},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-19836198731191092644668786352200738533}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":38315582065565284210827882797121836565},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":24858088016677872315734896184229908637}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-427323128576167488887641123019782430641},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-433226824154270665977603675373222748989}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1536415991997036420164637904762111123},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":572463101869304897087997879899687941}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":432484091379920320596736747315397839711},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":426229490667013872426336571479710599581}}],"phase_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":7500669148793720411796776093382068989},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-936522561051536264054685148574579307}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":75306730617726007403892760984345022553},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":73907686052641748284142982755336603431}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-2145777954816192136111505810954303417},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-69956394896838381794263430390161132721}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-13014167591102267531969522578465259481},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-14546708449791465610894425131717524519}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":882540427727407104172875616247997351},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":471583981508236138957329430094561027}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":1858123673729728543164993109071932925},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":13389247192868900145037606695714439585}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":25395846082458031015526292027001710323},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-25433204714110176296856798861932545545}},"total_storage_rate":{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":2545004223847180391807926761609888555},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":62586945595415709292215470783294304295}},"weighted_phase_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-7379972848182401556144699507929202179},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-28512046715677645111688582470799749895}}},"cumulative_boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":173923733235491066592668922294974954839},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":133422027991999699542270230807272279491}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1430546538878074162758226560123043451215},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":690387994185047442125110692227493762949}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1087570254258267429141778315421279085861},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":508788159334612616184734242056302194595}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":9467384899578035855882040157517265283},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-37629133439700364402591684490406832015}},"form_storage_change":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":340039863462462229575266316746821767609},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1360159453849848833521932791030415331509}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":59991116215455891217787611476462057381},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-29886684940782844246553880583740950769}},"phase_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":176598425163641673163115340255085248709},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":353196850327283241895650314842957160487}},"phase_storage_upper_bound":{"denominator":85070591730234615865843651857942052864,"numerator":90994254406380472829098847022497023305},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":468279803900694775798420278408722790443},"time":{"denominator":32,"numerator":369}},{"channels":{"boundary_form_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":38514203886341460989431288122779469793},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":144043106034419306652752734978013853867}},"boundary_phase_input":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-447930195209798151021751932218978665},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-2555943339211058826033762801859992929}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":316665717319342016455935942036703839035},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":77886265621719755786626848049029304599}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-186215808482561610469482936216799726907},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-188102488600446269718513640331555952403}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":212801737079699144489006361518410201203},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":49812398537058719785651185239836907529}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-63167842773450987500101617183148643599},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-266834253250431669619234697061216283429}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":23694226475037740180810840802024937961},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-5937330925586406686313590045698983045}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":18943508671336071160805818965014450225},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":16030693610595911982501395931002004671}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-10931647268486855261055487101386120491},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-24804892567833193454200534818139757947}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-34134126686571708343514275311137875801},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-69226288830816851261961009474212376457}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":488149455955193948043853629833740805},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":10315903758367320253888178068968415}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":69147905650289987115130193079711312149},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":68132527965988769785245199909680172223}}],"form_storage_rate":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":43188130178440249273075202830919272913},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":148659789432793229746745375276799216971}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":18352297589773012534274582968477269979},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":313449262768996891171077221477393739}},"internal_form_gradient":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":128091754877163293117063074611816660615},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":127126524162536583119814432182812353841}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-513155339252352233656552757489898772023},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-129297602938105510251240634225795086671}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-43558211030754167289729100179737218559},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-48354009983061414386651426983685742433}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":11145456861937949442838628891916112529},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":745892623958099720110075605840595711}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":98939576760799560348124665748223912619},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":44850553800505397054683995846234817879}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-34263374054447305949650729840933009441},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-48163866311244014936234285803970551367}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":46614674591924542643895544902492284975},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":33053648457865201811601540849099771123}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-107235521635236989810210514356769643101},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-27185100053272422123681034387997316869}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3067133489365383305692451245354019053},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1037067758797635547847347549673836383}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":108617276201035589023375763937022715303},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":214044649328451457351541841492614215185}}],"phase_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":7530037820800996488286509606067751463},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-15042074621589990961545954270510296045}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":75671700648978159086706562522324742543},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":18577267254892940685510837618347231201}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":-4311147328946870615434033105990976109},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-70234992197703030317715511380081308281}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-3466252298892223585086175076691748281},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-15391559414238156710744547986041416825}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":443463638148727178434315292316661499},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":59356249059357924234299182148437747}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":984170169306329018055985370401474507},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":14276374675518853080696856938083909493}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":6354298182792667720461628147330367683},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-12727144469233277715631483514233629035}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":159236525408745742230464196359895352883},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":60717821741771259055057077273573481231}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-13515995305015254861836614963781738769},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-27224145949250711636631220729652254509}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":355068879699671157120856211112971060265},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":136798038289681402041944123033319479191}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1430210591231666814144960246173879217217},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1380296748993992810720340053929638777223}},"cumulative_internal_conversion":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":272107629551947009776080609124481614473},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":508905702808150990018923396014356217247}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":38142995419115064824917488139125705121},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-75805924873564369541938354683222203839}},"form_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":683846736516947456885785007186801401559},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":683846736516947413341620146463837657159}},"phase_integral_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":15093738057431077421242902939986250677},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-60158002599435859846642319379834284091}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":352241183015929081300989229191657322039},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":44030147876991121782558891845666562329}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":363131504849791473244765659726879876431},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":468279803900694775798420278408722790443},"time":{"denominator":64,"numerator":741}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":152027572728055348092148367492937249237},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":142080885188584590229035637404713298197}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-8858397549339611075790737108808421683},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-5963618867565680004707152069600715517}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":156353624346250877482585845017788039483},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":19233544385083429899445725309348766043}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-92423207312533410842311755077339088593},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-373330886606282993165561095584116515179}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":52452864606695870802480900981438053147},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":196310868977725635011484401632963447435}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-124796996797505781326797399900701649829},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-263744731567449108797464237794665669889}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":23797075584753369920730182603790880853},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-23852940442999598624011899461963463891}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":17731226962543503063894846277424589937},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":3703160229038597498356480011671546853}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-10325463821377576155810530981050599427},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-23601715600433460882869828371109907187}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-34258024394441294208104724488856207655},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-17373115255445299576088736464071964607}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":243745600205261346235869999885041717},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":147902119303538526667208376110251289}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":34726877542040556521382158693094710319},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":8552313096239987317686573108824694577}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":167859683157748516376143010948579219059},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":143633983650621751819514009289373609145}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":15459351365566002351377541258399823799},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1981722384410556226377190940075040009}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1024060511946915096629830830705590139821},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":508266623631760961350097602933472051501}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1026102646716962071126899712608774037363},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-129247052295298035754537540958624010435}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-92543818781665071988056309300909060961},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-102096112710388934233286339827483489701}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5598675616123049611289279999712595721},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3002001404477990046389596487288713049}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":104564583223731657765714932793832616631},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":11920162687563449627479195444134738445}}],"internal_sine_current":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-10674645333200920909553617844472935597},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-14176254332590746697996193001246153609}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":54963585878129644638305864794142755043},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":41303802540136978990742170733798259279}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-13453094720509586884365377991375579627},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-54579251256475717300318226140327044115}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1531498773899367688371160479746211965},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":232324105727178891099834319888813041}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":27274425842046747140705292057589263401},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":26867883994347322519435173846318397061}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":15111807156399720248659270268584940081},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-15092786219435294081956886990658346475}},"phase_rates":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":19001078984759022356672828083994033591},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":18669564458194520451545318152045175809}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-69261234888274321613363668186803739011},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-17620669470340039183769621410977790509}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-3682201552925644819406460474357179889},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-8124550504162841446974214288025411113}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1782113798148092034951214675485934575},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":477783362691484377630869117691683535}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":4160492573100191430969019597019565763},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":15177222513482359895505485352770880817}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":3178906719999705505548637819256379643},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-1591756105079965411310527258393564161}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":155584901213450874264010435819562904307},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":58850538748718145217694597124915900489}},"weighted_phase_storage_rate":{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":-95896733939825329001035743195439959},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-25932906153185461384124815039541808167}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":362195172171298751562675665839202493823},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":140128059036288853375437145784992447117}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1429795353846541519875782555371903822451},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1379737659725158528219898758423113710143}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1089155175303048945464543258744413949633},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":508952149426535612430479111427014225997}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":9604327934867490972586742596777309237},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-76355307069758927085103981046748253233}},"form_storage_change":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":343748760101147214848131613799557955031},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1374995040404588769942114943536868190223}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":60762357551130219012077802926369785159},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-60546213020230602964181811014462136193}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":351344841973239801767433302605069545669},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":43918105246654961506330315187926654283}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":362343105102460588898814487984610760553},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":468279803900694775798420278408722790443},"time":{"denominator":8,"numerator":93}},{"channels":{"boundary_form_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":37493735105430359635695581323800375091},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":70048193728628412694486048029876953085}},"boundary_phase_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-2632391119463899284213444765044398935},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-13608506934802288836623271040221315541}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":154434310052811164247826638765334019863},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":152024142604643668100983766340249223413}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-45882933648842700586297743835262233687},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-370564933717337625854101121296554986983}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":25856794836775675803173911680227885293},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":193405457367776181325637283230936812065}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-246488274747180286832135402126381608577},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-32578340138787736898121045535701378737}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":11946745102851995099758635215988778201},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-11975063631481506831330278350530129725}},"form_rates":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":4129329905368060529433024480551306683},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":6796744616250625483089861157036686637}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-9715446862811899651400013288972175837},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-22390346954716734429596318753209186707}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-17188411400482582011236191287492275241},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-34874187641165302700104954335018220683}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":121771679597867966735954899987808813},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":130770870182112864654422268045662897}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":34874586691140517056282712321447991849},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":34347053796764867105441249957486040291}}],"form_storage_rate":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":40742021599021527681610700146313228611},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":138614980562372109265602418809206345723}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12590167403613684385480650215065104809},"lo":{"denominator":10633823966279326983230456482242756608,"numerator":-31930977089834526938955184577454629}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1023201898003838155448388279373168513419},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":507935247962822409498444840807258629069}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1025713010148398404821737128699595887727},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-1033388752462259611449673086397815694999}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-98052067067806379248225093177133388237},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-53781695144425802371989179453924188667}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":11246013514525530007455327863381992587},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3018382276759517441986792763643621445}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":55136805494639377735079298631809386847},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":50553409628634611449367494152031594507}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-51182288754770185493066303963421482999},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-65289839639342520670327225446042692137}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":31678207901934540213644394463937299779},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":12400668149376954930569709478244361445}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-107997973965270258249776847214030256939},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-219120983386793750777615129999943456813}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":382557014039952112024786252575510339},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":205414402533835161318201327596648023}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":219123490691734847998505849529712734319},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":215808903760739843514840378517101963869}}],"phase_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":3789124015893975405060942326114676071},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-7568230299383524117138135021375993005}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":76304568212431779376618977900985236073},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":9376903609333244375179495898796781901}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-69513369880766782778733573909432071457},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-70699308359846325017854220031319407713}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-7802735577109714525158412412739097321},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-4279811315048376138879978653711604447}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1789858640914996588360070421217078891},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":480390459487246475988577503071988395}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":17550590281536464446271071408877814709},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":16091650065093230610273059952261533821}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":25438027598791502572233823614892607749},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-25474629191241672649409610622268592523}},"total_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":75962954060623019562291324317212599189},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":113970746752624168756518935612755312101}},"weighted_phase_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-5521089137420035800930075975413858033},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-12322116904873970254541741598225516811}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":369225247503566943994368587337415064153},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":286823136234636620440982358572785858585}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1429301780511642038759992534478457997651},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1379099760962589670930682042593103335977}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1089745339400093336920112664223245126421},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":508928201193718236535274895038581135025}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":77384805105257503392299931750027697877},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-38453121588164887938391344102258415209}},"form_storage_change":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":86379021482958162306489505024998489157},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":345516085931832626259424640839035840039}},"phase_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":30576572209402086221578458824556227387},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-15234453035726292924211901259381540785}},"phase_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":175253782990650253226863148009485332165},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":350507565981300393992595139363769564461}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":361611672284789601502535779050086892685},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":468279803900694775798420278408722790443},"time":{"denominator":64,"numerator":747}},{"channels":{"boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":73949809197114783326872223627449972783},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":138090286135654926338919390728732260589}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-12180656911883677088013713824661029527},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-15267868423194810992037933427730851169}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":38143737630599323857782375542364392863},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":300479797614088196002781319449080180375}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-182272259111197628467484285400170507071},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-367908145974236001022971801202813573857}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":203929741250934586987615966855982058797},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":95266334389027985180505521976626843471}},{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":-3802404696572258610543204659324009837},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-257479911956315206532551745712242927541}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":23983393355458800498263169739666163463},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-24040805370384403306449009014015218721}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":15302362823792182124358792095186568429},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":6186908516539630307162547338947050943}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-4550950244664808949406690884303707357},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-21171393088945969415513604597179687631}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-68980719087368643237247833760040410959},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-69993703871763979361601673280061472677}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":121735201756124167454000966973062083},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":113667822657017172640045460324930839}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":70033811244786822881286185647955864477},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":17239747472001795455762388066987871991}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":158084052676256113840633048653677625571},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":33402293700738121578542003695373951507}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":9750361779107322966872576540611079183},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-3989626814857612996549511814720798481}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1022158275828052371922147888001828860395},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1015023935349405802690373256791103021689}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1025141447542966676625746225736527052085},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-516308795082215917718704952384798129485}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-51820279011602628817526143246224916261},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-113109241207053917789858227698556247227}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":11291445947954299637896293507554891929},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3032754460931920397917550044328558763}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":116065708819026285222270328673644730121},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":106936716532287007617461327678669327907}}],"internal_sine_current":[{"hi":{"denominator":1329227995784915872903807060280344576,"numerator":-233235817818598975498129577265083121},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-36956095357048900081425493779273580931}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":8973389789340614995363748717960640073},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":28972116486416036982622900865998889631}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-433418640648437112797473921469809467499},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-439783411762146369981948770432176570785}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3059539324162487848863031183639064805},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":714195993217665203389358038919680195}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":440035413819033071302010564574289452859},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":433282112062272402387376105967863381417}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":15194114966475782848128722493935556557},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-7586535992052052537882788798207792571}},"phase_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":38286232376929698765046020904109775035},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":75319974354776369861132538679183282357}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-69734619139513210789374399641148361273},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-70884754497441686813156110396724028999}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-16494907114195509335023988673769456799},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-9000947423738064591528727698647658715}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1797089437271878742177767617401457323},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":241338931820655753651511948235420921}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":2309053910251577877903761292527829199},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":17019507034130281828754081342601707905}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":6359379931992411845742450969567460589},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-25473888760523572418792498255098926199}},"total_storage_rate":{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":2316561522506715042653925955926113309},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":6890317045113894821683639698446249365}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-9824115235826351110781787474406373795},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-5841025520282542291807444901588954047}}},"cumulative_boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":188079021057898227465631429151244249551},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":73324029599311361278279801253298795825}},"cumulative_boundary_phase_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":357182703054724372849122972910731752973},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":172298009953781551770678783057959806541}},"cumulative_internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":545101193804244496342092408124293135379},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1017669388630490022461336531710847232621}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":77936361783530004825656217686585278153},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-77458560913020069551590628350420978661}},"form_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":694450934405632736200055977205313847037},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1388901868811265378063857046200653791199}},"phase_integral_residual":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":7693390353183702604716999004697626543},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-958322011580852217054497815322236485}},"phase_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":174864407423616521159490720126336596957},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":349728814847232927043667499751456644231}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":360936783453211816604272650614851379475},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":468279803900694775798420278408722790443},"time":{"denominator":32,"numerator":375}},{"channels":{"boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":72901117239489895157362124965912572055},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":136063182390813136275844334898616450819}},"boundary_phase_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-3452998761091162905826035204487370655},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-16905657924017465796443349082582843705}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":301551113067242088601998634151277222655},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":297031212184049403571801429650770967325}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-362136921244302837046833809480746205003},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-365361514121047408783937276566729655637}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":6282399481590053258798784373951621905},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":187691686429570856328549263910615515971}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-240190412978492444900885020201028811085},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-31787981305508608080335660187606366867}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":1504169704277097813232823304928824877},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-12062451586108355034415039258537038925}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":14086932358303853329569365072132081531},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":11154202164083854826960677600069131951}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-4242564148597158207088378282529989705},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-19945459720538824848386189705638257129}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-69196948742671170452310106780638853695},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-1097314425555900838607263064381339489}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":243528991228045902202927922423946521},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":48299987420068137841792895417571877}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":4394207877728902056631840772260679667},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":34606405903735060273447038531035563915}}],"form_storage_rate":{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":2393966098583594882556343229286042655},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":128622882426780218830478738086382310727}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":6945551120017138584584566671631244467},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-6916067349896628803963541103170918931}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1020929822937386189473829457611165143785},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":253498415042631204791178526443501922311}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1024387736739542358006372466076263141367},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-64478924691371581272396001310689820009}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-109308623960178065378907061978968041511},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-59366497805603711308848012515126675679}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":5666826287694465151411473720579225317},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3045160505316091729631991178350956191}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":121939866208216782199094240999612736637},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":112849988976040333491218831052226677889}}],"internal_sine_current":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-17067643446372631107360572351200004923},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-41282903851773610438594192549553909477}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":40124756319548613678517747727763109651},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":33161160626260578382122596654249875667}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-434777251641610458357123374417892282761},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-441256312064578834435264814011950257707}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":765068889778162206303404741676908069},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":303477771294730985202709518764320583}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":220876978992312241944879509208827097043},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":217438461108641029646180058873916970475}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":15224645822743380954030849322538727211},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-15202603965499930121327849406099089917}},"phase_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":38404014066249803039282282939629855379},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":75592502026978616785125527826387412091}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-69924853971275540264873533113512342647},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-4439931347749932650964553430271959061}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-17397007825835526966485442988779397617},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-4724235789907994001608407503248423187}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":225475853832417276759999861185095693},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":484652346929269823318516966752994659}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":4851833116750518262839275691511010645},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":17960633573402715270963981696775691083}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":25429742621263178577207914426597761845},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-25465888667802872801609820148371004369}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":144587267088058849056608900242631368959},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":106524350766812265889810288965504657121}},"weighted_phase_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-8626563221291223426997066431675360961},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-11049265829983976470334224560438826803}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":382992521856998632602265557518042802733},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":37459260008976851359506176026445978679}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1428083374951192898351649510042085629895},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1377591626915064095456221982475432381529}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1090527960317239796055337217811318985343},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":254336299493365904496537685180409023949}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":78489117891677852730183575051135811747},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-78012086237282243926758246176560440683}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1395508395936956281592383723984339736975},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1395508395936956184730844529152801347393}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":61944100764777640952562520684270270299},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-61730409615127458173208478456787361557}},"phase_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":349007767362601940353447285348383666485},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":174503883681300911096145145431831086271}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":360317736323702662168616709998190173211},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":468279803900694775798420278408722790443},"time":{"denominator":64,"numerator":753}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":143683348938257279540972093594648884577},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":134015609527573045627470479666866186379}},"boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-7711972247281832411382587359069016479},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-18522257686385560019345589000615144983}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":298072232022136483667405011303223274165},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":146851225325157601639932238886420219279}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-359841586736150372912962887679124135263},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-362925992343315410968043039456717747881}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":99087272387272245245823693539931369031},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":184881575613138815540812015657069089779}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-236997214565605404566407926171552079401},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-125548972026703041395136652263174463471}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":24143393575846875697878797637661762793},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-12101178228786072627132719900122986787}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":12871603260194489804386720671110263925},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":4967610738629058849849632841984706681}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-7865433021039339567394907964312367827},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-4678287775121818772778160500229756961}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-69402018354395692427046889793110614113},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-4403207129546319488828503601612516025}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":487442487239174229487363988599468385},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":39787109604826048265673003306475989}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":70569381894823675366648596065950281843},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":69455240281399867438301637436897306439}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":148363580209610343188539713955032353521},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":123662327385910562038673936169944963073}},"internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":2090667452612713875983641187771026035},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-9795422893809578136809563349495595651}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1019516815249605820875558834008907866593},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1012779863201213199092648232430234688635}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1023451754377270077262821606335006011027},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-515262164791785170933912265573775855331}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-115055538863136357370083283404791729203},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-124433925717007536586776388845336534925}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":11372639113168895737765508624857408543},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3055644019100869467537973002216239833}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":31973753512804800590485392021179636423},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":118845572906676325552053693581751236521}}],"internal_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-38431271024048083608451960195223884047},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-45622159599456954370555788138513624951}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":22184323747101706908167212598474653243},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":37365324992493174191696826368813724167}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-436065742012946997489482198016481679179},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-442658661453341386299240524089674395475}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3062691473916252592515033907253761197},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":499979564968373659189440790879657475}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":443400503458301243092750798325750285429},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":436400145242719414386220442618221327243}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":15248079893700912692193579889393347185},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-7612524722367034972824920932527187547}},"phase_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":77011295928720180549738909694279377101},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":37916417455883091726638866182110593261}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-35041980022414951888279194386757490685},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-71161649180398265802954905147616718881}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-18311657740169819134361005304686860989},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-4951068591547866500210889647275149285}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":452502932715264660100002154691994405},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":486320849969089224481902314946929853}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":10177561841529473245911585558809717789},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":18914860392685768739590925164765941783}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":25414715670512782501295531802017462257},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-25450648103271209311138435940262700947}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":140908067511700268109420422468268503653},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":6425547271276400337941780183515509417}},"weighted_phase_storage_rate":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-1863878174477518769779822871690962467},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-20853571045488156631605453233696812401}}},"cumulative_boundary_form_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":194863839419239721290374312202645984599},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":152978030884209898694918543472976090959}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1427360377553010226563082392477172909601},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1376723396086014772330315157991028546607}},"cumulative_internal_conversion":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":545361980195461118990605342086336259517},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1016886037525316294010987792439628489749}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":79042896357873940850285388154019892055},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-78566643577791747753604048206845417105}},"form_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":700942497825805016125555133769800281861},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1401884995651609932808355260371119071127}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":62343884484242946407204209708974264599},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-62131019848358572916308396396077435075}},"phase_storage_change":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":87085830044833870189077170881832573043},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":348343320179335359635786203641466984777}},"phase_storage_upper_bound":{"denominator":85070591730234615865843651857942052864,"numerator":89938386919925060588650497704317280383},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":468279803900694775798420278408722790443},"time":{"denominator":16,"numerator":189}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":141543458867881917592665690120138425311},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":65974018652091033242705474402729458915}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-17016914355713078394009244416706040051},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-314345227530850777660544478064025057}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":294713190172284753511955204491237250963},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":145246696837612266052733605775482453323}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-357659386860134436813176043891799149433},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-180301249194250196066515187679640192223}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":97670987588408462283507022535554931809},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":182101291606436199517488810255625763057}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-29221696691513030082150556838623417473},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-247861466218961224940514959812609203255}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":6053343365497993025953254038596839997},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-6068277139343778289964197913645285527}},"form_rates":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":2914237339970417144889886614209593193},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":2179362594639913218717452401269604711}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-14486232292410915321051296033148452077},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-4368767308738347061626840156069743659}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-69595616039714878695008109765228965355},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-70662961377837353058789293897701527391}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":488098297671760119956873465761988125},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":31298674310999997881164530362188155}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":35409824850004400101427104548390910975},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":69685949057298292595453005855176438477}}],"form_storage_rate":{"hi":{"denominator":2658455991569831745807614120560689152,"numerator":1121401267023636475193333336456575679},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":59366813881260412825116294256693189985}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1463277452014021217423690047829096767},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-6311024293574284882238648946702295453}},"internal_form_gradient":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":508959813260434929974566373746776436637},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":126422854370598966136393287680643664343}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1022333475515078200286378635785307339093},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-257300563624499725186774535019853754335}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-120880518895276103607453278596083278335},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-130211246276040693845959419548004003377}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":2852103204952492920468895650466971131},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":1532124767626226452358173795798371301}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":16741253165877921207985922373385782649},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":124922346016646515196131115889556561809}}],"internal_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-85477815759999445949559452399798694745},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-99941257404486497066000561149355702167}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":97244050688004157397755322869944390527},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":83162818830453505973136528308996918687}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-54660269018106060722472457895550462291},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-55498560086378280557213727051590227449}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":1533406026195285674106843067004970767},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":196655370565074353815908576027550417}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":444972982454700502591979708337186562815},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":437849731233681787234332430324087000435}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":15264417670895381603481308975274131181},"lo":{"denominator":5316911983139663491615228241121378304,"numerator":-238131414978501414621801660316386189}},"phase_rates":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":19295580115350081310936616910606034675},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":76041011021760194779321759076933190751}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-17552959334454130862238247794054251779},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-35626455627557506901303182639451740963}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-4809683026424111777676154168811651141},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-20723763490988025092155697303230006939}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":907852646552852620263498924570637271},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":243845230201235436290992457968391397}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":21315625559218505405485843971218771729},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":19882008871185434109425292195062429763}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":3174058136715595340674167148553475437},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-25428193076836612713751109973596170531}},"total_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":68611203917966189720264719698894558839},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":99098351435332226484905335729836214729}},"weighted_phase_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-3158477171546544692108613834326284617},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-19635276327188599165327252783550165241}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":396362528472911407467904828629673457885},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":312141126017053331756340725171208068691}},"cumulative_boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":713281354846293088006681604572569906987},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":343945090100855554999333381139209117859}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1090792551521485395225777419643664507945},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":508147189498896852401638959550437574775}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":39798759452634733998187164612640340153},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-79122056074280400218366493718031720521}},"form_storage_change":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1408033023920116504555992973497363898547},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1408033023920116402475315754555306245309}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":62746278743021559480541054329643496603},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-62534243069834211113306243559967405631}},"phase_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":173867043812479192126048579621407730047},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":347734087624958260096779046484297258793}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":359242952708107611163827690401589970609},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":468279803900694775798420278408722790443},"time":{"denominator":64,"numerator":759}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":139383002630890944435757784368213842715},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":16232609535637310491162212006200949419}},"boundary_phase_input":{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-4647838764824113963069393841956266683},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-21693637894982390561299573179964837233}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":291473878224394462704105780490268491179},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":143701941389270875516263898986820129343}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-355591157549914328896583160570409822493},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-179195956835640275186688783929933661123}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":192537922251142397801767730137307952689},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":89674843604882863201403769102191058655}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-230518628393313758632642719904481343823},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-122296780539276564763250312954603604789}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":758643993630145896050015847627272227},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-24337110479644494513019900844336130939}},"form_rates":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":10443542754209977228250828027618249645},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":7501462299486271874220997695433548687}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-1654619374445195477186907273994263115},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-8115906530017161992681299194824903585}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-17444358565667721569679047799558543073},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-35431377228972952214465043617156913375}},{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":61128641378808485153809501675730989},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":45676062133923106387172576366203477}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":71057807159214348115148554493511885099},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":34952309356879285381605160920626288987}}],"form_storage_rate":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":17343390125534961031116304005383160017},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":113842781823044580953549745150719879061}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1203110328201868969188138373157832715},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-961897692311466522122985695663439155}},"internal_form_gradient":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":508069363846301273548310623812233743485},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":252450740788076508280604338844219394639}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-255258243289385018081144608812349763679},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-256924182078215853108978253968145104849}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-126782722948700110678511995690189178629},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-34016028769978148605398655520673479171}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":11440982363782002392954301476853945049},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":3071022375730309556675940183154630539}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":70021857902992139358606989744164655169},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":131079128108611018974715244745179617973}}],"internal_sine_current":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-23527462667227864314242921088836885581},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-54325035328012559495554775530200457413}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":52881633341724494737645975961375119793},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":45806163543506524136698275123749248891}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-438424549731903174831216338702029397419},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-445243817636440448527003913957750786691}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":3072660650873436579438344126873268335},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":286991162489687531398132331669556507}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":446469369903176022986444266047682289755},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":439223673206279014760332243399054789295}}],"phase_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":7636834390147997793704803500142297855},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-7624349289978528936970298862474123719}},"phase_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":38660584257126173051992823482911999595},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":19054270772159169591828719938432077645}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-35154200037629622051696440360174106201},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-71312615911015330000001835753635308067}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-10089048527967949467098214817819311871},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-10827638246196293475757809272181669481}},{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":113805556063943923195133125410507111},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":488768391443294633236606437338542019}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":11144324809739495612223681783648017527},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":5215472793665311255981515627939924081}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":25363023827679068876230481366900113209},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-6349639077704989250545216452956796153}},"total_storage_rate":{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":4172820694306098820132143882391964729},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":95393091260774531581299343188561591371}},"weighted_phase_storage_rate":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":-652107348310565750587728475815301101},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-9224845281135024686125200981079143845}}},"cumulative_boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":402896106721234420488330974771933481763},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":318228354592917323190526554673533424723}},"cumulative_boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1425691239924181654645287697799773013971},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":687381735563547460219886303532012809845}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1090736155724850932617846725657422734537},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1015572955728560104911685679829127570183}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":40076403150916588304901176791728010991},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-79678145822774853170251188594552445399}},"form_storage_change":{"hi":{"denominator":42535295865117307932921825928971026432,"numerator":176744264577913825589001823510764627111},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1413954116623310499935926511834803770901}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":63151087073719877736427566988569427817},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-62939881719657811442747011029933393231}},"phase_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":173589201237981932779176724197586156485},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":347178402475963738290855006940712050557}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":358784405284048145974189672250902213275},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":468279803900694775798420278408722790443},"time":{"denominator":32,"numerator":381}},{"channels":{"boundary_form_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":137202364309139975742934260518577935291},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":127754482219717397061018911459002909589}},"boundary_phase_input":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-20147756062630087893251509880628629197},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-2906174653869387997278319550463230223}},"clock":"structural_t","external_form_contrast":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":288354147275365853700291848174493256655},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":17777107636789238937319663945150877935}},{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":-11051178080867370374780063156847359639},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-356295083365395665612515625218728043629}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"external_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":94880569310485660199456195620765291909},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":176625519911469764734651936293725699119}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-113615696344300829440339888271588856409},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-241293248159159846118731561773277420159}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}}],"flat_phase_storage_acceleration":null,"form_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":24333057239737502909809876464310117769},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-6098580254971395485322356314158336527}},"form_rates":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":4615976603548987818909168402835780565},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":6287828098176203798209678582901333003}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-2995907404776998991263762664415607631},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-7491988788046766672422155947190197199}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-69947169825151100589722336004272319423},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-35525193462129271181355569287059696459}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":490238452642642522531579409478396713},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":28816970576734517590972011690194551}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":71283538753900624731267470028328584549},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":70110936644264832361742843384705795849}}],"form_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":133992672436836580368734568780195443277},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":27248913491174601165494030073152389045}},"internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-3812389324555989139668714969335033003},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-18094867022618319602094219143117584081}},"internal_form_gradient":[{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1014174686139801346133676844152126663883},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1008040731992929945722294710322420310411}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-1019550417680134897604475660892247563525},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-513004003281398725374812440457360910379}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-132761253237451299178079147311184723021},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":-8874477093871601111090449874775582261}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":11470357690553676324191068359048915897},"lo":{"denominator":21267647932558653966460912964485513216,"numerator":192250532448853911333972586599616075}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":73117422389379241600654093096534628441},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":137314681861104151346812516702304419207}}],"internal_sine_current":[{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-51376014749930063258016729283673609051},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-29341034057668058897058508083145105831}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":114288344364409462103796325194592372411},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":100072586535330921748843841235285099705}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":-109872757431046180020004007427914600379},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-111605686797981470978632435972469339241}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":770064760664676753946808099944049169},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":90531183062582387594431890414379001}},{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":111971920835568763459300187675306024113},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":110130001748960914154499062797439219165}}],"phase_balance_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":15275851864772777880150875019437805023},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-15249933796686788090038488948843379929}},"phase_rates":[{"hi":{"denominator":85070591730234615865843651857942052864,"numerator":19356980264912311294085122450927764213},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":76361118289816283010393588398450352289}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-70373576658838892116600260414835143579},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-35670352700815962095046593489789272147}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":-21129609703815266929316527243217976747},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":-5649667587381853505875743178613860453}},{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":912782062741877182589853607714206879},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":122390490205135687619278297726258611}},{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":23273998398815454166725271386554717725},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":21854310377285743920288938141013139545}}],"region_indices":[5,6,7,8,9],"scope":["same_complete_sine_law_full_support_degrees_and_held_capacity","regional_internal_form_and_beta_weighted_phase_stores","internal_conversion_and_boundary_inputs_keep_distinct_causal_channels","signed_regional_form_loss_is_not_nonnegative_full_node_loss","channel_boundary_inputs_are_not_conjugate_boundary_work_components","direct_nodal_storage_derivatives_and_reconstructed_balance_residuals","optional_exact_internal_flat_phase_curvature_is_instantaneous_not_formation","no_trajectory_work_integral_monotonicity_or_formation_verdict"],"signed_form_loss":{"hi":{"denominator":1,"numerator":0},"lo":{"denominator":1,"numerator":0}},"total_balance_residual":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":12663215703223975163767623654982685857},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-25361777118510039568902410031694174959}},"total_storage_rate":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":129831516395210243410327602365262439519},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":91692831127999848280780340606255131135}},"weighted_phase_storage_rate":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":-2080578020813168479203483207466501879},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":-17302822836698556381195779686354425045}}},"cumulative_boundary_form_input":{"hi":{"denominator":21267647932558653966460912964485513216,"numerator":25582966721764084803205063639608863905},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":324216845946966576177761816148174186109}},"cumulative_boundary_phase_input":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":712373406929372934637645766637059273489},"lo":{"denominator":85070591730234615865843651857942052864,"numerator":343418413907973474985198309308150477089}},"cumulative_internal_conversion":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":1090557449975262370626924754643235154865},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1014724758836874871180337513306793933429}},"duration":{"denominator":64,"numerator":3},"form_integral_residual":{"hi":{"denominator":5316911983139663491615228241121378304,"numerator":1261071540849164542948381330462920345},"lo":{"denominator":170141183460469231731687303715884105728,"numerator":-40117367062649928450594250501794865979}},"form_storage_change":{"hi":{"denominator":170141183460469231731687303715884105728,"numerator":709825091699093989053397867302297510809},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":1419650183398187870577017271873387245387}},"phase_integral_residual":{"hi":{"denominator":340282366920938463463374607431768211456,"numerator":63558112047380989113704662750586583693},"lo":{"denominator":42535295865117307932921825928971026432,"numerator":-7918467164732326265805881255832302019}},"phase_storage_change":{"hi":{"denominator":10633823966279326983230456482242756608,"numerator":10833572428250391200861660791873541787},"lo":{"denominator":340282366920938463463374607431768211456,"numerator":346674317704012387968506969920666197397}},"phase_storage_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":358376079221000518012857862513480517265},"running_phase_work_upper_bound":{"denominator":340282366920938463463374607431768211456,"numerator":468279803900694775798420278408722790443},"time":{"denominator":64,"numerator":765}}]},"schema":"tnfr.sine-regional-channel-history.v1"},"analysis_error":null,"analysis_source_archive_sha256":"b3e8a15ba712e220fcf77d000ba0e9e96c58e1594eaa8bf9f7f22dabc7446397","analysis_source_sha256":{"benchmarks/conservative_regional_organization.py":"edb3809254c88c29886e45aeff015e0b15bb23a278a66417edb60b5d9864ce78","benchmarks/relational_seeded_response.py":"e8eaaeb3c83f67cede5d6820b4c70bbd276bbcfe2013ffb10f095e37fa35173b","docs/assets/conservative_regional_organization/declaration.json":"aefef27b7012a8115eda3cbf06adbcc3eb186123809622deb19c56fdbc66567e","pyproject.toml":"959bb90b7aa306e0625e47db0c9d9642186336d1c52786d03019f1e77b15c07e","src/tnfr/__init__.py":"ab4c5043a1af0f5af2fce08d4c995e1678baeeb75cf29277e5bf1e32751cc6c1","src/tnfr/__main__.py":"d48875c1b8c54e2c651283d37133b2e4e994359da694040ec9343982ce95469a","src/tnfr/_binary64.py":"e53eb0af7fffde7c4443189920f2542de9b16df4574397dc633c240762ddf2ca","src/tnfr/_coherence_validation.py":"7670433211c3a5c9313a7ffe643691faaaf4bd70a83508ff6bf1bd4aa3b8dd63","src/tnfr/_compat.py":"700aa23f2d93379b60b5c5cb28ac16b737a716a7d00991a5f0d0cf509c5fb9b1","src/tnfr/_exact_time.py":"69ef60f1405b6551f3d0fb64ad253dbe7267a053a6b390513c539a5a7a8878c0","src/tnfr/_optional_apps.py":"e869852b8ed42de46a2862f87ae7fdfcf84a57e891cb83768ba728f41e609157","src/tnfr/_remesh_contract.py":"f4430f1a431630837bd976333884ba5a69b6bc82b7452d03de9d471f6638165b","src/tnfr/_runtime_steps.py":"0c33d907eddcc987c75b3c31d85c38524da944b22c3e2769ac6ab1a0cc32a9e7","src/tnfr/_spectral_expectation.py":"4decac505b452cc259e75996a23b9d4da561f6f2c66b3b9fc8b81bb13ef5df3e","src/tnfr/_version.py":"8f29fe48d71bd59a3572dc2f328cf9f5f0f649011aac721f6b65e17d60d698ec","src/tnfr/alias.py":"378e781b833d228fc24d66315fe81a8edfe2ef7204d4ead8c0822fa9fc096cc6","src/tnfr/backend_config.py":"7c9f982399a07410697b7103e00f7239b721b65b488655246d89f1ccc359336d","src/tnfr/backends/__init__.py":"a61086d321a86c060d63912a31faf7ca826ec4de7caeba3aeea20a413a80db49","src/tnfr/backends/jax_backend.py":"c00e582887b5b5424f367768c727ab7432e505315c1ddffc2c381b8243f6cf12","src/tnfr/backends/numpy_backend.py":"cbecc8e16a2797e5006067e4ac5cfcd14d2678120f83d84d72d25f4ce4e35841","src/tnfr/backends/optimized_numpy.py":"45928b39b00e2ddb8d20967f87cc8e546d77ba37f928617f2aa34b7130bdd166","src/tnfr/backends/torch_backend.py":"1380ce7dfa4ff01308786a472ea234eda2983627131cb3f849a06dd4d1c40251","src/tnfr/cache.py":"9f165f80523c1dfe24a86769f1c99d4517225969ca6dd67d591a0237b22cc780","src/tnfr/cli/__init__.py":"20baf95cbc8d62d50abf3b92dce522444758e24f01770ed2df050cd7415512c2","src/tnfr/cli/arguments.py":"9db24d0d04e8a41a81b0f942b162723611a1b1b59f5127b0153d6145761ff6fb","src/tnfr/cli/execution.py":"87c2a84c93d3eef067e267b14a6f7750f669313fb5c82ff5c36fd253f81e54f0","src/tnfr/cli/interactive_validator.py":"3a7736fdaab23d03a80f2fc65e0f569d27be23804c67e5b94893eac7f03c15d6","src/tnfr/cli/study.py":"cc1022dd1da28b0ba16c955de947e989c6e2deb73994c5584b4eb2b4600ec4d2","src/tnfr/cli/utils.py":"e6811ad945c1e7239115c4f396d75927e41d4edcbb8cb062d79e96dff3dab21f","src/tnfr/compat/__init__.py":"895bb0f427320be2d8e94830a3626c4b88b4ce486338697a0d86bb09f93dadc3","src/tnfr/compat/dataclass.py":"e6e1e66f604df592033b7bf61d4570e45d73a84fe2abef15170e675b5a019566","src/tnfr/compat/jsonschema_stub.py":"ea9bdc047d4eec102362ce9f7b5985b13dc6b64f017aede62d7728d7fcfa8e4d","src/tnfr/compat/matplotlib_stub.py":"471622eafdd841fef60f033e1048b92ea69b2aa7a35a826fb41992d3837472b7","src/tnfr/compat/numpy_stub.py":"02aa92da75b59228f7cfc5f7fbe1147ecd2cd58c5c89914567cd0a8915554b9d","src/tnfr/config/__init__.py":"bada286fcdf9e5c6e51440cf191d9b25ad0ff1dfe9e6aa2bc4d78e4ae626258f","src/tnfr/config/constants.py":"74ea08804699cad1cdadca88c5f926b10de27847ceccacfa7e4afde26c356483","src/tnfr/config/defaults.py":"4dd5ee17edcd3aa212b2d5d81f96bde1f8a3ad99c6d454c8a5b1a4ef1f805bed","src/tnfr/config/defaults_core.py":"bf938cb6108005a519f7e184865366a0f00ccdfd4fd685fbb3a8ea7b73faf551","src/tnfr/config/defaults_init.py":"372ab327f0019146558dc5e69175582643507edd87fe866f7f7604b31af38808","src/tnfr/config/defaults_metric.py":"8bf0f45c088ad57b75462426e1a7b4ed662d325cd3a522dfae88d40e18028fa7","src/tnfr/config/feature_flags.py":"1f4ed57a5a6a4af8b260cb2921066a487f2060fd6c8406616e4ad488cb8c8a29","src/tnfr/config/glyph_constants.py":"7e6a2e7d4adeaee21e6ed56d48f6ef6fd8e8a6ea8bfe9b962cee8b809091b043","src/tnfr/config/init.py":"f1ad813f67df38968acee5ebf2a6d35736ffa61be2558047e32e3c8d1ef328e2","src/tnfr/config/operator_names.py":"54e1d832ed38b5468f33fa55cb402010aa9bdd555e019715d2cfe0b7b6c7a8d4","src/tnfr/config/parsing.py":"57f45b8b9d8606b08c935cba8143555ea5fa6f381570e207d3ad289ae8b6c8a5","src/tnfr/config/physics_derivation.py":"cf7bcdf28e7ae9347b02bd14c97c2b5bb75783ac0c0c66e13ecdfa98edaa573f","src/tnfr/config/precision_modes.py":"378433de6241ab3cfec78e4423d3876d8758e9ca95067be0aae13543726a60e8","src/tnfr/config/presets.py":"4f679c69549bd2e3b7ae6c713a138ee6cd721d9e710ddfb56b427b46f3b9cd42","src/tnfr/config/security.py":"bafdc9ed6186882421992d9830102e53d43e5ef3fd19dcf2061a9d1f026e8226","src/tnfr/config/selector_thresholds.py":"04556533b7c648523ae22a7f4cc38e7721ef2e3d53596edac9ff33a37aee86c5","src/tnfr/config/thresholds.py":"a8a19c664afe59313d3a37b699386e68ea62ffa158f6c01ad96265f8eeb5b8c0","src/tnfr/config/tnfr_config.py":"2ea35b746d4d79f1eea04ef485afa155a40add95d153ef8972c0f15468373251","src/tnfr/constants/__init__.py":"099f900f198dae3d5613ceb8edde0b50a38f5bfc60fcdccd26431e9455e61479","src/tnfr/constants/aliases.py":"6584166b3df1cd85f16db4818654c53bbabae2e2d05e4c57c1045ec82f5a73fb","src/tnfr/constants/canonical.py":"7b072c267291a1b1496453bf78c11047c17c68e3181208233e5b08072d23f2ab","src/tnfr/constants/init.py":"9993fc2fc8320d8897424f147fc57801f4a2764645ac6d6ca44eb47105e43427","src/tnfr/constants/metric.py":"28d0a9bd155b62a8852b2b1cb084a644a13a7604e288b03f8bd5f3d847d0a5cb","src/tnfr/constants/operational.py":"0e234b636387bc0b040fce640fd998d280ff55875bc9d42407d4f07f3aeac4ac","src/tnfr/core/__init__.py":"4396dc88f279820d0d4f9096ba4cc3d3f4b9cacbb03f1fa491e7c6afc8b4f27c","src/tnfr/core/container.py":"e25a419a1ea0399df85545942da2e80dc5b4053b07a2045e113ca64ed5ddcce3","src/tnfr/core/default_implementations.py":"492b2a9d1e8bf58eef87ebe224f7f6094ecd57bd64a7389de8bc6c76a5be0d13","src/tnfr/core/exceptions.py":"9857387b5410b565c1f0303df209e732746b51aeb9a8b4ae202378102b94b314","src/tnfr/core/interfaces.py":"346193c43a339ef4389ddce7a934f69fb9cdc965f75cc480b76bc20bb9a55fbf","src/tnfr/dynamics/__init__.py":"05dedab97e0f4e5e7f122be59db952285f0551d4eae68b712b66b25ab835d9c4","src/tnfr/dynamics/_euler_kernel.py":"2d355304c3b82fbdcde42a2c9b70d2d0ab9e53c9462e9746b74d30aab05635c7","src/tnfr/dynamics/adaptation.py":"96dd03f4655f5eee09ab628484261c890f65a34492f5389c6821ca4798f5cb90","src/tnfr/dynamics/adaptive_sequences.py":"6a6edc9d6c0da241bc65bc0a54c09ad8c23e8fa0eb3816d304e7547c1a979411","src/tnfr/dynamics/adelic.py":"17cfd6e7ba4cbd6986f33209ae70364921901fd57be160dfff57d34fe8b8c63f","src/tnfr/dynamics/advanced_cache_optimizer.py":"be1576c417a74379afe68cf593719712159d80d1e12cb9e35e1bf5d62b0a45aa","src/tnfr/dynamics/advanced_fft_arithmetic.py":"efbf67bd0f7bd8543532ef437fd003ef9f532df130553e1f5aba280fc6b2555a","src/tnfr/dynamics/aliases.py":"a1e41cb4e5fabb75553122980591dd9d4263e611cabf524aa23a354115f8ba9a","src/tnfr/dynamics/bifurcation.py":"f34ec3f46cc744c46af6f182a1eeb5f909dd820d8248d55d2c10875badff7e48","src/tnfr/dynamics/cache_aware_fft_engine.py":"53fafc605174ec0e015a14b81fcf51e5346d2d5f0e2d7975f5c96aa888db23ca","src/tnfr/dynamics/canonical.py":"f1e1d12dc30de0b96404cde724ea1beecd7fac30d95215ce8e3b43f2f277cb92","src/tnfr/dynamics/computational_hub.py":"ebfd14740c35e6a0ed096f58dc1137dae08fc74e5cd0a4dadf4e32d7506a7122","src/tnfr/dynamics/coordination.py":"3ccca48aa5929865577043503b123f61bfc9311663114db41490f711fff1b79e","src/tnfr/dynamics/distributed_fft.py":"9f1151effd2d137b397c844e87c4ef47c5f82d9545f6381105ca9004e77ecb0b","src/tnfr/dynamics/dnfr.py":"959d7f5c7977ce4f45aa97d9f79e5db275ab96e6a7e008072e852466ff04baba","src/tnfr/dynamics/dynamic_limits.py":"18381a8b2999d0ab0e9037603c3850850ec64c33f7f9ee40b3e83f4cd4b4a9c8","src/tnfr/dynamics/emergent_centralization.py":"dc7afc86cceb83f22609cd9a7cbeda6a87b7da3d693c2c5ddcc936b0d5a5beb7","src/tnfr/dynamics/emergent_integration_engine.py":"f5b504c332d53f00bb5310f0d06851eb95c650b134e9f96aae93a74cad0900aa","src/tnfr/dynamics/feedback.py":"0194c7370041eb3b6a70c7eb91b3a1a9b44947ea2a673852ed7df1878fba5a30","src/tnfr/dynamics/fft_backend.py":"96f8d6797fe7295c48510023aa7dc3e18ae6f446e7c7cc2ab35dccf2d0b5f862","src/tnfr/dynamics/fft_cache_coordinator.py":"e29945945ad6ed5d23b92c397dc7ffd11a5fc26b8221a3ae00c25e53a61afc98","src/tnfr/dynamics/fft_dispatchers.py":"437cdbad62d077b15bdec51fac1f83b45079e4cbd8d322f4c5861b1018979864","src/tnfr/dynamics/fft_engine.py":"2b0d096fca9ed790b59e53df5e255d0a0ef1adfef5cb776b6047ce9bc7e1297c","src/tnfr/dynamics/fft_workers.py":"fe176b05e896a548efe9e10bfcdca12233c1b3b24bfa86891db7acf9436eccb0","src/tnfr/dynamics/fused_dnfr.py":"67ebc6c994da1f26ff1e1265dc135efe1fc24d0114d1b021fb9e5978eec77b2a","src/tnfr/dynamics/homeostasis.py":"6a2af9f3c8b7432f911d3d382f10bbd350edb4b058a58e39dfc1afb42273e5a0","src/tnfr/dynamics/integrators.py":"23870dec4fb21f8eeef2cb1c5384feb4eb3423c663f979d45892e67f4f1b484d","src/tnfr/dynamics/learning.py":"cc00f759627dd6b9527d2aa16bc8638f2bd2bc2494fc472930f6d1d10a19df40","src/tnfr/dynamics/metabolism.py":"fe4cd312c3cbd3ee16da4e4424895e8f2c744085a5d22cd50f00b040ac297725","src/tnfr/dynamics/multi_modal_cache.py":"2e68fd4e034f7102ea76d24cd9811b1bc362c8f39fb52880274b963879f933de","src/tnfr/dynamics/nbody.py":"c8858288cb634511f0ba417b173dd08340641885782e757d4d546f79119f9105","src/tnfr/dynamics/nbody_tnfr.py":"7374015c9cb65e5ec61eff57543ecb86f6e3c10b0615498e9fbaf3a3d8e98649","src/tnfr/dynamics/nodal_optimizer.py":"581dcce218f26777c85b84f1a1f1584e27e1ca1b82107d990d7b358385c5d239","src/tnfr/dynamics/optimization_orchestrator.py":"3b566f657d15a325333e7a37b5d7dd7031acc4ea1022054a01d8907777fc005c","src/tnfr/dynamics/phase_evolution.py":"981526ef2a53e658462029c8e215e6b805f53e400d10318e0f64cfdbf074329a","src/tnfr/dynamics/propagation.py":"8af48d2b6050ca70dab283e783c98b89649b7ac456dda6ccc21be0f92785784f","src/tnfr/dynamics/relational.py":"61938d29e9c06b344c0bf4b04802b06dff45d2b89901a5f833c7057a115adfdc","src/tnfr/dynamics/remesh_history.py":"af19566e4ce1739e7b5a0da2c92e2cfe9c79b00bd8e4da4ae0896e74e2000d6d","src/tnfr/dynamics/runtime.py":"3142bbbbc7f61ad287937cab364ab9f711f39f0e8c71a774997ac895adc7f6d9","src/tnfr/dynamics/sampling.py":"f642656644432954869c29fd0b0540806c02afc9fda5967cc5304fd60c834f9d","src/tnfr/dynamics/selectors.py":"fa7ba1ff336d1b939d79282e1ff9ad550545c2126d56ba354c9955b5d22f4383","src/tnfr/dynamics/self_optimizing_engine.py":"279bc95fd73ac7033297c8ff950760569aa60e2824fe8ac6643d2e29dfadff81","src/tnfr/dynamics/spectral_structural_fusion.py":"4b5963f61c4d1747dbbf851a2f95454e3429fcb6af2b9dce9c0efc4bb74b23f5","src/tnfr/dynamics/structural_cache.py":"0485879d1abd12f38177eb35c44170fcde7e377bef9c97cdfdd02813a6d09d04","src/tnfr/dynamics/structural_clip.py":"4f258b2e09dd1aad6ae0ac72bbf391c2fd16d2e7d2d409f2b3ac99946e56bbce","src/tnfr/dynamics/symplectic.py":"b80853a3027b1e73f3f50315fc9aec515c181ea1c0b92f3f76cd7ddfda42ab49","src/tnfr/dynamics/unified_backend.py":"db6859f2f651b7ae34507783ca15a6be8e6432acdeee1fb238fe3f2a42361ef1","src/tnfr/dynamics/unified_mathematical_cache_orchestrator.py":"59f0a0c6ffe74cb38696fa88aafd104ea772f7a00ffbabb4e2d0a6e77f349909","src/tnfr/engines/__init__.py":"8a2ceb8de5c768e56518286b41ca2fffd6630bb0388b238545aa531585d95072","src/tnfr/engines/computation/__init__.py":"6579da3f05d2e1ebe79c248ff8cb6f403cedead1040544fe1229f983cf1d83c9","src/tnfr/engines/computation/fft_engine.py":"f407956b936211125aaa9300d8b924cfc8365dbd344c8fb952bad8bf94eaf645","src/tnfr/engines/computation/unified_fft_engine.py":"85b5d9c858f89744cfc2d72db73f507eacaa54e667d609564becb951e390cd67","src/tnfr/engines/computation/unified_gpu_system.py":"b8d58e24da7ef70a50c5ded72307e86d322a16743ab3d88e146428b24327be7c","src/tnfr/engines/constants/__init__.py":"dc5be03f165023b84ea31f226e3c4f0ed3d7791dcdbb4e0e35e0561a888c74f4","src/tnfr/engines/constants/canonical.py":"d604e7b5866741fdf878060bef3a623314b661b4f7ce6e6c064d3faaa3ad9c15","src/tnfr/engines/constants/operational.py":"eebbc6f9da6857e02bd9027ff63ccf3b341a4de0624d25ff666487fe3890eb4c","src/tnfr/engines/integration/__init__.py":"33250f7c615b9d95a4493b15aa3cbc1f46f5f79c9fe6b9bc09f5cc1f9d94d1ce","src/tnfr/engines/integration/emergent_integration.py":"f30f4b5626b0935c91f26960d200cd3f210b2ee5399ab0caa94ac5bea013b2f8","src/tnfr/engines/manifest.py":"74fac67f5cf0a3dc2b7a0718bad2353f2d1bce0e391bf27816802b06366331fe","src/tnfr/engines/pattern_discovery/__init__.py":"09fad197b243d39c5a6c0ded60280596605254a29da8cd077bd2f03397458649","src/tnfr/engines/pattern_discovery/mathematical_patterns.py":"8e460c68994813c6b419fc4b209390a50fa32b3e6102b75d01bdda35667072e3","src/tnfr/engines/pattern_discovery/multi_modal_cache.py":"650fdc4c6385e30616ef1ad4f097536c07e0a24ed04c92a1016997f07b0b5870","src/tnfr/engines/self_optimization/__init__.py":"e8e6756ffa211b9adc16392e30ff38abf8ced4f7cb01cfa1e699027765848c42","src/tnfr/engines/self_optimization/engine.py":"a1515f8c896ff9f16eb2dd147f8f07155e2ec1b5207789ea58a61e8c700f5554","src/tnfr/errors/__init__.py":"f59d528b609a7fd5d7b0629303b064cff8b8499cb92d88122eed018e1b812a8b","src/tnfr/errors/contextual.py":"d4f8b1b26f9604f1c9f2ada6202c1d837a5461d1e98c63af68839d79a4fd4ab7","src/tnfr/execution.py":"81d4cdd68059a9f4021c65e85849a58a36064d0f258f24c9059bc7453c294dfa","src/tnfr/factorization/__init__.py":"3f5494d8e0f6662b17b4e58ff75997274cf3acbda6639c468ba7185c8ae3e81b","src/tnfr/flatten.py":"47821afdb53547ffbaee852ec3cb59ad6549399cdc31e6c13acb6016964dba5a","src/tnfr/gamma.py":"f21003b17e228c855c8c6aa0a1524072b153b1620211678519c89c3e01498027","src/tnfr/glyph_history.py":"762b9258ff04022ee6a9efcf237d63432b76363573d47e470cb30b01ee562ec7","src/tnfr/glyph_runtime.py":"ab07d3a55bfa8b4c4773767dd488178909a7dc22f784155c3800a455a522b6dc","src/tnfr/immutable.py":"98d80eca6f110eddae8a28b567b849fd4d9877030af02d144c57d2e33c3d75e0","src/tnfr/initialization.py":"698ea361ec7e7607fc0f3c2e827b1ed9176c99f1c4549cd341f94a29b8756202","src/tnfr/io.py":"c487306c5f1fa40146ed493484518fcfe4b76269e84afc7ca9d13a13d51f53fa","src/tnfr/locking.py":"a2346d741f58640bf4cb191c533477a5784f1bf1c4c1a814fa15f4919727711e","src/tnfr/math/__init__.py":"f9d74a8ba7be1f72624f3e99ff9c63bb2275fd13c2e6e4553edff5698467cd40","src/tnfr/math/fields_symbolic.py":"946a7aedaa8ad17134e43f15aa706c107c8d8868e3064d21f516dedc6ffc9afa","src/tnfr/math/grammar_validators.py":"944d0528218af9259376768e31bad2bc0b65c28bff136a669ea9f797b9f2a34e","src/tnfr/math/optimizer.py":"52d3b20f7070de796d6549d09c33b8a89f41742feeeedb37dacb859c50b4d1ad","src/tnfr/math/symbolic.py":"007ece5c831acbf2034af5d2bf899d0b3efce23a9910932b14bda158374475fe","src/tnfr/mathematics/__init__.py":"91cee81403c9f178aee6a37e0f0ae4b12966e24125f18a92b5f9560f725924d9","src/tnfr/mathematics/_comparison_flow.py":"4a94540c9e1c794a415b6d7f972aac5026bfe402fdaf237e07e68a6cf7e42d35","src/tnfr/mathematics/_exact_linear_algebra.py":"8cbe1ff6f6534dd2950dadaaf3401c3d6c2d560f3b4be49fee9fdd6219c2d9ed","src/tnfr/mathematics/_exact_weighted.py":"6bb916d3172006a6d783fd5005fe0a7c499d72fcda333be715357d50e4d5c77e","src/tnfr/mathematics/_interval_taylor.py":"1a1c233cebb8963ce06bb1b08f41308ccc90554ecb10add37b4eb6312533a055","src/tnfr/mathematics/_neighbor_differences.py":"253a6e1ca539a27c555ea0b500f56d49e3d370778fb8d2bdbf24d481deaf3ba6","src/tnfr/mathematics/_phase_midpoint.py":"aea8e1902f83b7d585c31119f96039816dc607b2bad40200d85264446826d446","src/tnfr/mathematics/_phase_resultant_chamber.py":"06e06c2577d14f597150dbae44e4b45e1b4510a716323abb4e692d88086a28f3","src/tnfr/mathematics/_rational_interval.py":"1c19a6666c570d6667e8c3b93d56452f0c38fffecc50a48e81f39a7b9aa2f12f","src/tnfr/mathematics/_validated_taylor.py":"d9edab398a0652195b3e349142cb15265b118111cb5b6c0cdb0a7ff389460d8c","src/tnfr/mathematics/_weight_normalization.py":"da19f3db04024494e5fb1936db2c73b05ade9d6ff5a9b41d37dfb66e300c1d7f","src/tnfr/mathematics/additive_resonance.py":"37e87bd2c3c191337b34586dc270b16c10cd1ce7867482be582f777a0465ff97","src/tnfr/mathematics/algebraic_residue_networks.py":"0ea513a65f652b2d7fd9f09316f840017f324ea5ca41c0582c9e5aa32d20e4b7","src/tnfr/mathematics/arithmetic_pressure.py":"58d363524617966affa7d45f91c0bd7f586dbc27ed2d286077820a99fd65c150","src/tnfr/mathematics/arithmetic_pulse.py":"207b5c39f38005aced9e23c8f98f6a27bbf0f64a26d4d1bbc435254b7707c010","src/tnfr/mathematics/backend.py":"9e9682da38a43f12b797265c6ef0949025c8f4e63de87f1217e410b0f32a0ad7","src/tnfr/mathematics/cayley.py":"7a49548e4676a8f7e5df8af1b464ed6d28c886f791e16f6e6d0aec75f33209ac","src/tnfr/mathematics/crt_multiscale.py":"8a1aa5a564eb9fcac192ac10cde763c69152de01f72feafc3cd270c3041b75cc","src/tnfr/mathematics/dynamics.py":"af4a9e20bf767d360395c0e2c02ef67021d386b152f274fded82e8b7d9bd8f36","src/tnfr/mathematics/epi.py":"f60a879b264192b4a88225670177b281d9ce85ddcbb4f5b3efcc92d89de99f08","src/tnfr/mathematics/finite_fields.py":"6255727a8884a9c2e3470d70a7cd0450401e6ca34bdd0a912a9c5e298bad60a4","src/tnfr/mathematics/generators.py":"e9ec974ffafacb10c4f65b539830b3980522e27c3ec787f2dff177f24fb6d191","src/tnfr/mathematics/krylov.py":"ea7504daaf6e4693fcb47769caed924e893e198f5db4fbe7892efbc5d594078e","src/tnfr/mathematics/linear_observation.py":"c351faa608445ae0e1e698ad8c5bd4dea9cec9e1a18c10034648ebfa5dbcacd5","src/tnfr/mathematics/liouville.py":"00765fc693e9aba2bcacddb36c52a388b81e1f3d6af218226d3d828f5395d5f9","src/tnfr/mathematics/metrics.py":"e28e0fab028c6dd4fc55d22a7b1193959dee6de6efbcbf827350ec338e404bf3","src/tnfr/mathematics/number_theory.py":"668b2961391afa852213749f49fa2acff2e4d48f8c21162658dba4dee739693d","src/tnfr/mathematics/operator_certificates.py":"da55407ee78bd468eda6a718f6fca6457cdb33427f7d9ba4f3220ee190969ec0","src/tnfr/mathematics/operators.py":"a976a328667f4f00c15addf7f8d98adcbbd247eb71eae41ec5591c512c497a0b","src/tnfr/mathematics/operators_factory.py":"f402253ff0bb50ddac78d99a71e196f41e8bab87145b8d8532bc66ffe9a6448d","src/tnfr/mathematics/optimized_primality.py":"32017e869aeb963760d7ec5dcde2c40a9332c95b35139d204123ff5383bf2000","src/tnfr/mathematics/padic_tower.py":"26e80645d977f2062cb6a1b48d515a9bec8022c28652c73072de4ffc412242e4","src/tnfr/mathematics/phasor_resultant.py":"1c42646ea4bd2a802aaadac0114073d80ea2ee1964a6e667fff667d9167f7281","src/tnfr/mathematics/projection.py":"e6dbb739ef9f8198037c6e53204fc44e197da82f0d0be2876ef06640085b3a97","src/tnfr/mathematics/pulse_amplitudes.py":"0b81be2a7d6aed774e30eba36ba847a219c6fb92eebec1b866709196cf7e2cbb","src/tnfr/mathematics/remesh_audit.py":"3a3546abc3d9d844fa563bf49bcff54d4a4836c5d32f7e13c2e73536b3e1d709","src/tnfr/mathematics/runtime.py":"5ad8eb7599bf2ea88a370f85bc162eec213c75f322b7d7ff538137e309b5bdd8","src/tnfr/mathematics/spaces.py":"c67c029791cb60011ae0c4a1f029863c076a27f5f55bb47755d388c61ec18b89","src/tnfr/mathematics/spectral.py":"e431ee2b431414963a204573d394fe7b46d61f357f79d3a8a2ef58c715361ce0","src/tnfr/mathematics/trace_collisions.py":"f2ea0174704aec0abb884aaf6211607726747ef7c9ed46644ed231bd358ca90f","src/tnfr/mathematics/transforms.py":"df75cafe0694c77db103e8f7ab2e4adf7140104f26adcc542fd4b391238bb00b","src/tnfr/mathematics/unified_cache.py":"5a469c4d7930d01adfcfa0e10c16bfca1ddb8d542933e86b70b697c7fa22f0be","src/tnfr/mathematics/unified_numerical.py":"d8b48a6cbb588db76c05194601094063d7c9c15121275bd37f51537c5d90fb0e","src/tnfr/mathematics/zeta.py":"d369b74e927ae252670fb3f552b5df673630fc487e27a589748b3c2380303ac2","src/tnfr/metrics/__init__.py":"dc17fba29be3ef5dd598410f9e7f164360511ad06feb27e367a206cb769a07eb","src/tnfr/metrics/buffer_cache.py":"fb9fd5d6b25405f31f64983c8aa936a5155c1c6f2fe12987017ea2503744198d","src/tnfr/metrics/cache_utils.py":"9fd4ba0cdb7a65c5fb8d2e9a733d1605d3e1116585ed7da0b7d9b7866be3263d","src/tnfr/metrics/capacity_rates.py":"57fae93e225bd7044b31062adc124c7bf56385dad9e95ef920aa529f0155e19c","src/tnfr/metrics/coherence.py":"a300a79e6a4ad347a1e284c16ee43a0b9935680a2c4f1277b63aa075098fac7d","src/tnfr/metrics/common.py":"b78f1e9474e6cd3a094d11c2c03227a292e3db69391c7a4acee4d42655cda463","src/tnfr/metrics/core.py":"52bb13477477758b106600849e56f2a2173b68c808ddfc89e4642b49b74039c5","src/tnfr/metrics/diagnosis.py":"895b2a33529ab3c29e909c9015daab7abedc566626a3032aa2cfc283fe000ecc","src/tnfr/metrics/emergence.py":"8f58b053c4525f7bdcfb606a1852b29b0ebbe05c3e91fb7bba45a31a98d54f9f","src/tnfr/metrics/export.py":"58f4fb918562b9d1038fd8786ef308187dba5c3476931cf8d8e82455cc1260b8","src/tnfr/metrics/glyph_timing.py":"37040274c59b47a55bd2e70e90c4a25a0dc4ca22a4a8d7d5a375cbce80e915f6","src/tnfr/metrics/learning_metrics.py":"ad63fb7943f311f03bad99108bd53c73e64a48158b2e4781e43e3c9550a59e4f","src/tnfr/metrics/local_coherence.py":"a9bbd3fb18ed3e97325cf3817f348f0b5d5b3e817eedb338b930ca18a794561a","src/tnfr/metrics/observations.py":"21ae8329647c4e90c2fdc16818ce67f37b822fa493ab5411bb045cdaabd5103a","src/tnfr/metrics/phase_coherence.py":"4ab7ed79fa34acecdf6389ecd04f2b9f4315d3c94a4e0328a565d8b5d6828fb2","src/tnfr/metrics/phase_compatibility.py":"da98038f22ffbbbba49a9204d3ce2cc7586ee5a7eadf8dd45d660a0619333324","src/tnfr/metrics/reporting.py":"e53087d09cac95ddc907938604dfb70ba7786c75f20fe8e11ec1159f17a65ac2","src/tnfr/metrics/sense_index.py":"39b9c77c5a526b97fbb3434e4eb1d218ffc05c6dad97d03012b7dead2beb33d6","src/tnfr/metrics/telemetry.py":"5898370846b1245edf0872ee2a8ca431d14354ffa06e5417442fc87041505f8f","src/tnfr/metrics/tetrad.py":"0bedcedd1a44f5d08a5e01d72f8435f7b6b2556338c883d2a829ced5e0a0682b","src/tnfr/metrics/trig.py":"328fd27182278bd8db1a05637edf03e4587f27f133f039441ca34a9defa4ef15","src/tnfr/metrics/trig_cache.py":"9ad8b6ae5ae521d0d0c2e8da509c3aa6bad2289319d682195172c932e135458b","src/tnfr/multiscale/__init__.py":"ca3d3d0b74b3fe7b0b40cc14598f4593dd1dd3daa8fdd95163b3238446353b53","src/tnfr/multiscale/hierarchical.py":"f70cef0d4d0c87ba167e67662597186c14c91761f6661d2b374e5bfa9d2ebd7b","src/tnfr/node.py":"90e8dc9de00e363930db85607b6fdf584156ed19716f788778b0d4244deb9913","src/tnfr/observers.py":"d33edc8ce99a70374b6673a33dd11d1f399566b0dc9d4d4de47ac94e389b16a7","src/tnfr/ontosim.py":"ec47477479b7fc909cb4e1619ac170748ee614d827a69c0dbd6d6e36a33f7467","src/tnfr/operators/__init__.py":"0ca68d3c4c69728bccf2841696d359f1815feee5a206af70eef73e06905d28cc","src/tnfr/operators/_argument_validation.py":"54fcdcc9fc4cf7c48f13d9475268c5e7a794ca80dcae83f71b0b2d1cd237038f","src/tnfr/operators/_coherence_stage_kernel.py":"4f6094bf420827de65f5e230f00e25ec67ed3fcf4a2b3669f4063e903413616e","src/tnfr/operators/_coupling_stage_kernel.py":"a52fa7e65d3e15a83f95496e0acc9ffbaca367d9d5095f39c1883fe7d58a6bf2","src/tnfr/operators/_delayed_remesh_kernel.py":"42b207dd392078eda65f7beb1d4ddc5fba4f69445de25726f5e8a4d6d6612e7a","src/tnfr/operators/_diagnostic_scores.py":"3a4a2221d9fdab2481bc2b5bb0f8bbe78ff8dd17ac35f3c3a07c8922d74ae8f4","src/tnfr/operators/_dissonance_stage_kernel.py":"7747a362b6b47ed6bace32ea18e93830877a2d0c9f483ca4a7812ac7758ce6db","src/tnfr/operators/_epi_domain.py":"65f27564115c0e4ef496f6963ceb230473fa45b2d150d81529d363adf2c3912f","src/tnfr/operators/_mutation_gate.py":"090121ca050bacb38e50c417a87c5105fd70f2a3f7f681926a31abb5b532dc42","src/tnfr/operators/_mutation_stage_kernel.py":"6ae597fd9e5546627c180568a1df00f755eee7fffeabab91920cc6faac1a2a59","src/tnfr/operators/_neighbor_epi_kernel.py":"7fb633921c3204ea4d25e54e1d262326329fc7315d694bc778738227ea3f2c0f","src/tnfr/operators/_phase_gate.py":"79ab1749a8652ee233c5f799a804b9f65f9c6bc2c9ee48dc4b7eb6b608d6127d","src/tnfr/operators/_reception_kernel.py":"8835833c281a38e4949c9617d4a7d59e26874f85662ba8467920b5c40f468361","src/tnfr/operators/_recursivity_stage_kernel.py":"36469fb74e06db7bf26322ccca3239b7d423b77582f06333dbbf0527508d256a","src/tnfr/operators/_resonance_identity.py":"261a62ad1405ab9e2d44a4bab73bafd5d21cb326c277f79bfe6c33567948bab5","src/tnfr/operators/_scale_operator_kernel.py":"9a940a1bfcb3db974fe9a23ef81b004428b13d092b8b76f84a5b7f462cd7bcb0","src/tnfr/operators/_thol_config.py":"b55f7627677ad081d712737f8c2f4c0ff23c13e33378cf740cf65ecc3499e4f7","src/tnfr/operators/_thol_constants.py":"ecd79b2ad0b04a2c4791a4f85bbf95764793df7d9a374cda6e73653481a2c4e5","src/tnfr/operators/_thol_pressure.py":"fe5b88e40d447769a03e4f8582094a8e2bd7038c6418beeff9077851bab6402c","src/tnfr/operators/al_sha_stage_proposals.py":"717b0434180cd3730ef0c2ba83c1312785b091349a708ac147a53526b2ae5fd7","src/tnfr/operators/algebra.py":"1d3d5bec45ed9be22eaf44d3f12015f408d0c745d943384ac0dfbd94e155e19d","src/tnfr/operators/canonical_patterns.py":"2bce821368b8430b4ce0cbbfb86fe96c71f0a58453cca488f8d25640718ce1e8","src/tnfr/operators/cascade.py":"58ed0a81772b32f5505f3d701aecef8367993e579003e31ff098b9830081a088","src/tnfr/operators/coherence.py":"466847f086a344e5f28a001551230a21bb8695ffd431f78a95824c61a45a723d","src/tnfr/operators/contraction.py":"31aa468b93fb92a62644df555112cdef7732a88b0615c8766b6e827669a46ef6","src/tnfr/operators/coupling.py":"40d68f2c1ba9c92151e75e830677436cae33173a438c4a367f6d972657dee372","src/tnfr/operators/cycle_detection.py":"61a22e061e81f71969be1023c01d9e66326e29ae4aac17fddb2add80684c2078","src/tnfr/operators/definitions.py":"823878bd42539670f49b72a3fcc569421f449def517acbeaeefc1c4b5a56920f","src/tnfr/operators/definitions_base.py":"fadeddc7929ac346db8295d031cfd4ca49a6f0c52feb85f6fcd06177b3fdd0c0","src/tnfr/operators/dissonance.py":"c539c1251c0bfff2a25baa1413438a945caf35af3164607b4acfa96338664bc2","src/tnfr/operators/emission.py":"3c766bcf2769e836170d7b5177a2c58f28e429b040566cf629b18ff871cc9b42","src/tnfr/operators/event_remesh_causal_runtime.py":"5e3dccdce264c71a7d64219cf936bfe0019038026ecf23d5fa84c7505be4c327","src/tnfr/operators/event_remesh_runtime.py":"c7201386e98b7d00622d4e0c6a0b1739812b07e6de3c6b099504b7717713ebb8","src/tnfr/operators/event_remesh_sequence.py":"4c08ed283925b5b1e659739429ae30f8d07da4062d7ad70d12b7c51888d95d70","src/tnfr/operators/event_runtime.py":"f796ae4b44c82b0f4a5993bd8a57e52581c39176e2eb27aeb5f4416149e089fa","src/tnfr/operators/event_timing.py":"ebbbce7de008c47f70b5cd07ec79a687e0c6d604f6c89ebb6cbfcb1df52a6550","src/tnfr/operators/expansion.py":"373ac8a8fd747e34caef604cb7da0a029449226800af50a704426d1b9028e32b","src/tnfr/operators/factor_contracts.py":"c4c28749bb1ace09250e2440410935b5b5f6ba5f919f7cd7a5fe5349342428d7","src/tnfr/operators/grammar.py":"52ff5aca50045c905d288cede36c9ed70fdcd9bda4ed81694372130deacd52eb","src/tnfr/operators/grammar_application.py":"ed7bad24791a85d5069264d6e6208dc2c1a54147234445cb02ec9531cc422e0f","src/tnfr/operators/grammar_canon.py":"75d887071f3790503792751d3274e84b8f0ab501b09c01ed7010d347fec40ccf","src/tnfr/operators/grammar_context.py":"29cdef90f0e8e3b8a7a2638910f0e78d7969ec5ea40781200ef1191dec1986d5","src/tnfr/operators/grammar_core.py":"77b0b93cb02242a3d82cf6bbb5ecbfce11961fee7f58ced54d8df8bb889107e2","src/tnfr/operators/grammar_debt.py":"233f2eb04610371e727c437d010a203ae6aee7d424b5a9ae154d406a32b04698","src/tnfr/operators/grammar_dynamics.py":"aa0f580ac8f77ed7e94f202a9edc5b6093bd3e13c54f9706caf91e7894a9c0a9","src/tnfr/operators/grammar_error_factory.py":"a128231a9e881a429107d0a27c2baf0550fd0f4e91f3a3047e9ecec43a7923e4","src/tnfr/operators/grammar_evidence.py":"c7320bf67c17b65e9a0b05ed7c5b9c88ab31f7e1fb59c0a00089a25b318b7b9a","src/tnfr/operators/grammar_execution.py":"5caac7c7ab8618c9f2acbb4b99178d526c142ce44008f14fea93446c1a293c92","src/tnfr/operators/grammar_memoization.py":"24b9c0d8c4d1b8fbb23f31fa83d90276b5beb764e0e53245344deb0b2c554b77","src/tnfr/operators/grammar_observations.py":"713492fcd660b1edb054449b3b91b8728c933ca2a95baeef661cf27af106bd1a","src/tnfr/operators/grammar_patterns.py":"d9f952d3bfe419645cf07fe036236681c5ac18cf325b9be2351df63ff9c0935b","src/tnfr/operators/grammar_telemetry.py":"173d8b8675d12829152dba276d125abde7210b22ec27699f496ab71d189f0f55","src/tnfr/operators/grammar_types.py":"713c34cf3d8dad80f0911cd2d876e774532dbdf676e5d4810f2ad351ff703531","src/tnfr/operators/grammar_u6.py":"32189d42c9d7d3d8835696d6e2ee915bb5ae12d422eb04f465ceaa93d3f6dd6c","src/tnfr/operators/grammar_validate.py":"c4858b12bceca97d3713b2f377347818bf5c735f06004929458d3a50285e50e0","src/tnfr/operators/hamiltonian.py":"f9d49616bb1cd0e5f2880a71bf7f0f9a9b9fd0ccd466387dd19ca3f8d3c1629a","src/tnfr/operators/health_analyzer.py":"27c66f8ba906472e8af3916190ffa2615dde06cbcd9130f07f3c9dc3a587f5f4","src/tnfr/operators/introspection.py":"12aaf1df3ac4b5c12e56d2e3de3c31bfcee6bb6dd409ae897e2a7bab459f75fb","src/tnfr/operators/jitter.py":"83176da63b322b0d2ee0a3d86a6ce8bc89700bb6d2fb89236295df829b585338","src/tnfr/operators/lifecycle.py":"bea4e48881e739edb6060349054cf8e007e04535079e5e4c5bc46948f27758a7","src/tnfr/operators/metabolism.py":"c8c8295e538da32176b7ad2b70dcb2a443a420e0f8f892b3268f9fea5aff9323","src/tnfr/operators/metrics.py":"2a20d12e7acc37fe1f9f857ce196d169e0139421db245a07282a2bc1d90225f4","src/tnfr/operators/metrics_basic.py":"a1e3a4cf65d8456ab159e3a807ac9f12115452d783673ba70f2254264b5edc42","src/tnfr/operators/metrics_core.py":"2a2b6b7d280bae281de000b54e57af570ec4a984e0ac54913d780c9acf7fd0bc","src/tnfr/operators/metrics_network.py":"bb6e6ddb72c893ca94279d4710dbb6534d0d208160b53d3403cc2034e3f4c748","src/tnfr/operators/metrics_structural.py":"48a253abc944679afa3e2e5e5e091b864731b4f7f8ad2828d17ea9e9673f13d1","src/tnfr/operators/metrics_u6.py":"63fd2c526d01106f330e4aee97f0b4c59297063ac14788e65f7491336a8cf0ac","src/tnfr/operators/mutation.py":"b97ffb27d685f1c5fcbac946885e8a76765b88dc3caa68d79cdd4ae7d44cbfa9","src/tnfr/operators/network_analysis/__init__.py":"e4a240cd1dde7e742a60bd7c38484200fd863e9f5a1e9d25f33e3688e9dc529f","src/tnfr/operators/network_analysis/source_detection.py":"83bc7cb8b03579ccddf404d166853886181f1da41b56bb4c2473fcbdcc0b4311","src/tnfr/operators/network_stage.py":"63d7885ddc46a239f186a0064eb4cd9db0a574c5ffa901c7d3777b70d91d2aa8","src/tnfr/operators/nodal_equation.py":"07f6abf1f47fd055cea7ce191e2376415e53487ac0707543ee0d942233fd0870","src/tnfr/operators/nodal_remainder_runtime.py":"af6c99c0bf71b7d6536b6ee118167276b2fb510c9794c6379cd66b4924bfae85","src/tnfr/operators/operator_contracts.py":"fa0e2a2655a275da2e713b1462e8618cf28057646c4198b922c9752925a8535a","src/tnfr/operators/pattern_detection.py":"2e060ab51a664088d334ed251a022628f92698a7d7c3ab8099c44c5fbc70eddc","src/tnfr/operators/patterns.py":"3e3b326a9f9c9aeef22fd36a6d6b820d664831e9ec9022bb8d0797ef56d1297d","src/tnfr/operators/postconditions/__init__.py":"2a4cca110746454aa1eafcc43975e76c18a3307769bdfd683505d50553c09a7c","src/tnfr/operators/postconditions/mutation.py":"ed6cbf27de28d16303ffd54a703bfdddf2e20e357562fd21367735571590e84c","src/tnfr/operators/preconditions/__init__.py":"2906e68c364c3c5372289f981c46813e02fe00a0978f1bdf285980263c0d5754","src/tnfr/operators/preconditions/coherence.py":"3c5766aae8e015cdae5690d513ad6b6362985aba20dc2497f823995020ef1318","src/tnfr/operators/preconditions/dissonance.py":"41de677680e3a61c8fca993e8a95a0b81fc44d1fbea10659b38f56e3b099ef30","src/tnfr/operators/preconditions/emission.py":"420460b62ac3d9c6d0ae469a1f7a49539e1ff2b7569a5afcc6ef24e687653409","src/tnfr/operators/preconditions/mutation.py":"49c26f5b1956e01690329eda970689eb6bd280cb8e3feeaa05b61b96951a3c69","src/tnfr/operators/preconditions/reception.py":"241dcdc42814acf062f7b1860773b1ad8c5dc40ddecfdfee84df1d1c85c3e5bc","src/tnfr/operators/preconditions/resonance.py":"640d52d85631b4de77fb393ca64dd6f60372291267fac2b36b1c4c011d8a1d8d","src/tnfr/operators/preconditions/self_organization.py":"1e2012c5ff78e2952d5338b45aacd9897e6d755007de50738078feff45deb708","src/tnfr/operators/reception.py":"78c04e7a20216e66c1e026592096fef199a46dc1b1bd2c166d3192867e061624","src/tnfr/operators/recursivity.py":"4a4f1223e7ce07913897b15b2ddb04aa062732de22782880afc56c9e859b2738","src/tnfr/operators/registry.py":"c81760edcde6464c88c98cd67675b0440e96c980c0a4f60b5333080ec3b8a248","src/tnfr/operators/remesh.py":"a3a37926e8d8b6808d4564131913a3c1068c80d8eba92e61d5114e9b4f05c9fb","src/tnfr/operators/resonance.py":"3063024626bca625e0f9c2a6073f597565c502ae9e45ea89a306a4bd8c258b61","src/tnfr/operators/self_organization.py":"f2e94d6d4a0bdb08d0f49c6a96abfc9ffdb8cda12275bf2a77abf4e4d9abc4d2","src/tnfr/operators/self_organization_selection.py":"3e57929a47ada1f417690c663c93edd655c5a9f9a662cd570573ed31fcb0e281","src/tnfr/operators/silence.py":"94e326de62b4c8bd8b403f563c1c64306ff2cbb360cf34478fd766b3939110b9","src/tnfr/operators/stage_contracts.py":"dfd8da35255ebff3a7170b93a941f64d8428a885d53762ef1dfd3b571014c5ff","src/tnfr/operators/strategies/__init__.py":"8a07ce0533e1e60ed95f2deeebacf1353dbdb31587282e8d11c38899e4d0359c","src/tnfr/operators/strategies/defaults.py":"8c98c36d1e45ede4c4ce52dc0646ea1c3c3ce923ab736feda4b435cf98742ae5","src/tnfr/operators/strategies/gpu_strategies.py":"3cd80eb353057899d9a356121e5b3d764135c0573738867f9008624ee6aeaf73","src/tnfr/operators/strategies/strategy.py":"033eee1a280b082a4a97a5ba92ef5a09cf67d054016549b98b6a788d9702931a","src/tnfr/operators/structural_units.py":"d97f09dfddcee2a67de927180454452f98c1acb0bcd7702ecb60e1d85e58e870","src/tnfr/operators/transition.py":"2cd419043cc32b6cee85623b48db97e6e31055bc8cb1e46df767f2432b818b76","src/tnfr/operators/word_execution.py":"4c2ebb5550c539772601e9c94caec4806527473bebe25b5be763d8165997f303","src/tnfr/parallel/__init__.py":"9b1d718608b3864995ff4e32da458617a4c4abfe841323b1b8a3219d2dbfc700","src/tnfr/parallel/auto_scaler.py":"310d84307397980f46597e78829525e69729e6013326cb9bb341fec0d3d54c4a","src/tnfr/parallel/distributed.py":"a047ffac8b28dc0a702db493e0fa2a0281e55368f085973289229da7b577078b","src/tnfr/parallel/engine.py":"40845fda79fa992ca224169a7a7d5d0fd463a5375f449df142e53fb7320dd38b","src/tnfr/parallel/monitoring.py":"dda6a95d80e92c550865868e1bc86119305e55cb20dd95f44b18754aa4ab1ae6","src/tnfr/parallel/partitioner.py":"94c27d9ac437b07646ab85e1135850e59fcdcaf34f92496d3d246d7f44973d05","src/tnfr/performance/guardrails.py":"c6ea5d521e9835534b4d568c6b79bd3189486073fcd5cb356d85ddf4c1defc04","src/tnfr/physics/__init__.py":"89dc5e1710ad125ff26dd36d6667452156d7d95cb192daafb07cd5c6a3fef231","src/tnfr/physics/_coherence_fit.py":"a656091cdc362510e57fc7d66db6dc8db744a6006de4575f5138030295e55936","src/tnfr/physics/_conductance.py":"e4242342dbe17ea4e4b7007f021ade2c4d5ce49238f563b93205b3c85b866856","src/tnfr/physics/_cycle_algebra.py":"2ddde66fcf724144293b949bfbed109c5b2e2e18ef16e2437fb8851b843ed8d0","src/tnfr/physics/_edge_semantics.py":"1624468173279dfe7e8af10728ba03fbdaab043d9ac0a6286a5be636ab264464","src/tnfr/physics/_exact_linear_algebra.py":"614a36132d5fc6e32565c8a883a6a63df43e4e52b82fcf2839b9b7c9b3527877","src/tnfr/physics/_exact_metric.py":"762239316d0cb831688cda739652897720a2ef2ec4d262442c73f0cdbafc65f9","src/tnfr/physics/_finite_linear_algebra.py":"becc8e6075031983b566194399740eef8aff39f1962aecac3bc03e5e7770cd8c","src/tnfr/physics/_helpers.py":"4c6d352c1838eecd850ffaa9642d106ba53abcad2a1c00a44f5084c53b9d056a","src/tnfr/physics/_neighbor_epi_realization.py":"7eaeb19f1627cdcbf5cd3a529e2c38e2ceff55ced7c2ee89c152f2a3e42098f8","src/tnfr/physics/_potential_kernel.py":"48e700438a46fa3533afbbff20f51bf01cf59963a481933bd1d4078da10306d2","src/tnfr/physics/_relational_reflected_flow.py":"68ba11b95d443c4a0e535a536aa6c41f8910d63a81c706e4d318063e67a1bc36","src/tnfr/physics/_sine_admission.py":"7c88072a18fb92359663075757456c857f14f569f0967f4e0dbca86dad37e74e","src/tnfr/physics/_sine_preparation.py":"d590f824ce3a7241054cdd4104e170f423ad4187fbb8ba78df4c211a637fb2a9","src/tnfr/physics/_sine_sector_boundary.py":"c0b728087b116f1e3adff1d19ed7ec92e0c4477f1a0678cbaafd9fc4eda65ade","src/tnfr/physics/binary64_nodal_flow.py":"f12e6a7ec027673a0abfd114b12a811863150285b41282872274431dc80e357b","src/tnfr/physics/binary64_p2_reception_stability.py":"6b3b8a80cf33b45fa72a468867cced87a794ac060f1458f512d10b8913d96362","src/tnfr/physics/binary64_pressure_equilibrium.py":"71d3e51be59f23b767e6b102431095fb3790dd1505561edc09552239f35b10ee","src/tnfr/physics/binary64_remesh_relative_defect.py":"caec0a875798a87dff30848ce9ee707fe186f968db69d721229c52d9e2ae627e","src/tnfr/physics/c6_carried_affine_mean.py":"5043935cabb12910747ce7bdd57be80b58803b56de086c72f54bf87c534f4e5c","src/tnfr/physics/c6_carried_balance.py":"2bac287a3f416894ec28c4c3389b15b38ebefa7ab5ff24cb3e603898f9270865","src/tnfr/physics/c6_carried_cell_escape.py":"af628fe0f694b8f1f6c4506200766387c50a29c221def22a9a43cd2ba91eafba","src/tnfr/physics/c6_carried_cell_graph.py":"370474317c37c9fc170cf55e2d3b4df1aa4041d24cc9ed4ed86bd017d36aa502","src/tnfr/physics/c6_carried_closure.py":"12d1a0093b3e829ea8e6c8bcbf2b6ffe6b9ebcebf0ef16619986f3ff7f318aed","src/tnfr/physics/c6_carried_excursion.py":"e0724ce1c3e2a58feb1f423046624c61c97fba5d292c5488b4813cc39ee58dda","src/tnfr/physics/c6_carried_mean_cylinder.py":"312cd7dd191934591822661a9785c977608f5c3d65f8fed94176d525a22cbb5d","src/tnfr/physics/c6_carried_passage.py":"a854824f1bafe86b2744044e802f4eb8ad01b953282cc14858eccfd4a23a6520","src/tnfr/physics/c6_carried_profile.py":"bb56f475ba8151e376be3e62639ad2372016c0ebd326cb219d0401503ec55bc2","src/tnfr/physics/c6_carried_relay.py":"387408ae20750a4d8f891745ba8e7074bd8327093231c97944ce937be9abb07f","src/tnfr/physics/c6_carried_return.py":"ae9d31acc8cf5384b6cc36e963b3b07ffadb6eec0d7fe8450c40607759cd4791","src/tnfr/physics/c6_carried_tube.py":"ac7b2c889ba3bacaa0102e9c352f8826d78de05fd37150dfede9c173873deb11","src/tnfr/physics/c6_carried_viability.py":"d09e01ba432c938fe720b69c8ff41cbae9e23b5f66f932d008344156231d4436","src/tnfr/physics/c6_phase_orbit.py":"93a793157ec843c8266d6a017c8f81be4f97c3992042896faf6fa6ad94c03c82","src/tnfr/physics/c6_pressure_lattice.py":"66e5531548e9878fdba560fc058971ade458913c5f84e945118cd1843e6e7ee2","src/tnfr/physics/calibration.py":"83e8846c67b765f2ef18e600593b2a0047a36b3cbaba9e4d0203128bbb32285a","src/tnfr/physics/canonical.py":"5f320cfa7f572ff0c8dd6c8e9568baea7de4d2349e7ae9fef94974f3bd157d3b","src/tnfr/physics/capacity_feedback.py":"7dbc2f203cbb35300bb31ba16b8fa3e049f63190d817f2b514b066d0694f3889","src/tnfr/physics/capacity_localization.py":"362998be5b8f6b6d39d70efce1b4686c42afd0e66cea70cc8da1ed987f4bb146","src/tnfr/physics/cell.py":"ce7bef00efebeb0a8c359123bcd9304b67b0162a379edb9ee18c3330592b65cf","src/tnfr/physics/classical_mechanics.py":"f4207054861204bab24b8e9503989a4131cb2234d18f2ee614a5074d8bc7718b","src/tnfr/physics/coherence_geometry.py":"7e295b8f3de7e0aadccf97621de2e8c6f3a60ebfe7f446c4599d86a78cb76af5","src/tnfr/physics/conservation.py":"6018da9afd44f0ba20f86a9ffa201f7cb68cb308bdcbb753aaa9fb963a7a0db4","src/tnfr/physics/conservation_gauge_unification.py":"276d8cfca44d8edf136de6452d2eba2aa0b1545f4025bf934921a1365a9648ed","src/tnfr/physics/core_research_integration.py":"678dcbea8cb80a0425133163df395dcad21c19317ccfba0efdc6acc9c09b7f53","src/tnfr/physics/core_research_trajectory.py":"56209d1634d1d4986512cc40c47fc846a9c0cedfb49caff5de6251412dbb5a59","src/tnfr/physics/coupling_support.py":"baa342f6444d5130ed90904f5f47ed5dd136c8cc94f669ae32064f06b9f04363","src/tnfr/physics/coupling_winding.py":"807c56d1b110ef400bdf62961074894beb63c909e38ea2c3b51cfb96c1dd77d1","src/tnfr/physics/cycle_memory_relaxation.py":"43330de5d7c5eeec1d95f573343af3f8efe9f45c13d543c341d52b4e043e0a07","src/tnfr/physics/cycle_relaxation.py":"7355a069bcb685e28f6d8185593f0b6d6c42cb3bcc7e319f129e4ac2daf88ad5","src/tnfr/physics/cycle_support_dynamics.py":"acb6b3d628c34d16c411b28cffcce13cfa8226bbe640afb4092b02936c532b6e","src/tnfr/physics/directed_diffusion.py":"82384e7aa9219d0d8826fe1d19eb63fdf7dbd5619706b3f9956b43b4d15f91f0","src/tnfr/physics/dissipative_conservation.py":"19803a85f7addfb221398fc15f2d59ececfc3882287a2d3132dbd678a0d17afd","src/tnfr/physics/emergent_particles.py":"5620bfbc391585fcca6500b622d890016aafff0630def507d8292721219afe81","src/tnfr/physics/epi_memory.py":"d504a205a707dca44b91ddf4557e2f8f43d281461591cdca3e9d1ef30f5f6e56","src/tnfr/physics/equivariance.py":"1d612c436f935ad9dd2912cb0e9e43e93fcdd3109d4b7f38b02b22905c80fceb","src/tnfr/physics/event_duration.py":"8cd48f7f8413cc91f2bca24b89e875627f05b751170bdfda9630f57034254505","src/tnfr/physics/event_refinement.py":"64081eac638fe1dd9b60f17a50d8c2cb0f163804ee9e27b4bcec6b575f714451","src/tnfr/physics/event_remesh_reference.py":"9f8a1a600095a4ae0947544dbf575690108499ec6bf85427ba31ea93c5981dc4","src/tnfr/physics/event_remesh_refinement.py":"68e6f85aba292e7abc9910f46cc610b122ca489328ed650a21cfe7ea9b7b5085","src/tnfr/physics/extended.py":"592dba72cd3cc293fb20d3906ec48d643550263855ad18d1e6d9ad62c9142ba4","src/tnfr/physics/fields.py":"6f7628259be00bde7b51b7732b521b9e52839cf3b139dee967152456c00d65b1","src/tnfr/physics/forced_support.py":"d8714ba8db18640595e192e605986114da79d34f78f606aff098873d92d3f5fd","src/tnfr/physics/forcing_realization.py":"f4a46dcac10a9bd45f7a0bba7cc698ff47f799bde9c9c028f8eac50b8f27493b","src/tnfr/physics/form_geometry.py":"9292f461f4598a5ffc0f1ba86593fd2245c0a7ebfbf5227452bbf50215c3fcbf","src/tnfr/physics/gauge.py":"801844b10759d64c91a5a52fe1ed5099308ad28c071d328daed275dfaf297316","src/tnfr/physics/geometry_realization.py":"62c673ce6f8873f2f6cc97f9fa14aa2e3f998b2942aeb825aa87e53efd9b4001","src/tnfr/physics/heterogeneous_vf.py":"dab685131859224e54412dcbd3eea4841d4917f409aa7eb675bb63305a0e68b4","src/tnfr/physics/hybrid_operator_stability.py":"7a6ebfad8629f2590c39e3bef7954cbdefcbc9ab4bedbdb6c5c37c35fb788cd7","src/tnfr/physics/integrity.py":"0af66f9c8cd642f940f799828f2f0581c6321fb1810b9915a8eaedb43580f8af","src/tnfr/physics/interactions.py":"e32329c8cbd86f8f6f7ca580e6e325ca797e5b21aac63fced6f02d005074a63b","src/tnfr/physics/joint_quotient.py":"d2b009103d9855218b2949c26ffdcd8c4b91cf16deb9b301fe9cd914c9e19ec5","src/tnfr/physics/life.py":"5e515d710d41f88a170ef75bfdc98175fccdbe4cddcdac87373a5e718870df3d","src/tnfr/physics/lyapunov.py":"f7756eae94ad12fcd2656503e34fd0c9f85dd18354c4533dddf32d8c7a85a857","src/tnfr/physics/metriplectic.py":"e6a9bd97dd0b571f374e2502c12141e2fe42854ca6c4a3bab3dfa45751c70f6b","src/tnfr/physics/multiscale_coherence.py":"0566c5de3314f077d638021d38e78a8354f89046eef2546538a4b0958425340d","src/tnfr/physics/mutation_trigger.py":"26b70dcd00eceeb68cea50928ad1da37ad9c3b9e8811b0abcc25e3fad567c45d","src/tnfr/physics/network_stage_stability.py":"15ff48137791e7a9d785e55fbe5a2f8dad3a07e6e87d8fe8be5532f2be960411","src/tnfr/physics/nodal_remainder.py":"2de1f13ffbc5d89679bbd327c5c77a15b541cfeb484d4dda1effca8bfd06d56d","src/tnfr/physics/nodal_remainder_pressure.py":"13b65c5df03873e363a7233db2f9f3bfd4033de6bed04efc95dbf0992f7f4265","src/tnfr/physics/nonnormal_prediction.py":"f28275806f2697092c01a6624f937370ae6cabda255bedcaae3573036faa4a91","src/tnfr/physics/observability.py":"7219f83ab22de4736171a0c537e4eb2e05f2610ea4eabacfeb1e749edaecaaa6","src/tnfr/physics/operator_equivariance.py":"3f473a168a4174f0509389a219dc40e948fe5345b6face71af7d2f658ed7900e","src/tnfr/physics/operator_quotient.py":"4b6dec3abcd930768431340bed38969a6659fce0a35be85e722edf1335d2cccb","src/tnfr/physics/p2_phase_form.py":"b86f063dc37405f3aad16fe4d84e7d3bcb18fa39a148e6012a8c9faad160012c","src/tnfr/physics/p2_transport_reference.py":"5f92492fb1846facef8f01e0b9fa8e6b3d5ca2049dd18a05e41bc09acf8f5439","src/tnfr/physics/p5_hidden_form.py":"76f09531c69a25ab57fbf0991533402bb3a7d695694e82d3cd1cb2c4f2dbc91e","src/tnfr/physics/p5_memory_truncation.py":"7932aefa53d2cf3f176c0cad4c7c5fa67c00f2c15ed12abdbeec6e8bdda06909","src/tnfr/physics/p5_reduction.py":"6f4bf7acefd5c7ba2ad71deedaa32cbfa133356d821c7639e541ff2c34a70880","src/tnfr/physics/patterns.py":"642500e98875ac20c2a40eb64ac01fbe77dad28b3e93d1200db54ce6861750d8","src/tnfr/physics/phase_chart.py":"ec243973604fadb673225bc9cf0700155e8d5f6883e07ff225287da3b685d3b9","src/tnfr/physics/phase_curvature.py":"4f5ab5ec22fed8516a1f2552cb5161fe245f4489dd9999dfb8e74b420958fab8","src/tnfr/physics/phase_cycle_geometry.py":"be9703237dd5d282086678e5946d2e8ab658670fe66e87a6e100134552607fc1","src/tnfr/physics/phase_quotient.py":"f15ab03a9808378b7c5811b31daf7d5c5106a739e0c39fba9a7057a5555e8c6c","src/tnfr/physics/phase_response.py":"db6e80c6f35abd985f884619dd2652f53e52ef33c384bace7746079389ed3a30","src/tnfr/physics/phase_resultant_sectors.py":"e0aacce6071fa62a24518395dcc9200cc8b255ba763a1b225aa54d789564761d","src/tnfr/physics/phase_scaling.py":"cc6abf6ab0684dc4921751b5f39889870081972968a4a2248a60b8eca0419f57","src/tnfr/physics/phase_transition.py":"161d21b4ad151147a6d2455e9ec5537d41c73da2255be06d39b7997211bd6fda","src/tnfr/physics/pointed_symmetry.py":"576fed57ffd4d5495ceb91be02a63f03f2e04800831f843e75a69918a3cdfad7","src/tnfr/physics/pointwise_stage_stability.py":"27f3dad6d7b5ae5cdfb8aa11e8b34f915dcf3e96d1b6bc09127a6736e00c88c6","src/tnfr/physics/quotient_structure.py":"23c251d6d8b24a5c5a9d8817e03de9e86ced321e5c3c25d6895b98b9db9326a4","src/tnfr/physics/reception_realization.py":"36a310cf4bd2d87510e95965a055d9ff847de0dc416abb33e62d6be479687f90","src/tnfr/physics/reduction_certificates.py":"2a03bb98100ddff615e047f0299772656e3202f2ac3fd72741eb833d12b7f7bc","src/tnfr/physics/regional_phase_lock.py":"1249f5018b31d00bc8e62f6eb6ed4a8aed46b310c3e873f6e9e14f47633743da","src/tnfr/physics/regional_response.py":"24cc756cbf0b8b0b02bea029be99caf61c9f29c4da43d65e182bba5c8e80fbbe","src/tnfr/physics/relational_capture.py":"bfff0e0827d434b3ce70c4492fd2ad646238fcaaa69d831cf7201dc942ba00bf","src/tnfr/physics/relational_cycle_memory.py":"2716d8517108c06fd7ca239dde2345f4af75b0b96193a3ec2f9ee062f1cad1b4","src/tnfr/physics/relational_memory_contact.py":"9b8fcdb9784e784696f90f39d7113947b8366817e9698883d6e6455f271697b8","src/tnfr/physics/relational_observations.py":"211cf7dd8a6d5e8b5d2acfddd394c9ac57e44acd9a5e94ad738e075cf5ff5221","src/tnfr/physics/relational_reflected_boundary.py":"deae406c7f8a8bc722251da243d992a10a84fb7707caea452c6c2b4cdf04c7b7","src/tnfr/physics/relational_reflected_equilibria.py":"b5c100d0553e03ec65441ddd921c77379e034a5174f8ec29f2241d8bb281715c","src/tnfr/physics/relational_reflected_transit.py":"3de5d84a7a4018bc4c0ec585976426439c5919f9ba723331b4ec5b25b1614655","src/tnfr/physics/relational_regularity.py":"bb8bb74cbf24702ee3b400bef8b8e26f4a64b2f6a471226a855f0f51763e9eb8","src/tnfr/physics/relational_sine_bridge_memory.py":"f810925db55c6f468c6bb24c4d628269120857019a2dbca78f9c507f7c7ba026","src/tnfr/physics/relational_sine_budget.py":"3c601cf5c8aaed26430f823c8299258e8c912122e4de7ce1f3ed4a8f9c293799","src/tnfr/physics/relational_sine_comparison.py":"da7b7839be39c1352fa7b437d391854b97e7fb4d4e9d09287a86c974c0dcd6eb","src/tnfr/physics/relational_sine_composition.py":"3df9152f139addc18b831f40093260136ab730a75d46e8a6c59a1b35952ed1ae","src/tnfr/physics/relational_sine_entry.py":"bd8e9b3405339d3dc6a9d6a3d06b6ba7e3f90aed3196bf678d5824dc64987d57","src/tnfr/physics/relational_sine_equilibria.py":"8392ddbb6616a7b47b71b78b8688374c56b608ed318913572d6187bd32757760","src/tnfr/physics/relational_sine_forecast.py":"a787ebfd7ed7a181d9452350cab9f7aa821d74db4cfc1de1ca248207848daaba","src/tnfr/physics/relational_sine_formation.py":"bac9ec33626a7e9c83f72a5ea42f82ab5222743a8c7c505a3ef4d114847d7d48","src/tnfr/physics/relational_sine_mediation.py":"ff3ba1ea93d8b6875aa0da868a1374da029463834e2670f2b5f338af25d6adb1","src/tnfr/physics/relational_sine_observation.py":"f96e0778873d6cf7af9bac4a9b1289c6b950d2e7d7d2beacfcdd52b3df01988b","src/tnfr/physics/relational_sine_pattern.py":"7c787737045f8261877afa2d4b33b8d2e51e630fe4bbeda0de597a490cf7dce4","src/tnfr/physics/relational_sine_recovery.py":"6607284a423f79fe47ad93b700afbe3897935cd9f89d357619d25a1465b63810","src/tnfr/physics/relational_sine_reduction.py":"a01e3482891b4aa52246e3489a01651773b1663e6352381ded468db2b9e6ae62","src/tnfr/physics/relational_sine_regional.py":"de37c6ce5da7b4cef8d680fb28b983afd56751eb66d6a9b7b8b4573ee0757575","src/tnfr/physics/relational_sine_resonance.py":"63a76fa4bb2e6dcf0a137e59131b7a363a2bcf9d81b4b034fee6edb531756690","src/tnfr/physics/relational_sine_sampling.py":"96c6f4a371bf9fe551f62338548e1bcb15561f90f60349175dd9555a1e78f866","src/tnfr/physics/relational_sine_scale.py":"106eff1080dfff3f34c9f948e7af52f8c9c557e1528ce16e13315db3efca8a1a","src/tnfr/physics/relational_sine_symmetry.py":"b75625cbce980e8ddbb8e1fa3b4238ae13221ac6dfe8efd126ed7951a063813a","src/tnfr/physics/relational_transit.py":"fa401436138c9b72674d20267aee65c62992bd38c1e98428bfa25f2caaeec13e","src/tnfr/physics/remesh_history_stability.py":"c08580884b56850c267acad9a996c8edc3210cabd0725d7b84e030a326d617ad","src/tnfr/physics/remesh_schedule_policy_stability.py":"a35a2ee6636f00019be27527d2b4b520e8b452d85e18404d88e04a92d82014f3","src/tnfr/physics/remesh_schedule_relative_defect_stability.py":"19871ca4ad6319785954e08e73190b25b6cd74663c574730428f528642fe32d1","src/tnfr/physics/remesh_schedule_stability.py":"a364e98fc3dceb0c06b76bd5eb7dc8180a85751ad5d00fb4f9c6450f8142f95b","src/tnfr/physics/resonance_realization.py":"06ff79fd5bb9891aadfd34f56b8939dffabcd1616762c1b5bca1767cfced4b73","src/tnfr/physics/reversible_eigenmode_reference.py":"b2eb890bf8e3c49ec1bd7e7549e6fcde1bf7811ff5c9afc252af3c5e214776f2","src/tnfr/physics/runtime_eigenmode_reference.py":"4ffc3a58f49a5b059ed9774bfa8b39af019ed17b178785754403d82082640c2b","src/tnfr/physics/runtime_flow_stability.py":"42e3d615b65f5464a387ebbd23c60497b4cb329ee497e432630bad1b6e05e0ff","src/tnfr/physics/runtime_p2_reception_remesh_policy.py":"bf6d377baa8bec95889405fe0b42a6119084d86a9ef59716b6aa433b32ec3a97","src/tnfr/physics/runtime_p2_reception_remesh_sequence.py":"ac2114bfec757b208f04ffbd4f8f44202b1382b7aabc231709832c25abfb868d","src/tnfr/physics/runtime_p2_reception_stage.py":"57ae0d55a83b254206875e26736f33ca25b27992e19c219cb29b23b2e10804c2","src/tnfr/physics/runtime_remesh_history_stability.py":"b4f9bf3e48e3b478feeb978b7b9dd0dde8c4e407865dbd8405df2548b29668c7","src/tnfr/physics/runtime_remesh_schedule_block_margin.py":"52c53c15d1a34df991b31e0129df5b2bb213a973064f9f863ad4e3f3fe64bf32","src/tnfr/physics/runtime_remesh_schedule_relative_defect.py":"05d022d31aa4ed8aa1709dd448488ab6c19e9c589c42be32f4d6a24d5c3d4b24","src/tnfr/physics/runtime_remesh_schedule_stability.py":"3caf2b2a94a13b4258da7901ec961e68ffeb6598560897c20770ef05f56bcb4c","src/tnfr/physics/selector_symmetry.py":"50ba45af2ccd47b8ed64336b7b66c6522c14e33bf63976d323b274fe29f8cb12","src/tnfr/physics/signatures.py":"e2284db53b268f3d2f2eabe3677c524e1fd4cbf12f7f3c9ed3acf747876e0fac","src/tnfr/physics/source_relative_form.py":"4cdb8c86750e6f6e45a19460679f399d336f936770d5f53481e200fdf4c601de","src/tnfr/physics/spectral_certificates.py":"56f86e7872dcc7994de296003ae119b46ffa34ca887ff692bc05219ceb69f175","src/tnfr/physics/spectral_conservation.py":"94532e9856ac323a14ec10617e898eff12ce3072933789ab2cc190671607eccc","src/tnfr/physics/spectral_metrics.py":"c8a0eca977198719f090226cddf028764b8ac9e60db4ffc5a603d9d9e9c3fdb0","src/tnfr/physics/spectral_projectors.py":"902abf72d1782c3e39494776b47d08459ed9d3fa4e3d975275ef74c471e4e90e","src/tnfr/physics/structural_diffusion.py":"6d4ac3fed688869e36246a7afd5e5f3bf41485e7faaa5e76d006400285b28b20","src/tnfr/physics/structural_morphism.py":"85e2a838c37100a720f0a15615f157287e2624d9b8f99ae21cbfb31d2bfbc45f","src/tnfr/physics/structural_state_distance.py":"a82570a2aedcfe9ffae79913385752bf688ea81591f96d4490448c4dc2a322ff","src/tnfr/physics/support_transport.py":"2e8aa6d0237ffa5891d5acab4694c3ef3f31b1aedc63125fa233f1b9c7072e42","src/tnfr/physics/symmetry_sectors.py":"6b80e049aa55331ef82445c7a213319b498c690f7a700b565c255434025a7893","src/tnfr/physics/symplectic_substrate.py":"7628bb71757ffccd99d340d21661da73077f64e0ccb02e4f00e2f1cd25dcf4e4","src/tnfr/physics/telemetry.py":"277d4ba95b8dbb0acd3346e6f230c3b73a3749ffccab57b4ba817da735e7d8c6","src/tnfr/physics/temporal_identifiability.py":"bba8d4180709628fcc3667eb849429c86db136bd176a50193c17fbf29c2fa29b","src/tnfr/physics/topology_transitions.py":"10ab80e656e55da9ff32d3c4fa4b151bf367335e8c954f7b3a59af88f453c9b9","src/tnfr/physics/transient_u2.py":"4955569f0df90e2ee5ec36a85e9c99d5f8f9ec254dd383c085886a026289e92f","src/tnfr/physics/unified.py":"53415cd8ddec7c14c74bff2c88f6727c46a12b2bc5e7835e5b6e081cf12addeb","src/tnfr/physics/variational.py":"5328ff7ba7b519e3aec291e56b9d2f130d3d301ba9c0967e1b0f6e9488ba7534","src/tnfr/physics/vectorized_ops.py":"63186cb44d652da06653a3b802f6b0328230d388849abf4e576ac9f98d1ae01e","src/tnfr/physics/winding_certificates.py":"0374fe2660493dc6e02d660f79a4f7fff3988cf729d96db9f7969b2b961ab22a","src/tnfr/physics/word_equivariance.py":"c84a8141a0038187e1b5a7fab82baf62ca9c0d0d86519818857cfdaad97a8440","src/tnfr/primality/__init__.py":"ae7303b354f90c232d1dcfe99cbb7949ca948fa9c35f9cbfbdefc4bac4aaf6d8","src/tnfr/recipes/__init__.py":"aa8305fe0ceb879af89e462799c0bb7a0d0ce4738ffb25f38d108926531d1d20","src/tnfr/recipes/cookbook.py":"6b151017b0cd94b3de04fb74f19be8fb74d76bdf5cdf75499115477e5a111b77","src/tnfr/research/__init__.py":"69716651c3a282500df3d7a2686e6e1e02aeeecbf16e9a1d6b3af9be72e5016a","src/tnfr/research/certificates.py":"e493f7a8ee624c826dea37a90762cea16f71bb4449e356202e9f4801736fd3ec","src/tnfr/research/circularity.py":"73e09df30def315cae82f899997a20050a820f5b5a45b3efdd75cd7db9a424ea","src/tnfr/research/claims.py":"40aed80d5e22fb6be5eaf4e0fff6ce6a60f1af593b273cc3efa8416e7eb1a292","src/tnfr/research/core_manifests.py":"cea6a64aeec6fa0fd449dfb35d8633ed849b24cd02a5f70142fecbb09ce20ffd","src/tnfr/research/evidence_sidecar.py":"37699d9845f63fedb97e7ce2da46026fafab517a53953e63662b72fe0b3592a4","src/tnfr/research/history_affine.py":"3b36ac6d7bf30fa120de8cdf12d9feee4e8a9b0b0f87430efc7172ff9189ed4f","src/tnfr/research/manifests.py":"6a778271843775aa4e27734701166384133a157c0f62a5d8f95997da160e9092","src/tnfr/research/phase_form_response.py":"f23272ea6e7d0fef8cddf71f2d01bec0242aeda5856f8c507f959ec1fd281b1f","src/tnfr/research/recorded_support.py":"51bdeae44504c2c16d6b77cb8f639e44b2f401468330c499d24875440f81a8a8","src/tnfr/research/relational_acquisition.py":"28438d5aad09966010373dfc0e36a968fc82d9389e46e84e7e525ecd29752343","src/tnfr/research/relational_capacity_discriminator.py":"6a1e90fd2eb2af6ba197f1906bdc33581a2c407c9d77514a85c1dd43d0e2c6c4","src/tnfr/research/relational_formation_robustness.py":"8ba42c09d405aa66baf1611fd2d23a56f5e8d00969b40643e53165a794338f7c","src/tnfr/research/relational_receiver_barrier.py":"49f7d59c34e1125bf8eb9b67feedffffbaa135608f39b609573de16c21be4c39","src/tnfr/research/relational_seeded_response.py":"6f1d672914e4d1b11c7c51823c057c2487122298e4e5b4b73fac397d1e7e0e5d","src/tnfr/research/relational_sine_prior_forecast.py":"c2e02facd5783861e1192287602b4ffe9c544f48bd7e5d142dd56741c07ffb52","src/tnfr/research/relational_sine_prior_source.py":"650dcd8384c078c1ea68c49d031634a7325c1fc970342f8d6b3acae98db784a9","src/tnfr/riemann/__init__.py":"fec7a30a2c51a4efa3781b4a64a7ef6eda1771cca28c35c78d609b4f62b4ecc8","src/tnfr/riemann/admissible_family_sweep.py":"55295663f529d3066a97bf0ee65fbf07c5eecdd34992fb2da9a14b264dff67b8","src/tnfr/riemann/admissible_rescaling.py":"bbb77107253d427f0b2ff684b1675e06d2a564f689e72b434f39557e2e6844da","src/tnfr/riemann/alpha_sweep.py":"228d0ba35adc082e7ccedaf9feef4f3d9b2fe5b0356cf7e4c9afd56972ab3756","src/tnfr/riemann/analytic_continuation.py":"30c491da97dbed63cba16b89e7cf583c25a751239bed849e5af7581e7cee505a","src/tnfr/riemann/analytic_continuation_dirichlet.py":"d1f08e3875c468ac895cbaf3cd99d4ba3c92cd8c72fef1054da973572a945ec9","src/tnfr/riemann/coercivity_uniform.py":"52a073c08a1cb03f276dc2be6eda6fc4b4ff06e8007a21d093db239159509a90","src/tnfr/riemann/dirichlet_l.py":"19aae166a6d920bcb7cc424a90129ce5d6d5c850f1e64262ba78e93337922b28","src/tnfr/riemann/epi_type_signature.py":"981874250bab45ccb6f24deb3f22899217381cc0175534127f20537fc412f64c","src/tnfr/riemann/hilbert_polya.py":"eb77c48ffb444445abd2295f13be004c79829857320f58292ee9856186a3cb86","src/tnfr/riemann/li_keiper.py":"a7bcc19f2d245edcee9e4029ff648ccfaf138d61fe4086ea34dfffe4f56af831","src/tnfr/riemann/lyapunov_spectral_positivity.py":"c0046c9f096853879cca9a999ca5582f53789928a0b3bc7bbf1dbb189b06de47","src/tnfr/riemann/nodal_pulse.py":"fe051de728ae3b3db2c754d915c1fb9736dbb0d3e7f3d0fc4f9e6e2b670f0b90","src/tnfr/riemann/nodeaware_gauge_sweep.py":"48e0917df4d770443b4e05de55e13020d275ff0d7cad7d3e706e4c8393801821","src/tnfr/riemann/operator.py":"8324d371fefc08e9e594945ca8312f58d25a4397b209bd2b61905466a76f8324","src/tnfr/riemann/operator_catalog_discipline_signature.py":"c5a349abfd28942197dbcad3fbc5bef37ba03ef95b851621d6686267349cf06f","src/tnfr/riemann/oscillatory_correction.py":"b381e4ff15ee3da41535ad5b84864fd6bbeeab9ef03f98f68ca45de3846c968a","src/tnfr/riemann/paley_gap_coercivity.py":"058d0c336843fb0ede1c5adccbc31d9f2e7e6e279a931b59f92a97cb0a5c1996","src/tnfr/riemann/prime_ladder_hamiltonian.py":"4cdf7ccc895bff49f88be460975aea06702af61934c3e808f68d03d452f6bb4d","src/tnfr/riemann/pulse_coherence.py":"3048a78a5b35895c1bd3c35d9d9c8b28e800c869ee64d78196a1b5be6c4cf44d","src/tnfr/riemann/remesh_infinity_residue_split.py":"f2f728253111214e4899f84ec05b6b90cc3f1cd8c22ebba984147eebe3e6fde9","src/tnfr/riemann/remesh_window_type_signature.py":"0d9e0226392977f7a5e0bd2f508eaa7c1ac678534fd40a64525715c62068c80d","src/tnfr/riemann/spectral_emergence.py":"b33f0b2454b839a3ec49140f90c3d2509b1f86f5abbb0f6da19908b0e9e0bcc1","src/tnfr/riemann/structural_zero_density.py":"115e9ef0c67b2e770143f340e9c0032e7cb9464708208dc4010c2d05ff5f4982","src/tnfr/riemann/telemetry.py":"1979dbe12e35d0ef55312e3f9edc06f80d41eae2ef171949453b3cc5a6bd02c0","src/tnfr/riemann/twisted_admissible_family_sweep.py":"1f1ba36bf3a5bc390ce011de45c7ef7aa20b1cf33b92db2a7e77802377b82bf8","src/tnfr/riemann/twisted_admissible_rescaling.py":"8340b6444f474dd15af053313ad60dc8135fcb9223427adebc41e0972946581e","src/tnfr/riemann/twisted_alpha_sweep.py":"6489672f558c482c41beecee2022bdc66170625a6ce0a3b0ad637fa5c06cd65f","src/tnfr/riemann/twisted_coercivity_uniform.py":"a1c34397a46e09103884ab2521a0d87204fc264fbca518e595bbc0c6f6b14e8c","src/tnfr/riemann/twisted_hermite_family.py":"92dcc7c09dd35c4db6145f8e24c31cbc180d37e19ca685fd4b3626d8483c0613","src/tnfr/riemann/twisted_hilbert_polya.py":"2d53d9fb471cd612c8d3f90cf5b288898c4721cf3b0dfd77f28191942aa1a87f","src/tnfr/riemann/twisted_li_keiper.py":"4a901b353fa072f55782180d1d54d344e6b23c1b94f62b490f0faeb52017e100","src/tnfr/riemann/twisted_lyapunov_spectral_positivity.py":"d36331dc39f27e858328aaa2c20121b24306d1ac2f07277ff3bb01799c91cb9e","src/tnfr/riemann/twisted_nodeaware_gauge_sweep.py":"3295bdb14f1cb605e22e6a204ff0e5c65014f5690ba8cee058fcf7484c589773","src/tnfr/riemann/twisted_oscillatory_correction.py":"3324ad9197fb119a2990414b4f89a4b45110870efe77b76e6059a867bef076ed","src/tnfr/riemann/twisted_paley_gap_coercivity.py":"d2b4d41439fe30331304972bd0d2c3a47f91ee79c66ab6cce7217add8bc9e35a","src/tnfr/riemann/twisted_prime_ladder_hamiltonian.py":"e7f3e293bb0c125687edd01042b79c0d78ec636322325f631e3dafbd9df215a8","src/tnfr/riemann/twisted_spectral_emergence.py":"59a19958b919f7edf960dc510d9e49b048333ac8ebb3a024764cd730ec88933b","src/tnfr/riemann/twisted_structural_zero_density.py":"5b407b8f72c4c306a0d63abd182ed4a989e1d18002adcdfb4c420cf26007d70a","src/tnfr/riemann/twisted_weil_explicit_formula.py":"cae3f557c20bf74a20470b098fcb6bff0b9ae64f5a6a44e4feacde4a55ea9905","src/tnfr/riemann/twisted_weil_positivity.py":"87239a2391879c0028234ca654c3ed61e51acedd6513f1df2c4ab2d17e0410ca","src/tnfr/riemann/von_mangoldt.py":"c93cc9be0a6b6471848075792f8ab170bde4dd76453a4f94655505cbee0fa273","src/tnfr/riemann/weil_explicit_formula.py":"79b96d5e30f252ce4774a3c18986758a63879b9663b4cbcdf496be8c11145a2a","src/tnfr/riemann/weil_positivity.py":"6afe6b90db31b06cadbae2fdabc1480b67ecc9970d475b0b788593ea3f89f29e","src/tnfr/rng.py":"f903ce8a348ec112f1acc1f052e622fde1232a7ae926e0a177b4da46b5405842","src/tnfr/schemas/__init__.py":"01169c30731c439086cd847f4a06e4f85dd26aa02bcb22ecee75be7f62a4a32a","src/tnfr/sdk/__init__.py":"4a9df1b24bf6d0a9622fef2fcfffb11ebdd625c1f506cf16e9d36912caabfe19","src/tnfr/sdk/_defaults.py":"f43e93165438cb101d99aebe4381992313cd1e0cc2ee030c3d9e4ce748fde23b","src/tnfr/sdk/_state.py":"fe58b6b6ffbbb9761952cec1423ccf57af748318cf45f3edf54fb54822f0d6c5","src/tnfr/sdk/_topology.py":"44347caa35cfb28de1f04eec2dca6fb72cdd67a2ca2f35d586149d641fc98ade","src/tnfr/sdk/adaptive_system.py":"dab9ddf12a04c32b977dc3e1ba806279f980ce266575d74f19f7e510c55b864c","src/tnfr/sdk/builders.py":"7587ba4f23654fdb7e0d666c8a2ebd5e5237fcb8e584e6d802b209519d5cde8c","src/tnfr/sdk/fluent.py":"97966b76841d3641ffa7583e4053dc4473d2b6f8256f814eaae8de3141237cf6","src/tnfr/sdk/relational_reports.py":"fa1c4b29cc7316e21ecce91fea4ffed0ca6c36cdd529e31cf8e9b89827e5733c","src/tnfr/sdk/self_opt.py":"6f4e4b3942d53e367678e41e6a5e09eb7e90944e92d866ca649e2aab2c4360e2","src/tnfr/sdk/simple.py":"d29192465c81a162a366e81ad7cd53fe7a075d8f17f601057069ec14c3be3b99","src/tnfr/sdk/study.py":"9aa960f235ddacf58291ca102aec5c3fa422a2835b384f6951b8b73c11010bfb","src/tnfr/sdk/templates.py":"0f7c244a9bfcdd11b8bd6093f36270b428c930d99c027d3636c9a37569bbfdcf","src/tnfr/sdk/utils.py":"633e747bf8ea951b98965714b0bb05ce4a778042bc2db3474c27b40c571abed7","src/tnfr/secure_config.py":"dc70df868deae4b80bb0bb233c6efbf3eb8aea496792a53b37f010aeb06785ff","src/tnfr/security/__init__.py":"900951841fabf4b883177ad6202410c65860d24758e0fd4b331e18aaf96d1a7d","src/tnfr/security/crypto.py":"cd1881d91a5e30ffcb70d219280eab724b35c46f604d3ef468f070ea6dc1cb0a","src/tnfr/security/database.py":"75092c9a0ae68457a50d6a8a82622e4db2febf24b0e292f2833e547b80e02682","src/tnfr/security/subprocess.py":"e4b16a82659c903ce48eebeb215e40d06824a7e62ccdcc543ea445b30f0d7a2c","src/tnfr/security/validation.py":"4191618c487237fd22e3665456d27caf458159b805872f3e605a6e26738ad0a6","src/tnfr/selector.py":"73cc46d6c3f8befba3433d780bc1820c1700baa0fb7df984e1ea185b5a2c40d2","src/tnfr/sense.py":"ff6f11fd5108073dcb276572cb69e100e74938616e7f8fbcd10f307fbd1a72de","src/tnfr/sequencing/__init__.py":"1d809e41c7e7dba543e5afc1d14413fabc54a6c9ca0d9b106c6241b4200133fe","src/tnfr/sequencing/patterns.py":"579d184a746e93ac99690883623c805f1898bca87c32b6a40f8fb4b958198082","src/tnfr/services/__init__.py":"a17ace6f1fabb53218ab291f9e6c5a8d4e6e858a7b3a526f11c0ce62df423e9d","src/tnfr/services/orchestrator.py":"c323258bef8fd51eb084ee9fee665350ab21ea2257b617c0bf19a54f0f934e2e","src/tnfr/sparse/__init__.py":"c9424a2e8e5c029e994c20adf752aea18f026c037b29e2fb0f54d7bc8f7891bb","src/tnfr/sparse/representations.py":"946a6c0a0302fa16affda52a3f5e0bada1af39a2b4632bc563951e2929078567","src/tnfr/structural.py":"ad63324740f7c10a26c2a56a988ec27f4a6102423cad1380835c10745b405572","src/tnfr/telemetry/__init__.py":"a82d838244c5a748374b540aa66605ac8e490c14fa79bf90cb8b868d02e4417e","src/tnfr/telemetry/cache_metrics.py":"06b5b1a075f2c920d0e9e71075cc28df269da31ce31d6a10055364ff5b55720a","src/tnfr/telemetry/constants.py":"39be4d7e106002d639bf86c3b6be5d83dfaef40c93a8765787ffa3c7d0e1c707","src/tnfr/telemetry/nu_f.py":"a6e05dd6781c0cdd3ceb4a8712effdb8b1d0ec88435a8d6c0bb808d3dad6b47e","src/tnfr/telemetry/unified_telemetry_system.py":"3e983144858ffd32edb273e9678f744a3549828d476ce555bd0c0d4f86d2ad5c","src/tnfr/telemetry/verbosity.py":"0627f52f2a60f2a2441abb9a840232b94cf0e516f89b2c32582b4e47e3cedf46","src/tnfr/tokens.py":"4abeec8009c9833970020abaef3dc89f1cca978f564843f43b5675644a26b5c5","src/tnfr/tools/__init__.py":"b922586186952cd85830d6edd5c7142d67c76bfe72e253518c7b6950b54cdf00","src/tnfr/tools/domain_templates.py":"52d08b89aecc411dd1cbbc7ee08f10442182964e491a20e03ea99dca9441701f","src/tnfr/tools/sequence_generator.py":"52cd118cdfbe6b0c35e1953bf403be0e356121981cf9c1693dc065c5910cf232","src/tnfr/tools/tnfr_is_prime_cli.py":"ed33b59a83adb87a448f75c02928f138d7c701ee93c9bcd0db3cda1d839de72c","src/tnfr/tools/tnfr_is_prime_cli_optimized.py":"090e49dc99abd5e1092c28451d6fbb690fad750532fb41d858853f05d2eeed3e","src/tnfr/topology/__init__.py":"6b2c8e0a71e45df172f9f77d849f6f9ddf5caee24e79ec0bcb1db2e84b71dae3","src/tnfr/topology/asymmetry.py":"2312bda1695f88be653e56494295fe8266ba3408242b2100b88f56d17b85174e","src/tnfr/trace.py":"07e6b53c5db599f9010940c9b3060ab03d5e90a1a7a79a308d56f15f352ed3ba","src/tnfr/types.py":"3929876daa8d3952e3e1b80ebbb437588461d13e55c2c9e5093ae68eab82e1ee","src/tnfr/units.py":"fbc065da5ae591cc2032ef54554da37e72040584b6f0a465c3fc8f3311126b51","src/tnfr/utils/__init__.py":"4bf4a4664e2661928c8bf6224a5d7f6ccd38c5e701719acafde5f6b69aee49d4","src/tnfr/utils/_structural_signature.py":"9559c4a98b85faecdb3c2aada29299433f468c5b15299150647c4aa01d5da4df","src/tnfr/utils/cache.py":"dc45e00c777b5e13726103df8f97ede2de01dc507e33d0c268041f204b348f3d","src/tnfr/utils/cache_layers.py":"fd1879c2412e8b620fb9077786ad15685a9fc9f56e4f7504bd98980ce73981ae","src/tnfr/utils/callbacks.py":"61320c4a4b50ee0e4be1524ee94f30d3fb905a94582b53fb7d81cb72b97466e7","src/tnfr/utils/chunks.py":"6fe39c67e22230f9d9a65e513b356f0149e476dda2a6505511c4b5491eb8d6eb","src/tnfr/utils/data.py":"cd1da0675dc915a06b117b22e1bfd56bdcaf7a69aab3aba3d3df97eb1d4c6ba3","src/tnfr/utils/fast_diameter.py":"14cb11a521c357ff252964332899538644b85235b78fdf550164e20011eb03ef","src/tnfr/utils/graph.py":"c879155866bea82279e08cac35b1304180108f4c5d19869b80eb07228143ee8d","src/tnfr/utils/init.py":"83bd7b06c816f4b07c7b8a0d457b087ab15049c781681b0d9d9bec4cb3dd2d3e","src/tnfr/utils/io.py":"cab0a59521cdb0576261213e229ae211a50ba20b6da92b0b8de3e8892547bee7","src/tnfr/utils/numeric.py":"a5b50acffc2869b989d700894126a22511f875a3b347f1cfcdc5bc2d0a959394","src/tnfr/utils/topology.py":"e42b528643d3ecf5cbb0e0678e1b5c5e8b8b303df6833b031df521a68e9c396c","src/tnfr/utils/unified_cache.py":"877ce5705cd5c650df9ada7036c6c8e8c17fde40ffd3e195e637d4cc263cae6a","src/tnfr/validation/__init__.py":"fba144cd3044772e585ef923abd2fc19bd6f41f9d5d4a35b602a2678a3acec20","src/tnfr/validation/aggregator.py":"72e4fe76738a6db945ad79b42318ba615daed0fafd84b2cfd77e2d81af38af23","src/tnfr/validation/base.py":"9c298400424cf8e8afc819d3e21baace4c7f57bf527c62e4c098ee68f36e4a39","src/tnfr/validation/compatibility.py":"71942925dc54d1f2efcbf62d4f0f741ff67c204a9d48160c5b1a99a39cfdb555","src/tnfr/validation/config.py":"744060aed3e23b4b715eddd2d8cc2e708f99d05f35b036eef6fe14cc7e74ae97","src/tnfr/validation/graph.py":"54a828797a406645273b0da581f8c7d821f4be7e015ba33793d9893034e5dff6","src/tnfr/validation/health.py":"7d0096b3bf5288fc1f4960a0d4b97f6e99b533d2bd6c071c217a150c380871be","src/tnfr/validation/input_validation.py":"81b199e53a007fd614cae733cafcdae7ae5eea86d26381de56c1e11348ecb755","src/tnfr/validation/interface_baselines.py":"35d58c1da9c62623f6f45ecc34148ab156d858ae24f05315bbef814b4da466f8","src/tnfr/validation/invariants.py":"426a745d7da8122eb8ece5c1a52586849f2993a59b62048b6b14bf1e480f0d63","src/tnfr/validation/multichannel_interface.py":"870c747a1af1b633d23a7199824dbf94a80ee8af9780c9c3a413df0693dd6e69","src/tnfr/validation/nodal_prediction.py":"2c75faaed04ae88e45f201be1448c3cdd74fceb611682438f7d08ffb480a489a","src/tnfr/validation/p2_transport.py":"fc508f62ac363a01704a7dd0d536dcf0891bf80fe519b8791dad2a2ddce8bd25","src/tnfr/validation/phase_gate.py":"b5354c876739846034b67e121600f2e658e00112363c78cb6fc544c6e6bad6b2","src/tnfr/validation/rules.py":"fefc51c79831097bfde038aa376f346d2e6027be76c1ac3cd882fd390a8487ac","src/tnfr/validation/runtime.py":"22f9665c7a2032eaec7689613725a81eb5ba7c8dc4ebadeed467b44345e4e563","src/tnfr/validation/sequence_validator.py":"416a4a0d1eceda871ab383d8726328dc15246eeeb820f97acacb4d2a372ec48f","src/tnfr/validation/signal_confrontation.py":"24a5a824e9ebb22380bbd69a70809bf883ab07cbf35b954400bd47376b7897f8","src/tnfr/validation/soft_filters.py":"97c00c1575e28052314c8c7378e87790f466639330992c807e6b9a9f7eb0c168","src/tnfr/validation/spectral.py":"47a491e46d89baa4bef32f1248c91ed5ad3d1f95edf0a202ef021e458c9723cd","src/tnfr/validation/structural_interface.py":"2a11401554a452ec915dea4ea547d48dfdd3fb30748a65b5d034a892d7f705bf","src/tnfr/validation/temporal_interface.py":"69a439be5cd8b85f5788da165d39acffc4a06ae2d219c16a37ce403e8232fd62","src/tnfr/validation/unified_validation_system.py":"7e2bd24be1900422d60c5ef26e6d424d7a8eec360347b633a0365414807f21ee","src/tnfr/validation/validator.py":"d43ba5f700fe8bec2c55b3bf64af9c412227e8a38ce770f3a4e9845dc64e6f3e","src/tnfr/validation/window.py":"ad959025b6bd8a418b720969e170e256ff7761a8251b5e179576d389f819afc8","src/tnfr/visualization/__init__.py":"d54a2c7db3d9b8d3d16d75c33c377e8d9c8a595e59d4f6dcfc260808ef643aeb","src/tnfr/visualization/cascade_viz.py":"d6111095c1012d2bfee3ef935fc5b9245e98f58a2c0d8c05ca6caec50bff1b3e","src/tnfr/visualization/hierarchy.py":"9f8f46bce8b5b335d1cb628b0976fa983d58f7a2dbd28c498e7660bc368583bb","src/tnfr/visualization/sequence_plotter.py":"b6e5d97c082d3a11ec20cd4bef746374a7177856a63d3bd065413d89196f922b"},"runtime":{"implementation":"CPython","interval_method":"rational_outward_dyadic128_machin_trigonometry_v1","platform":"Windows-11-10.0.26300-SP0","precision":"mathematical pi and outward exact rational dyadic128 intervals","python":"3.12.10","randomness":"none; no RNG or seed"},"schema":"tnfr.conservative-regional-channel-analysis.v1","scope":"retrospective_analysis_of_supplied_Taylor_enclosures_no_solver_replay_or_authentication","source_archive_sha256":"6ea1a4daf22f87510a12712710c8d8587a24752bc10b1a97ec03e20eaeb3a256","source_protocol_sha256":"57498a5f1b70c957f00f3811d199e887c6d769d41d1be915279870f4c7a17de8","source_response_sha256":"8b4cf1bd20d186c3280ce28ab31092104a4a4e718a90d2b7849b2fcc1e0657a1"}