"""Detached stationary geometry and one actual continued-contact capture. ORGANIZED_CONTACT_MAINTENANCE.md owns the fixed complete law and source admission. Geometry, local stability and inclusion of an acquired source are separate results. No trajectory, origin scan or frozen producer is executed. """ from __future__ import annotations from dataclasses import dataclass, replace from fractions import Fraction as Q from ..mathematics._rational_interval import I, cos, pi_interval from ._organized_external_interaction import _Q as _RECOVERED_RADIUS from ._organized_external_interaction import ( _SOURCE_FAILURE_NAMES, _assess_organized_external_interaction, _derive_organized_external_interaction, _OrganizedExternalInteraction, _OrganizedExternalInteractionGeometry, ) _CAPTURE_THRESHOLD = Q(1, 100) @dataclass(frozen=True) class _ContactStationaryMode: """One spatial mode, retaining its two complete form/phase tangent rows.""" internal_mode: int outer_mode: str laplacian_bounds: I aligned_hessian_bounds: I antipodal_hessian_bounds: I trace_bounds: I aligned_determinant_bounds: I antipodal_determinant_bounds: I @dataclass(frozen=True) class _OrganizedContactMaintenanceGeometry: interaction_geometry: _OrganizedExternalInteractionGeometry antipodal_donor_phase_origin_bounds: I modes: tuple[_ContactStationaryMode, ...] aligned_relative_stable_modes: int antipodal_relative_stable_modes: int antipodal_relative_unstable_modes: int conserved_mean_modes: int near_carrier_instability_coefficient_bounds: I internal_phase_defect_threshold_bounds: I aligned_stability_certified: bool antipodal_instability_certified: bool near_carrier_obstruction_certified: bool scope: tuple[str, ...] = ( "full_fifty_four_spatial_modes_and_both_complete_tangent_rows", "aligned_outer_origins_and_antipodal_donor_are_separate_stationary_controls", "two_neutral_modes_are_the_conserved_form_and_phase_lift_means", "negative_hessian_directions_use_joint_form_phase_instability", "triangle_period_obstruction_only_excludes_an_all_edge_acute_chart", "near_carrier_defect_bound_is_a_conditional_equilibrium_instability_theorem", "stationary_geometry_supplies_no_acquired_source_entry_or_identity_loss", ) def _derive_organized_contact_maintenance(): """Rebuild fixed full-state modes and a conditional defect threshold.""" original = _derive_organized_external_interaction() geometry = replace( original, external_phase_origin_bounds=I(0), scope=tuple( ( "external_zero_origin_for_the_aligned_stationary_target" if entry == "external_pi_over_two_origin_supplied_from_primitive_preparation" else entry ) for entry in original.scope ), ) pi, gamma = pi_interval(), geometry.gamma_bounds gamma_squared = gamma**2 inner_cosine = cos(geometry.alpha_bounds) outer_cosines = tuple(cos(2 * pi * k / 5) for k in range(1, 5)) outer_modes = (("common", I(0), I(0)), ("hub", I(6), I(-6))) + tuple( (f"ring{k}", 3 - 2 * cosine, 1 - 2 * cosine) for k, cosine in enumerate(outer_cosines, 1) ) modes = [] for k in range(9): internal = I(0) if k == 0 else 2 - 2 * cos(2 * pi * k / 9) for label, outer, antipodal in outer_modes: laplacian = internal + outer aligned_hessian = inner_cosine * internal + outer antipodal_hessian = inner_cosine * internal + antipodal modes.append( _ContactStationaryMode( internal_mode=k, outer_mode=label, laplacian_bounds=laplacian, aligned_hessian_bounds=aligned_hessian, antipodal_hessian_bounds=antipodal_hessian, trace_bounds=-laplacian / 4, aligned_determinant_bounds=gamma_squared * laplacian * aligned_hessian / 16, antipodal_determinant_bounds=gamma_squared * laplacian * antipodal_hessian / 16, ) ) relative = tuple( mode for mode in modes if (mode.internal_mode, mode.outer_mode) != (0, "common") ) aligned_stable = sum( 2 for mode in relative if mode.trace_bounds.hi < 0 < mode.aligned_determinant_bounds.lo ) antipodal_stable = sum( ( 1 if mode.antipodal_determinant_bounds.hi < 0 else ( 2 if mode.trace_bounds.hi < 0 < mode.antipodal_determinant_bounds.lo else 0 ) ) for mode in relative ) antipodal_unstable = sum( mode.antipodal_determinant_bounds.hi < 0 for mode in relative ) outer_cosine = outer_cosines[0] defect = Q(5, 4) - 5 * outer_cosine * (1 - outer_cosine) return _OrganizedContactMaintenanceGeometry( interaction_geometry=geometry, antipodal_donor_phase_origin_bounds=pi, modes=tuple(modes), aligned_relative_stable_modes=aligned_stable, antipodal_relative_stable_modes=antipodal_stable, antipodal_relative_unstable_modes=antipodal_unstable, conserved_mean_modes=2, near_carrier_instability_coefficient_bounds=defect, internal_phase_defect_threshold_bounds=9 * defect, aligned_stability_certified=aligned_stable == 106, antipodal_instability_certified=(antipodal_stable, antipodal_unstable) == (97, 9), near_carrier_obstruction_certified=defect.lo > 0, ) @dataclass(frozen=True) class _OrganizedContactMaintenance: form_error_bounds: tuple[Q, ...] phase_error_bounds: tuple[Q, ...] external_interaction: _OrganizedExternalInteraction geometry: _OrganizedContactMaintenanceGeometry control_host_form_upper_bound: Q control_host_phase_offset_upper_bound: Q control_joined_form_upper_bound: Q control_joined_phase_offset_upper_bound: Q control_form_excess_upper_bound: Q control_phase_excess_upper_bound: Q control_initial_excess_upper_bound: Q control_attachment_work_upper_bound: Q internal_boundary_excess_bounds: I control_capture_barrier_lower_bound: Q outer_one_initial_internal_phase_defect_upper_bound: Q outer_one_initial_defect_margin: Q outer_one_initial_defect_domain_certified: bool control_initial_cell_margins: tuple[tuple[str, Q], ...] sufficient_margins: tuple[tuple[str, Q], ...] source_certified: bool control_capture_certified: bool control_identity_retention_certified: bool control_convergence_certified: bool admitted: bool status: str unresolved_conditions: tuple[str, ...] relative_phase_origin: Q = Q(0) capture_threshold: Q = _CAPTURE_THRESHOLD relative_preparation_dimension: int = 96 protocol_revision: str = "4c4addf1" outer_one_maintenance_status: str = ( "unavailable_full_source_maintenance_not_assessed" ) other_origin_maintenance_status: str = "unavailable_source_inclusion_not_assessed" scope: tuple[str, ...] = ( "actual_outer_zero_source_after_the_complete_single_history_observation", "six_independent_original_sources_and_all_ninety_six_relative_directions", "separately_prepared_beta_zero_contact_without_source_reset_or_extra_waiting", "sharper_control_storage_retains_every_continuous_phase_drift_and_fine_error", "fresh_c9_boundary_owner_and_new_cross_edge_barrier", "all_future_six_inner_one_and_nine_outer_zero_windings_if_capture_is_admitted", "asymptotic_convergence_on_the_conserved_mean_leaf_without_settling_deadline", "no_all_future_positive_individual_inner_gap_claim", "attachment_work_separate_from_historical_preparation_and_observation_costs", "legacy_pi_over_two_comparison_verdict_is_not_a_capture_premise", "outer_one_near_carrier_obstruction_is_not_an_actual_source_loss_verdict", "initial_defect_domain_inclusion_does_not_prove_it_is_retained", "no_fundamental_physical_identification_or_autonomous_event_selection", "no_trajectory_frozen_producer_replay_or_registration_scan", ) def _assess_organized_contact_maintenance(*, form_error_bounds, phase_error_bounds): """Rebuild actual sources once, then admit the separately prepared control. The shared primitive-only owner admits all twelve original allowances and rebuilds acquisition, recovery and the complete observation word. Its old pi/2 comparison is preserved as evidence, not consumed as a premise here. """ source = _assess_organized_external_interaction( form_error_bounds=form_error_bounds, phase_error_bounds=phase_error_bounds ) geometry = _derive_organized_contact_maintenance() host, observation = source.host_acquisition, source.observation_protocol g = geometry.interaction_geometry.gamma_bounds.hi duration = observation.total_elapsed_scaled_time q = _RECOVERED_RADIUS # Phase-only observation commands cancel exactly after the complete word. # The real motion between those events remains in these global bounds. host_form = host.full_form_error_upper_bound + g * duration host_phase = host.full_phase_error_upper_bound + 2 * g * host_form * duration form, phase = max(host_form, q), max(host_phase, q) # Each of the 144 unit edges has coordinate difference at most 2*radius. # The phase potential's linear terms cancel at the actual target, while # its global second derivative is at most one on every edge. form_excess, phase_excess = 288 * form**2, 288 * phase**2 excess = form_excess + phase_excess work = Q(45, 2) * ((host_form + q) ** 2 + (host_phase + q) ** 2) internal_boundary = host.internal_boundary_excess_bounds barrier = min(internal_boundary.lo, Q(1)) pi, alpha = pi_interval(), geometry.interaction_geometry.alpha_bounds initial = ( ("initial_internal_positive_gap", alpha.lo - 2 * phase), ("initial_internal_acute_gap", pi.lo / 2 - alpha.hi - 2 * phase), ("initial_cross_acute_gap", pi.lo / 2 - 2 * phase), ) margins = initial + ( ("frozen_control_excess_threshold", _CAPTURE_THRESHOLD - excess), ("control_capture_boundary", barrier - excess), ) source_ok = source.source_certified one_phase = ( host.full_phase_error_upper_bound + source.carried_phase_drift_upper_bound ) one_defect = 90 * one_phase**2 + 18 * q**2 one_defect_margin = geometry.internal_phase_defect_threshold_bounds.lo - one_defect capture = ( source_ok and geometry.aligned_stability_certified and all(value > 0 for _, value in margins) ) unresolved = ( tuple( name for name, ok in zip(_SOURCE_FAILURE_NAMES, source.source_admission_flags) if not ok ) + ( () if geometry.aligned_stability_certified else ("aligned_target_not_certified",) ) + tuple(name for name, value in margins if value <= 0) ) return _OrganizedContactMaintenance( form_error_bounds=source.form_error_bounds, phase_error_bounds=source.phase_error_bounds, external_interaction=source, geometry=geometry, control_host_form_upper_bound=host_form, control_host_phase_offset_upper_bound=host_phase, control_joined_form_upper_bound=form, control_joined_phase_offset_upper_bound=phase, control_form_excess_upper_bound=form_excess, control_phase_excess_upper_bound=phase_excess, control_initial_excess_upper_bound=excess, control_attachment_work_upper_bound=work, internal_boundary_excess_bounds=internal_boundary, control_capture_barrier_lower_bound=barrier, outer_one_initial_internal_phase_defect_upper_bound=one_defect, outer_one_initial_defect_margin=one_defect_margin, outer_one_initial_defect_domain_certified=( source_ok and geometry.near_carrier_obstruction_certified and one_defect_margin >= 0 ), control_initial_cell_margins=initial, sufficient_margins=margins, source_certified=source_ok, control_capture_certified=capture, control_identity_retention_certified=capture, control_convergence_certified=capture, admitted=capture, status="certified_beta_zero_control_maintenance" if capture else "unavailable", unresolved_conditions=unresolved, )