Child OZ context and three-sample timing

1. Model and evidence boundary

This is a conditional event/observation admission for the connected child 2_sub_0 of parent 2, after the actual word VAL,THOL,UM,SHA. The joint-window result retains all 21 nodes, 53 weighted undirected edges and 42 form/phase coordinates. On the original structural clock, let

\[ t_*=3670017/524288,\qquad J=[3/128,13/512]. \]

The complete unforced law holds support, conductances and positive capacities fixed, with declared real phase lifts:

\[ S_i=\sum_{j\sim i}\sin(\theta_j-\theta_i),\quad p_i=\frac{S_i}{\pi d_i},\quad M_i=\frac{\nu_i}{\pi d_i},\qquad \dot x=MS,\quad\dot\theta=ML_Wx. \]

The child has only parent 2 as neighbor, capacity represented by 121.6 and conductance represented by 0.7862678209336036. Its own source glyph history is empty and its U2 debt is zero. The actual source form is below the strict OZ minimum; event-free continuation enters the admitted domain later. No parent history is borrowed. Sections 2-5 admit the event and observation analytically, without executing them. Sections 6-7 separately specify and retain one frozen numerical acquisition and OZ; no second birth is executed.

The fixed-cell reader re-admits the six joint-observation artifacts, their source associations and the complete retained SHA certificate once. It rebuilds only original cell 12 from its primitive tube and actual law. The earlier first-cell selection remains inherited evidence, not a repeated search. Frozen derivative jets retain their producer provenance; byte associations are not authentication.

2. Canonical OZ at the left endpoint

Select a child-target execute_network_operator_stage with Dissonance() at t_0=t_*+3/128. The shared ValidatedSequence admits the concrete OZ,THOL,SHA word with nonzero initial form. Its future THOL handler supplies U4a context for OZ. A planned prefix supplies no executed U4b history; SHA is one selected closure, not the only U1b closure role.

The actual strict OZ policy is resolved by resolve_oz_strict_policy, which is also consumed by runtime preconditions. Form minimum is represented 0.2, maximum absolute pressure 0.8, minimum capacity 0.1, and advisory minimum degree 1. The signed form minimum, inclusive scalar comparisons, empty-history overload check and warning-only degree policy remain intact.

Throughout the same retained cell,

\[ 0.2008<x_c<0.212,\quad 0.034<p_c<0.037,\quad 4<\dot x_c<5,\quad111<\ddot x_c<129. \]

A later acquisition may materialize form and fresh pressure with separate absolute errors at most 2^-24 each. Even after these allowances, the OZ scalar conditions and positive-pressure amplification branch hold. Achieving the form allowance does not by itself establish the pressure allowance: the latter needs its own full-state and pressure-computation association. All other consumed runtime coordinates must be finite and admitted, with the actual support and held capacities preserved.

Noise is disabled. For the actual represented gain

\[ f=5937139912176161/4503599627370496, \]

the raw binary64 pressure is q'=fl(f*q). With u=2^-53, the multiplication error is at most u*|f*q| in this positive normal domain. The admitted ranges also give q<q'<2q, so the subtraction q'-q is exact by Sterbenz. The local increment is positive. This is an instantaneous hybrid reset, not a finite-duration pressure flow.

Propagation remains enabled and uses the dispatcher's default phase_weighted mode. The actual runtime examines direct neighbors. Its phase weight lies in [0,1], and the final frequency factor is one. With D the upper bound on the local increment and W the actual edge weight, a conservative floating-point bound for the proposed parent increment is

\[ B=\bigl(DW(1+u)+\eta\bigr)(1+u)+\eta, \qquad\eta=2^{-1075}. \]

The absolute term also covers subnormal rounding if a very small phase weight occurs. Here B<0.01, below the unchanged propagation cutoff, represented 0.05. Thus no parent increment is committed in this admitted domain. The canonical stage still records a graph propagation event with an empty affected-node list; enabled propagation is not synonymous with a nonempty effect. Reducing the cutoff changes that conclusion.

Successful actual execution would append the child's own OZ, incur one U2 debt unit and advance its operator-step context. OZ does not advance the structural clock or create three temporal samples. Its detached preflight may compute acceleration telemetry, but the stage does not commit that as newly acquired history or a live bifurcation flag. The strict validator's successful probe writes precondition context, so the analytical consumer uses pure policy resolution rather than probing the retained graph.

3. Pressure refresh and continued motion

Let y=(x,theta,nu,U,W) be the continuous coordinates and held geometry. The pressure-refresh equivalence applies algebraically after re-admitting this actual weighted 21-node law:

\[ \pi_y J_{\rm OZ}=\pi_y,\qquad \Phi(y,p)=(y,p(y)),\qquad \Phi\circ J_{\rm OZ}=\Phi \]

on these continuous coordinates and refreshed pressure. The source storage

\[ H=\frac12\sum_{\{i,j\}}W_{ij}(x_j-x_i)^2 +\sum_{\{i,j\}}(1-\cos(\theta_j-\theta_i)) \]

does not consume stored pressure, so the OZ jump and pressure refresh have exactly zero storage work. The fixed smooth complete vector field is unchanged; uniqueness then gives the same continuous continuation. No old 20-node coefficient or changed-capacity certificate is transferred.

This equality concerns the specified continuous projection, not the complete runtime state. Glyph history, debt and telemetry differ. It requires an immediate full selected-law pressure refresh, before any evolution or controller that could consume the changed pressure/context. A stored-pressure hold, generic mixed-pressure callback or autonomous grammar-sensitive controller is a different model. Uniqueness compares the same exact initial y before and after OZ; it does not identify a finite-error acquired point with the original exact-flow point. A later numerical acquisition must keep its entire subsequent sample error independently bounded against that original solution.

The stage callback is opaque to the dispatcher. A later execution must use the declared constitutive writer and the existing pressure-only preservation guard, checking every retained coordinate, capacity, edge and clock. Graph transaction rollback does not guarantee rollback of external callback side effects. Even though propagation is inactive here, the refresh contract covers the full network rather than assuming a universally local footprint.

OZ can therefore provide grammatical context while its pressure effect is erased before this selected continuous law consumes it. This is useful compatibility information, not evidence of a lasting excitation, autonomous event selection or a newly discovered physical force.

4. Prospective samples and actual reader arithmetic

Take the first sample after the event and full refresh, at the same structural instant. Then acquire the child's own form at

\[ (t_0,t_1,t_2)=t_*+(3/128,25/1024,13/512) =\frac{(3682305,3682817,3683329)}{524288},\qquad h=2^{-10}. \]

All three times, h and 2h are exactly representable in binary64. The true three-point stencil is a positive average of the second derivative over this entire window, so it exceeds 111. For materialized sample errors |e_i|<=epsilon=2^-24, its additional error is bounded by

\[ \frac{|e_0|+2|e_1|+|e_2|}{h^2}\leq\frac14. \]

The shared sample budget retains a genuine global third-derivative bound from the complete source law. Its separate point-derivative truncation term is not added to this whole-window theorem. No timestamp jitter or unknown clock scale is admitted.

The reader-arithmetic owner follows the actual timestamped acceleration reader, not merely the symbolic second-difference formula. Form differences are exact by Sterbenz because the positive represented forms have ratio below two. Division by h is exact power-of-two scaling. The two represented secants lie within [4-2^-13,5+2^-13], so their subtraction is also exact by Sterbenz. The remaining multiplication by two and division by 2h are exact scalings. Every relevant nonzero intermediate remains finite and normal. Timestamp subtractions are exact because their exact result h is representable; representable timestamps alone would not be sufficient.

Consequently the conditional reader roundoff allowance is zero, and the runtime result, if supplied with these genuinely acquired, correctly associated samples, exceeds 443/4=110.75. This is above the unchanged THOL absolute-acceleration threshold, represented 0.1. The helper rejects invalid inputs and explicitly abstains for valid unsupported arithmetic domains; it does not fabricate samples or certify their producer.

5. Scope and implementation controls

The analytical consumer admits this event/timing composition from fresh primitive evidence. It leaves the retained source and all frozen artifacts unchanged. At that original SHA source, executed OZ and measured history remain missing; the future word cannot remove its child's U4b rejection. Section 7's separately acquired successor has its own executed context and observation provenance.

At later acquisition, the final timestamp must equal the live graph clock, the final sample must equal live child EPI, and all samples must descend from the same full-state evolution. Copying parent history, taking tube midpoints, reconstructing samples from the desired acceleration, or relabeling times does not satisfy these conditions. Operator recency counts actual operators; uninterrupted continuous evolution and sampling do not add glyphs.

The synthetic canonical-stage controls check the actual reset, empty and nonempty propagation footprints, grammar debt and guarded constitutive refresh. Independent manufactured polynomial histories test the reader and strict THOL gate without representing them as the child's response. The reader tests compare the runtime arithmetic to exact rational stencils, including signs, error corners and unsupported domains. The source controls reject altered primitive bounds and associations; the composition controls verify this actual source's conditional margins and present abstentions.

This result closes analytical compatibility of one child OZ/refresh/history schedule. It does not execute the selected word, admit a second birth in full, select an event autonomously, or establish recursive population growth. Hierarchy/metabolic limits, child identifiers, post-birth isolate completion, cross-birth U6, all-time maintenance and physical identification retain their own obligations. The execution plan alone specifies the next action.

6. Retained interior bounds and independent numerical acquisition

The middle observation time lies inside original cell 12, not on the retained endpoint grid. Let the original duration be H=1/512, the source-box Taylor order be q=12, and a_k its retained interval coefficients. Its retained remainder R_H bounds H^(q+1) times the normalized derivative throughout the admitted whole-time tube. For 0<=s<=H, the same exact trajectory therefore satisfies

\[ y(t_0+s)\in Y_0+\sum_{k=1}^{q}a_k s^k +(s/H)^{q+1}R_H. \]

At s=H/2, scale the remainder by 2^-13. The original Picard inclusion covers this shorter interval; the derivative and source-box coefficients retain their original producer provenance. An endpoint-error enclosure alone would not justify this scaling: cancellation at H need not hold inside the interval. The shared reconstruct_box_taylor_partial checks the original full-duration arithmetic before its partial evaluation, preserves the source at zero, agrees with the endpoint at H, and rejects extrapolation. It does not independently rederive stored jets or prove the upstream Picard/regularity premises.

The sample certificate re-admits the actual source and rebuilds all three full-state enclosures. For an independently acquired represented value v and an exact-flow enclosure [a,b], it uses max(|v-a|,|v-b|) as a sufficient error bound. It does not require the represented point to belong to a much narrower exact-flow interval. Every one of the 42 coordinates and 21 fresh pressure values is checked against the same original solution with allowance 2^-24. Pressure error against that solution is separate from the constitutive writer's 2^-46 evaluation-error budget at the represented point. Original principal branches are checked for both the true enclosure and the acquired state. Bounds and cached verdicts never supply acquired observations.

The acquisition adapter uses the shared complete-state RK4 kernel with refreshed full rows at all four stages. It integrates independently from the actual SHA point; it never initializes from a retained box midpoint. Source reconstruction preserves node/neighbor order and execution context. The live graph is protected while the numerical solver works on detached tuples; at each requested boundary the adapter installs both complete rows and the exact structural clock.

Before OZ, the full acquired state and pressure must pass association. The stage's raw reset is separately recorded, its continuous coordinates checked, and the full constitutive refresh guarded. Only a committed event is followed by the first child history sample. The shared flow-boundary recorder extends actual all-node histories, keeping the parent's older observations associated rather than leaving them apparently current as its form evolves. After three boundaries the child's final timestamp and EPI must equal live state. Read-only strict THOL and grammar probes do not execute their proposed event or complete the word.

The frozen protocol selects step 2^-14, segment counts (384,16,16), 416 total steps and 1664 field evaluations. Its 600-second cooperative execution budget excludes source re-admission. Raw state, four-stage rows, represented quadrature residuals, times and source archives are retained. A failure preserves the attempt and any acquired prefix; no retuning, retry, longer horizon or second birth is part of that protocol. The existing exact-flow certificate is reused, not regenerated. This is a new numerical acquisition, not an independent physical measurement or a new exact-flow source family.

7. Retained result: executed OZ and the child's own three samples

The protocol, source archive and freeze preceded one attempt. Its result is acquired: 416 RK4 steps, 1664 full-field evaluations and exactly one child-target OZ. No parameter, threshold, step size or horizon was adjusted after evaluation. The complete original SHA trajectory and all earlier artifacts remain unchanged.

The raw event amplifies the child's stored pressure from approximately 0.0345998575022 to 0.0456133342057. The graph records one propagation summary with no affected neighbors; no parent pressure increment is committed. Form, phase, capacities, support and structural time stay unchanged across the event, giving exact zero storage work. The guarded refresh restores the selected constitutive pressure before subsequent evolution.

The child's own retained samples, taken after that committed refresh, are:

Elapsed structural time	Acquired binary64 form	Certified form error, approximate
3/128	0.2019455475026296	2.805e-14
25/1024	0.2061135276419602	3.005e-14
13/512	0.21039599029387335	3.211e-14

The response retains the full 42-coordinate state and 21 pressures at each boundary, not only these displayed child values. Maximum state errors are below 3.22e-14; exact-flow pressure errors are below 7.46e-15, against the separately fixed allowances 2^-24. The constitutive writer's independent represented-point pressure errors are below 2.22e-17, within 2^-46. All original principal branches remain admitted for both the exact-flow enclosures and numerical states. Displayed decimals summarize exact records.

The actual timestamped reader returns 120.04361511376919, exactly equal to the rational second-difference stencil of the represented samples. The achieved sample-error allowance contributes less than 1.261e-7 to that stencil; the whole-window certified lower bound remains above 111.0743950. The unchanged threshold is represented 0.1. Final time and EPI agree with live child state. The reader's internal physical_time label denotes timestamped rather than operator-step history; the clock here remains structural, without a laboratory-unit identification.

The child now has executed glyph prefix OZ, operator step 1 and U2 debt 1. Its detached strict THOL probe and incremental grammar admission pass from its own current evidence. The prefix is still incomplete: the promised THOL handler and selected closure have not executed. No second birth, post-birth continuation, cross-birth U6, autonomous occurrence or physical identification follows from these observations. This closes acquisition of the previously missing child-owned evidence, not every obligation for the next operator or for recursive generation.

The independent retained-response controls verify byte associations, primitive event effects, recorded four-stage arithmetic and full-state carry without replaying the response. They rebuild the certificate and actual reader from primitive records; favorable cached verdicts are not premises. Source-validation calculations and original Taylor-jet provenance retain the limits stated above.

The separate child THOL admission consumes this acquired endpoint to derive a conditional nested reset and complete successor law. It does not change this acquisition or evaluate a second birth.