Default parent-target UM: complete reset and identity boundary

The canonical default mathematical UM map on the retained 21-node THOL successor selects eight new links, including the child. Its complete event work is positive and its endpoint lies strictly outside the previously maintained twenty-node radius-1/16 identity. This is an analytical selection, reset and obstruction result. The first runtime attempt rolled back after a pressure-guard false rejection. A separately frozen corrected transaction now commits the predicted successor. Primitive inclusion transfers the existing conditional half-unit motion certificate to that endpoint under its selected complete law. No new trajectory is evaluated; autonomous enlarged formation remains open.

The research program owns status. The actual retained birth provides primitive input. The coupling owner, candidate-selection owner and hierarchy composition retain their general contracts and different preparations. Their old factors, selected support and maintenance coefficients do not transfer here.

1. Admitted source and analytical scope

The source consumer verifies the existing THOL archive and response associations, reconstructs the original temporal certificate and re-admits the birth reset from primitive graphs. It retains node order, neighbor order, aliases, all 45 old edges and conductances, capacities, hierarchy, clock 7+2^-19, stored pressure and the actual VAL,THOL prefix with explicit zero U2 debt. Invalid persisted debt cannot be replaced with reconstructed zero debt. Only declared event metadata and the alias-owned maximum for the distinct raw pressure may differ across that birth; policy changes reject.

The source includes parent 2 with capacity 128 and isolated child 2_sub_0 with capacity 121.6. All old sense indices are supplied as 0.5; the child's absent value is consumed by the UM default as zero. This is a declared default, not a measured child property. Its previous temporal baseline remains unavailable. The live parent-target UM preconditions and grammar pass in the prospective VAL,THOL,UM,SHA context; no additional stage is run.

Keep all four default UM branches enabled, all-candidate count zero, no restricted node sample, default U3 and compatibility thresholds, and seed 17. Count zero makes sampling and its seed inert for selection, but the retained execution inputs are still recorded. The phase, capacity and pressure factors are the actual represented defaults corresponding to 1/(pi+1), 1/(4*pi) and 1/(2*pi).

The reset predictor constructs rational interval enclosures of the ideal algebra using those represented coefficients. Sine, cosine, argument and shortest-arc branches use mathematical pi, while score denominators and configured thresholds retain their represented constants. Every branch is decided from the whole interval; unresolved cuts or thresholds reject. The unchanged negative lifts at nodes 10 and 11 remain unchanged. Only updated phases use the certified interior zero-to-represented-tau chart.

Ideal enclosures are distinct from a prospective absolute numerical allowance epsilon=2^-40. Every selected/rejected gate has clearance greater than 4*epsilon, but this does not establish an error bound for an unevaluated implementation. Future runtime filter arithmetic and reset outputs need their own comparison. The conditional work/identity enclosure below assumes the proven support, exact preservation of forms and old weights, and error at most epsilon in each changed phase, changed capacity and new conductance. No arbitrary backend or libm guarantee is inferred from those assumptions.

2. Full candidate inventory and reset

All four existing parent neighbors (0,1,4,5) pass U3. The circular consensus includes the parent and those four old neighbors. The child is not yet a neighbor and contributes to neither that consensus nor the capacity mean. With represented factors b,a,c, write

\[ \psi=\arg\sum_{j\in\{2,0,1,4,5\}}e^{i\theta_j},\qquad \theta_j^+=\theta_j+b\,\operatorname{Arg}e^{i(\psi-\theta_j)} \quad(j\in\{0,1,2,4,5\}). \]

All other phases remain fixed, including the child phase. Only the parent's capacity changes:

\[ \nu_2^+=128+a(3/4-128)\simeq117.87376674577816. \]

The ideal consensus is approximately 1.256088230894206. The new parent phase is approximately 1.255573638657544, old neighbors 0 and 1 move to approximately 0.303286280606, and old neighbors 4 and 5 to approximately 2.209722808889. The parent raw pressure is reduced to approximately 0.000107330657724, using alignment over the final gaps to its four old compatible neighbors. This stored channel is separate from subsequent constitutive pressure on the new support.

The sixteen nonneighbors are inventoried before the reset. Snapshot phase admission first excludes eight; they are not reconsidered after the phase changes. Every remaining candidate passes the final phase and score gates. For positive forms the exact score simplifies to

\[ \omega_{2j}=1-\frac{|\operatorname{Arg}e^{i(\theta_2^+-\theta_j^+)}|} {2\pi_{\rm repr}} -\frac{|x_2-x_j|}{4(x_2+x_j+\epsilon_{\rm form})} -\frac{|S_i(2)-S_i(j)|}{4}, \qquad \epsilon_{\rm form}=\operatorname{fl}(10^{-9}). \]

Here S_i denotes the supplied sense index, not the sine pressure sum. This algebraic simplification retains the runtime's positive scaling denominator; intermediate floating-point operations remain a separate issue.

New parent-2 neighbors	Ideal conductance, approximately
3	0.999973924748
10, 11	0.800169237172 each
12, 13	0.999830739220 each
14, 15	0.799830739220 each
2_sub_0	0.786267820934

The excluded nonneighbors are 6, 7, 8, 9, 16, 17, 18 and 19. The smallest accepted score margin is the child's, greater than 0.0277 above the default threshold. The proposed support is therefore connected, with 21 nodes and 53 edges. Its 33 independent cycles cannot be represented by only the two original winding labels. No exclusive-child candidate list is supplied.

3. Complete work, new rows and observation weights

The work owner rebuilds the reset from primitive state before consuming it. For the selected edge-only storage, unchanged forms and old conductances give

\[ \Delta H= \sum_{\{i,j\}\in E_{\rm old}} [\cos(\theta_j-\theta_i)-\cos(\theta_j^+-\theta_i^+)] +\sum_{\{i,j\}\in E_{\rm new}} \left[\frac{W_{ij}^+}{2}(x_i-x_j)^2+ 1-\cos(\theta_j^+-\theta_i^+)\right]. \]

The old-edge phase work is not discarded when a new link is added. Direct jump algebra avoids mistaking overlapping storage intervals for equality. The ideal contributions are approximately

Contribution	Value
Old-edge phase work	+0.40817044439
New-edge form storage	+0.01053323147
New-edge phase storage	+2.76393387948
Total	+3.18263755534

Including the stated conditional numerical envelope gives the rigorous coarser containment

\[ 3.18263755531<\Delta H<3.18263755538. \]

This positive work belongs to the supplied hybrid reset. There is no declared autonomous event selector or reservoir providing it, and it is not laboratory energy. Continuous conservation after the event does not pay for its storage jump.

On the predicted connected support, both complete rows are rebuilt with actual new degrees, new conductances and changed parent capacity:

\[ p_i=\frac{1}{\pi d_i}\sum_{j\sim i}\sin(\theta_j-\theta_i),\quad \dot x_i=\nu_i p_i,\quad \dot\theta_i=\frac{\nu_i}{\pi d_i}\sum_{j\sim i}W_{ij}(x_i-x_j). \]

The child has predicted fresh pressure approximately 0.00005213909, form rate +0.00634011 and phase rate -4.98155. These are instantaneous rows at a hypothetical endpoint, not recorded motion or observed child rates. Its coupled dynamics would differ from the preceding frozen-isolate law.

The full positive weights d_i/nu_i are now available. Their total changes from approximately 100.03125 (with zero isolate weight) to 107.1100275. Full connected means, old marked-node observations and pre-event component means are different quantities. Neither the old component's restricted rows nor its independent conservation statement survives the new cross support.

4. Strict old-identity obstruction and remaining question

Keep the original twenty marked nodes, their original phase reference theta_*, common-origin projection P=I-11^T/20 and declared continuous lifts. Their identity condition remains

\[ Z^2=\|Px\|^2+\|P(\theta-\theta_*)\|^2<1/256. \]

Before UM its squared radius is approximately 7.74063e-6. Direct interval evaluation after the ideal reset gives approximately 0.368259295161. Even the conditional numerical envelope obeys

\[ (Z^+)^2>0.36825929515>1/256. \]

The original small identity therefore fails already at the mathematical event endpoint. Refining an old trajectory or applying its maintenance certificate cannot repair this domain mismatch. The result does not prove instability, winding loss, destruction of all organization, or failure of TNFR. It establishes a change of geometry and a different maintenance task.

A useful simplification for that task follows from the complete law. On connected positive support and at positive capacities, an equilibrium must satisfy L_W x=0 and the bare sine-current equations. Hence stationary form is common, while stationary phase is determined by the bare support, with conductances and capacities still retained in storage and dynamics. In an acute chamber the child leaf must have the parent's phase. This reduces the stationary problem; it proves neither existence nor capture of the predicted source. Full edge branches, not just selected winding summaries, must define any successor chamber.

Verification uses source controls, selection controls, work/identity controls and an independent high-precision comparison. The latter checks all candidates, the complete reset, all old/new edge work, fresh rows and marked geometry while forbidding proposals, execution and numerical flow. The retained THOL and history artifacts remain unchanged. The following runtime evidence has a separate scope and is never replayed by these analytical controls.

5. Single runtime attempt, rollback and guard correction

The protocol and primitive source with predictions were frozen with all 820 Python/configuration/instrument source members before one attempt. It requested one canonical parent-2 stage in the unchanged core context, with seed 17, default all-candidate selection and structural time 7+2^-19. No SHA, IL or continuous step was requested.

The raw callback record contains the predicted eight added edges and full represented reset. Its changed phase, capacity and conductance values satisfy the original 2^-40 farthest-endpoint error bound, and its primitive coordinates and held parameters belong to the independently archived conditional motion family. All 53 original branch labels match. Complete proposed storage work includes the old-edge phase changes and both new-edge contributions. This is a raw intermediate observation, not a committed successor.

The failure record shows that the callback's non-pressure-state guard rejected during refresh. The shared atomic stage rolled back: the retained rollback endpoint has exactly the frozen before state's typed persistent signature. The live source therefore retains its VAL,THOL prefix and isolated child. The raw VAL,THOL,UM history is evidence inside the aborted transaction only. There is no successful stage result, response or passing verdict to infer.

The separate detached diagnosis uses a restored copy of the raw record and the unchanged archived guard. It constructs the shared graph-owned cache manager and evaluates only the declared pressure map. The permitted maxima change from approximately (0.00012071, node 3) to (0.07039394, node 11). Persistent non-pressure state and cache-owned payload remain unchanged, but the guard follows _tnfr_cache_manager._graph_owner back into the original graph dictionary and signs those already-excluded maxima again. Restoring only the two permitted maxima restores the frozen signature. This identifies a recursive reference false rejection, not a forbidden form, phase, support or history write. The refreshed copy remains explicitly detached; it is not a recovered runtime commit.

The current execution owner uses the shared structural signature's opaque-reference option for the separately protected graph dictionary. Direct non-pressure state, active alias identity, inactive aliases and cache-owned payload remain protected. The separate correction record binds its source and synthetic controls without replacing the failed producer. Synthetic controls cover valid refresh with a populated cache, forbidden cache-payload and state writes, typed metadata, durable raw recording and stale-source rejection. The retained-evidence reader rebuilds raw inclusion and rollback without replaying UM or the diagnosis.

The original attempt remains failed and immutable. It establishes no committed successor or theorem transfer. The separate transaction below retains its own prospective archive and response; it does not turn the detached diagnostic copy into an execution result.

6. Committed UM and separate assessment correction

The corrected protocol and source were independently frozen before one attempt. Its 820-member source archive differs from the first attempt only in the documented runtime guard and the instrument that binds the correction. The scientific protocol, primitive preparation, predictions, default factors, seed, clock and numerical allowances are unchanged. All 689 prior frozen artifacts remain byte-identical.

The primitive response records a completed shared atomic UM stage, its durable raw reset and its pressure-refreshed endpoint. It has all 21 nodes, the unchanged 45 old edge payloads and exactly the eight predicted additions. Every form and excluded phase/capacity coordinate remains unchanged. The changed phases, parent capacity and new conductances satisfy the original farthest-endpoint 2^-40 error bounds. The parent has actual prefix VAL,THOL,UM, zero U2 debt and unchanged temporal history. The child has no invented temporal baseline; hierarchy and structural time remain unchanged.

The original assessment remains 25/27. Its two failed predicates are reader defects:

• Every old-edge form-storage difference is exactly zero from unchanged represented weights and forms. Enclosing each nonzero energy before subtraction lost this correlation and produced an interval containing zero with positive width. The corrected reader subtracts exact rational energies first, then encloses the result. No tolerance substitutes for zero.
• Canonical edge insertion adds _dnfr_prep_dirty=True through the shared topology invalidation owner. This is the sole additional graph-context field, already present in the earlier aborted raw reset. The corrected reader requires this exact Boolean in both raw and committed records. It continues to protect the flag across pressure refresh and rejects all unrelated context changes.

A separate review protocol archives the corrected reader and independent synthetic regressions before the read-only review. That review obtains 27/27 on the same primitive response, rebuilding state, full work, both continued rows, means and all branch labels. Only the two diagnosed predicates, their aggregate and the old-form/total-work enclosures change. The original report and response are not overwritten; neither an event nor a trajectory is repeated. The retained-evidence controls independently check the corrections, source associations and exact endpoint inclusion, while forbidding producer execution.

Complete event work remains positive, approximately 3.1826375553413957, including old-edge phase changes and both new-edge storage terms. The old marked radius identity remains excluded. These facts belong to the supplied UM event and do not derive an occurrence selector or its source of work.

The actual endpoint's 42 coordinates, 53 conductances, 21 capacities and all 53 original branch labels belong to the previously certified conditional family. With the same held support, positive parameters, zero forcing, complete two-row law and structural clock, the finite-motion theorem therefore applies to its mathematical continuation: every original principal branch remains strict through elapsed t=1/2, and the initially negative child-parent relative phase velocity is positive at t=21/512. The theorem does not require another runtime trajectory. Its archived derivative jets and remainders retain their original producer provenance.

The UM endpoint itself retains an incomplete prefix. A separate SHA composition now closes that selected word and admits the changed-capacity law. Its vector field and weighted means differ, so the UM motion certificate supplies no post-SHA retention claim. No IL intervention, child U5 observation, cross-birth U6, autonomous formation, periodicity or physical identification follows. The execution plan owns the next gate.