Retained forced-support regional observations

Frozen finite regional comparisons and their original preparation and numerical limitations.

Part of Forced support balance and model boundaries. Section numbers are stable across the collection; hypotheses and model changes remain local to each result.

Archived research record. This preserves conditional derivations and source-bound evidence. Its local next-step language is historical and does not schedule work.

6. Bounded executed comparison

forced_support_balance.py executes three cases with the shared nodal Euler integrator and duration dt=1/4 per segment. The causal case begins at time 0.5 with the actually born and connected child, then executes 24 segments while holding its support, capacity and phase. The prepared compatible control executes 12 segments; the prepared clipping control executes two. The latter starts with uniform EPI 3.99 inside [-4,4], using the captured heterogeneous capacities and phases.

Every one of these 38 segments records the before-state, raw integrator endpoint, explicit full pressure refresh, independent forcing capture and finite error budgets. The campaign verifies unchanged nodes, conductance, support, capacities, phases, effective weights and forcing. The three reused two-segment birth preparations are recorded separately; the complete artifact contains 44 executed Euler segments. The final parent SHA in the causal case follows the measured endpoint. Each executor invocation owns its transaction; the outer campaign is an observed finite orchestration, not a new changing-node executor.

The recorded finite results are summarized below. Displayed decimals approximate the exact rational read-outs of represented states.

Case	Elapsed time	Observed mean change	Clipped segments
Causal attachment	6	-0.00010809228696952129	0/24
Prepared compatible	3	-1.1533598133637477e-16	0/12
Prepared near-bound	0.5	-0.0015017826861904956	2/2

The causal reference has compatibility residual approximately -0.0003191519727040398 and mean drift -1.8015381161585726e-5. Its relative H-variance decreases from 3.687922367686489 to 0.06603591731695654, approximately 1.79% of its initial value; the Dirichlet error decreases from 7.192753706434506 to 0.08734582300741148. Both remain nonzero at the measured endpoint. The largest captured pressure defect is approximately 4.48e-17 and the largest held-input endpoint defect approximately 1.12e-16.

The compatible control has exactly zero forcing, drift and relative profile in the exact reference. Its observed mean change is retained as a finite numerical defect, while its H-variance decreases from 3.534687651989093 to 0.3587332981472503.

The near-bound control clips in both segments despite a negative reference mean drift. Its aggregate mean endpoint-defect contribution is approximately -0.0014927749956097026, with a largest component endpoint defect of approximately 0.010852609921791328. Local upper bound contact therefore materially changes the mean budget; it cannot be explained by the small held-model drift alone.

Every captured mean identity, centered recurrence, raw energy budget and relative error energy budget has exactly zero rational residual. The complete data are generated as artifacts/research/forced_support_balance.json by

.venv313\Scripts\python.exe -X utf8 benchmarks/forced_support_balance.py

The finite decay supports the held-support interpretation. It does not establish the measured runtime's infinite-time limit, self-restoration under later operators or empirical correspondence.

The 29 independent exact controls in test_forced_support.py include a hand-solvable heterogeneous pair, arbitrary initial means, the profile's uniform nonzero rate, cancellation between mean defects, clipping, an excessive Euler step and tampered public caches. The nonlinear forcing capture has 16 independent checks in test_forcing_realization.py. The 13 bounded campaign checks are in the runtime test suite.

The child-target Coupling follow-up adds exact same-EPI reset budgets when capacity, conductance or forcing changes. It keeps the original derived profile as a separate fixed comparison and continues from the retained attached endpoint before its terminal Silence action.

8. Retained THOL regional audit

thol_regional_balance_audit.py applies section 7 to one authenticated sixteen-node snapshot at t=0.5, immediately after the original all-parent UM attachment and pressure refresh. Before computation it fixes eight actual parent-child pairs, in retained birth order, plus the complete actual-child cohort. It validates their birth receipts, hierarchy, parent pointers, source state, forcing decomposition and original model digest. There is no partition search, graph reconstruction, new native call or trajectory. Nine regional observations are not nine independent experiments or nine certified NFRs.

The full graph has 24 undirected positive-conductance edges. Each ancestry pair has one internal edge and four cut edges. The child cohort has sixteen cut edges and no internal edges. The normalized EPI coefficient is retained as approximately 0.18315345241335917; it is not refitted. The following decimals summarize exact rational rates in the declared structural time. Grouping by parity is only a presentation of the eight preselected pairs.

Region	Negative internal term	Boundary term	Non-EPI source term	Model variance rate
Pairs 0, 2, 4, 6	-0.336177322	-0.377518225	-0.007512998	-0.721208545
Pairs 1, 3, 5, 7	-0.008502957	+0.015068434	-0.000818827	+0.005746650
All actual children	0	-0.005023392	0	-0.005023392

Four pairs instantaneously reduce their internal contrast and four increase it. Thus a whole-network attenuation score would conceal different regional responses. For the child cohort, the modeled variance decrease comes entirely from the parent boundary. Its weighted-total influx is approximately 1.3525044630156273, with an additional 0.039791667697099464 from the capacity channel; phase and topology contribute exactly zero to this cohort's weighted-total rate. The capacity source has zero centered-variance contribution in this particular cohort. Zero aggregate contribution does not imply that a channel is absent from the complete network dynamics.

The child cohort's fresh-kernel variance defect is approximately 8.351053868395752e-19, and its stored-minus-fresh residual is exactly zero. All nine observations close all four exact model/stored identities. The conditional child rates are approximately 0.1739957797926912; held-parent profiles alternate approximately 1.0665389696346133 and 0.6469908610321591. Actual parents also evolve, so those conditional values are neither observed equilibria nor a new frozen target for later scoring. The audit identifies a boundary-supported response, not autonomous regional maintenance or its absence.

Reproduction uses the original retained artifact without replaying it:

.venv313\Scripts\python.exe -X utf8 benchmarks/thol_regional_balance_audit.py

Input: artifacts/research/thol_native_runtime_response_2026_09_18.json, SHA-256 71252d116d8933d15a797707ed9f44ed865406422da6db492b48f6989d739c95. Output: artifacts/research/thol_regional_balance_audit_2026_09_18.json, SHA-256 a1cbda157979dfc85e49aed747ab68d1758ab543ab70588ea0060f33536f1a84. The output records its working-source scope and digest sha256:21d3bb97569d2ca6dbce5c206df2732397a038135990fc91baf70c4106f51921. Ignored local artifacts are not promised in a fresh clone; the tracked derivation, source, portable tests and input binding retain the result's scope.

The regional owner has 33 new tests and the retained audit has 19. A combined 313-test validation covers those tests, the reused full-support, forcing/target owners, grammar/contract/sequence witnesses and selector symmetry. It passes with zero failures. No full-repository, laboratory, infinite-time or autonomous-emergence verification is claimed.

10. Retained temporal regional identity audit

thol_regional_identity_audit.py applies section 9 to the original control interval t=1.5 to 1.75. It keeps the same eight ancestry pairs and complete child cohort as section 8. The identity contract retains ordered EPI, its full-metric regional mean and centered form, represented phase, capacity, membership and boundary support. Only the explicitly labeled relative-EPI comparison factors out a uniform regional EPI translation. Neither vertex survival nor exact relative-form inequality decides whether a reorganizing region is a persistent NFR.

The offline reader authenticates the retained input, ancestry, original model, source captures, full support and metric, clocks, ordered IL writes, Euler entry/exit and later phase-normalization/coordination boundaries. Complete retained JSON references preserve the available bounded histories, selector configuration and counters. They do not expose opaque resource contents or recover an unrecorded past. No live graph is reconstructed, pressure kernel replayed, native step executed or new trajectory generated.

All nine regions retain their membership, support and capacity; all nine change both their weighted mean and centered EPI. Their represented phase arrays also change. A represented-angle difference alone is not proof of a changed circular relative pattern; normalization and coordination remain separate stages. The following decimals summarize exact finite endpoint differences, not instantaneous derivatives or integrated physical fluxes.

Region	Initial variance	Final variance	Variance change	Weighted-mean change
Pairs 0, 2, 4, 6	0.902258620	0.821047349	-0.081211271	-0.009957785
Pairs 1, 3, 5, 7	0.024179569	0.024454198	+0.000274629	+0.009676222
All actual children	0.002657877	0.003925631	+0.001267755	+0.015229068

Parity groups only summarize the preselected pairs; the artifact preserves their individual exact values. In the child cohort, the finite variance change is approximately 0.0012677546577278922, with this decomposition:

Contribution to child variance change	Value
Initial internal term multiplied by dt	0
Initial boundary term multiplied by dt	+0.0015088569377293777
Initial centered phase/capacity/topology source terms multiplied by dt	0
Generated-pressure realization discrepancy multiplied by dt	-6.412689936119145e-19
Observed IL pressure-write term multiplied by dt	-0.000364318044755452
Euler quadratic term	+0.00012321576475397104
Combined endpoint-defect terms	-4.001406686548848e-18

The parent boundary supplies the growing child contrast, while IL reduces part of that first-order drive. Section 8's earlier negative instantaneous rate and this later positive finite change are different observations; neither alone establishes instability, recovery or loss of coherence. There are still no internal child-child edges. Boundary-supported contrast is compatible with the conditional nodal response in section 9, without making its held-parent target an actual maintained equilibrium.

The captured phase source changes after integration: the largest absolute component difference is approximately 0.0317983299409307. Capacity and topology source differences are exactly zero; normalized channel weights are unchanged. The endpoint phase source is therefore not the source consumed by the preceding EPI integration. No generation-time forcing capture exists in this historical schema: reusing the entry capture at generation is a conditional identification, checked against equal EPI, phase, capacity, support, ordered neighbors and source configuration. Historical IL rows also lack a resolved retention factor. The artifact records their observed pressure writes and explicitly leaves IL_factor_certified=False.

All finite weighted-total and variance identities close exactly. The portable audit tests cover independent arithmetic, identity distinctions, 28 malformed-record controls and a read-only retained-input smoke test when the local input is available. Together with the finite observer and reused regional/support/ forcing tests, 156 tests pass; all four changed Python files pass flake8. The result is finite retained-record accounting. It supplies neither a causal execution seal nor autonomous source maintenance, future stability or a physical-emergence result. The known phase-enumeration sensitivity remains an explicit boundary for subsequent source-maintenance claims.

Reproduction consumes the same pinned input as section 8:

.venv313\Scripts\python.exe -X utf8 benchmarks/thol_regional_identity_audit.py

Output: artifacts/research/thol_regional_identity_audit_2026_09_18.json, SHA-256 57cc9774c0645779d6e54df5fff2e0f1f33fe4bc7390bce5c90c04a869ab3745. Its declared working-source digest is sha256:f1e3ad6b0a8e6b30b12019469ea0f654b3432fd397b314b91173fdf815a2e775. The local validation checkpoint is artifacts/research/regional_identity_validation_2026_09_18.json. Missing ignored input is an explicit reproduction limitation; it must not trigger an automatic rerun of its historical producer.

13. Versioned phase correction at the retained regional state

thol_exact_phase_source_comparison.py performs the predeclared comparison at t=1.75: one legacy replay matching the archive, one exact_components_v1 call and its node-order reversal. All three retain the same primitive components, local neighbor order and archived effective gains. The two exact calls have identical aligned raw proposals and realized phases. Only the reference and new source-order phase outputs receive fresh forcing captures, using the same endpoint EPI, capacity, conductance and original enumeration. The existing source audit and regional observer perform all nine exact balances.

Compared with the legacy output, the new phase differs by an almost common rotation of approximately 0.001213708823288334 radians. The maximum anchor-relative pattern residual is 4.440892098500626e-16. The maximum phase-source change is 1.072266750968715e-16; the maximum fresh-kernel pressure change is 1.1102230246251565e-16, affecting five of sixteen nodes. Kernel-defect differences are retained separately. None of the nine model variance-rate signs changes. Pair 3 remains positive, approximately 0.0007715771064528146; the child cohort remains positive, approximately 0.005813679258034855. Historical stored nodal rates do not change.

The distinction from section 11 is substantive: that earlier comparison used a different archived enumeration output, which changed a regional rate's sign. The present alternative is the explicitly selected exact version, not that archived vector relabeled. With unchanged local targets and a common global gain, changing the global target within the same wrapped-displacement branches produces a common rotation in exact unrounded update arithmetic. This explains why absolute phase motion need not change relative phase pressure; the observed binary64 residuals are still recorded rather than declared zero by a tolerance.

This closes the bounded numerical gate, not arbitrary runtime invariance, transcendental accuracy or regional maintenance. The native default remains legacy. Section 14 uses already retained paired endpoints to separate regional perturbation recovery from loss of the control's form. No additional numeric-policy sweep is required by this result.

Local output: artifacts/research/thol_exact_phase_source_comparison_2026_09_18.json, SHA-256 1a59e2a2f0f4634dfc393096fab94550d2feeb1f119df3dfa90e8c33e1ee246c. The study used exactly three detached coordination calls and two forcing captures, with no native step or historical producer rerun. Its ten new portable tests and the reused source-audit tests pass 53 cases.

14. Regional recovery versus loss of form in the retained paired window

thol_regional_recovery_audit.py reads the authenticated control/child-Emission window at six predeclared times: 1.75, 2, 2.25, 2.5, 2.75, 3. It uses all eight actual ancestry pairs and the child cohort. It executes no dynamics, coordination or pressure capture. These observations retain the historical legacy phase policy; they are not a continuation of the exact-version comparison in section 13.

For each region restrict the original full-graph metric h_i=d_i/nu_i, checking unchanged support and capacity at all twelve branch endpoints. For paired difference delta=x_perturbed-x_control, let P_R subtract the regional H-weighted mean. The existing paired-distance kernel gives

E_delta = (1/2) sum_R h_i (P_R delta)_i^2, V_control = (1/2) sum_R h_i (P_R x_control)_i^2.

The readout retains the separate mean offset, control centered vector and its drift from the initial control. E_delta/V_control is available only for positive control variance. The evolving reference is fixed by the archived control branch, not fitted to the perturbed outcome. These are EPI response diagnostics, not a complete definition of NFR identity.

The following endpoint ratios compare t=3 with t=1.75; values are decimal displays of exact represented rational calculations. A ratio below one means that quantity decreased. All 54 regional endpoint observations are retained in the artifact.

Region	Paired centered error, end/start	Control variance, end/start	Error/control ratio improves?
Pair 0	0.287757	0.262526	No
Pair 1	0.215629	0.932912	Yes
Pair 2	0.278658	0.262344	No
Pair 3	0.215169	0.700275	Yes
Pair 4	0.278660	0.263815	No
Pair 5	0.215161	0.732370	Yes
Pair 6	0.278949	0.264487	No
Pair 7	0.212958	0.689536	Yes
All actual children	416.642313	4.091503	No

All eight pairs reduce their centered response error at every recorded step, with endpoint reductions of about 71.22%-78.70%. But the even pairs' control contrast decreases faster than the response error: smaller absolute error there is not improved fidelity relative to the remaining pattern. Only the four odd pairs improve both raw and contrast-normalized error. This does not retrospectively select those four as confirmed NFRs.

The child cohort's centered error grows from 1.697128915806442e-9 to 7.070957167203885e-7. Its factor of 416.64 starts from a very small denominator; the final error/control ratio remains only about 4.402362158591030e-5. Its mean offset decreases from about 0.07059424 to 0.04870253, so mean relaxation coexists with increasing spatial error. Every control region retains positive variance at all six sampled endpoints, but every control centered vector changes. Neither exact original-form maintenance nor full engine-state return is established.

The result refutes a uniform regional-recovery interpretation of the earlier whole-network attenuation score. It does not refute TNFR or demonstrate unbounded instability. The recorded IL/EN/AL policy, changing control forms and shared transport remain part of the explanation. The largest child-error increment occurs over 2.25 -> 2.5, which contains Reception and subsequent integration: its error changes from 1.162021485807489e-8 to 4.894373864559578e-7. Isolating those already recorded stages is the next direct mechanism question; temporal coincidence alone does not attribute the increment to Reception.

Local output: artifacts/research/thol_regional_recovery_audit_2026_09_18.json, SHA-256 5a926d82a5cbb2d2ea8f51fd1fbfe9d033aa5a59caff797f465ed0efdaeec8b0. Fifteen new tests and the reused regional-identity tests pass 49 cases. An independent standard-library recount verifies 559 exact checks over the 54 regional endpoints, using the original full-graph degrees/capacities.