OZ-RT-BZ-T3-010-C: exact shared-coefficient extraction gate

[fyremael]

Scope

Advance T3-010 from cell-local exact rank/consistency to bounded global shared-coefficient compatibility and exact solution extraction for the existing SUPPORT_LOCKED_ORIENTED_ONE_BODY_DEGREE0_WEIGHT_CORRECTION_001 class.

This stacked PR is based exactly on validated T3-010-B head 3a6cfba4d8fc5f44d0b9f17e9521e9df43e83fc8.

Mathematical gate

For each independent channel (n1, n2, n3, k1), use one exact rational unknown per scalar-family × support-locked oriented primitive correction weight and require that same coefficient vector to satisfy every structurally active shell stratum and every overlapping harmonic-block projection simultaneously.

Rows are namespaced by the original B cell id, so equations from distinct shell/block projections cannot cancel against one another during global stacking.

For each channel compute over exact Q:

• rank(A_global);
• rank([A_global|b_global]);
• global unique / affine / inconsistent classification;
• a deterministic exact particular solution only when globally consistent;
• direct exact substitution into every active local B equation.

The l1 global system remains mirror-derived: reconstruct it independently, mirror the extracted k1 coefficient map, and require exact substitution into all active l1 cells.

Claim boundary

This stage does not perform full correction-layer recombination, finite-boundary assembly, complete symbolic flux substitution, or final n-holonomic recurrence search. A globally consistent channel is not by itself a correction certificate. A globally inconsistent channel excludes only this declared support-locked degree-zero class.

residual_sum_zero_proved = false

proof_effect = NONE

promotion_effect = NONE

t3_status = OPEN_WITH_CHARACTERIZED_BLOCKER

[fyremael]

T3-010-C exact negative-frontier checkpoint

The bounded exact shared-coefficient extraction gate has now been read back numerically from the frozen registered C head:

ca02bb6dad2970c169eb9b8745c871d4332447fb

Authoritative governed replay remains Programme policy run 31484794547, with Policy shard / contracts job 93760003619 SUCCESS and Policy shard / campaigns job 93760003586 SUCCESS. Because the completed campaign job did not retain producer stdout, a disposable diagnostic branch/PR #440 was created from this exact C head. Its only change was a test that ran the unchanged C producer and then the independent C verifier before emitting a compact ledger as GitHub check annotations. The intentional diagnostic failure occurred only after that independent verification completed. Diagnostic check: run 31546295933, contracts job/check 93959458224, head 317c06dcb94e39432221f3b7ead7da26305c3b19.

Exact global systems over Q

channel	unknowns d	global matrix coordinates	target coordinates	rank r	augmented rank r+	nullity	classification	exact solution
n1	116	14,784	13,156	67	68	49	EXACTLY_INCONSISTENT	no
n2	116	32,254	29,822	67	68	49	EXACTLY_INCONSISTENT	no
n3	116	52,070	49,358	67	68	49	EXACTLY_INCONSISTENT	no
k1	158	25,355	19,175	110	111	48	EXACTLY_INCONSISTENT	no

Every independent channel has 100 active cells, 0 structural-zero cells, and local classification histogram {EXACTLY_INCONSISTENT: 100}. No exact solution was extracted and exact_substitution_checks = 0 in every channel, as required for an inconsistent system.

The independently reconstructed mirror system is likewise:

• l1: unknowns 158; active cells 100; rank 110; augmented rank 111; EXACTLY_INCONSISTENT;
• mirrored k1 solution satisfies l1: false, because no k1 solution exists.

Independent replay status:

INDEPENDENT_T3_010_C_GLOBAL_EXACT_SOLUTION_REPLAY_COMPLETE

with:

• globally consistent independent channels: 0;
• globally inconsistent independent channels: 4;
• exact-solution-extracted channels: 0;
• producer_matrix_imported_as_authority: false.

Therefore the declared correction class

SUPPORT_LOCKED_ORIENTED_ONE_BODY_DEGREE0_WEIGHT_CORRECTION_001

is globally incompatible. The C producer terminal is:

BOUNDED_SUPPORT_LOCKED_DEGREE0_CORRECTION_CLASS_GLOBALLY_INCOMPATIBLE

and this is reconciled to issue #403's admissible operation-level terminal:

BOUNDED_CHANNEL_HARMONIC_SHELL_CLASS_EXHAUSTED.

Consequence

T3-010-D full correction-layer recombination is not authorized, because C produced no globally compatible coefficient vector to recombine. No support enlargement, coefficient-degree enlargement, rational-prefactor search, adaptive basis growth, or reopening of the generic 198-dimensional raw-jet class is authorized by this result. Any broader correction class requires separately governed authority.

The recurrence-search gate also remains closed. In particular:

residual_sum_zero_proved: false

proof_effect: NONE

promotion_effect: NONE

t3_status: OPEN_WITH_CHARACTERIZED_BLOCKER

PR #430 should remain the bounded C result for Human Steward disposition; this checkpoint creates no merge authority.

[gcl-release-trust]

Advisory visual status report — PRVSR-LIVE-PR430-cd967335c55b-20260813115252

• operative state: UNKNOWN
• freshness: CURRENT
• exact PR head: cd967335c55bd9899e1e51647d294d128be33fcd
• source snapshot SHA-256: d2740dfb3575c4a017a5a63492d2b9fc7cc67a3d0b3f0ae03c9e3a04c71debc8
• durable archive: governance/pr_visual_status_archive/grandchallenge/MATH-PROGRAMME/pr-430/PRVSR-LIVE-PR430-cd967335c55b-20260813115252/

This is a deterministic, derived, advisory presentation of governed source state. It does not create review, authorization, merge, certification, or propagation authority. The target PR head was not modified by archive or transport generation.

Phase 1 archive branch: prvsr-advisory-archive/pr-430
Archive path: governance/pr_visual_status_archive/grandchallenge/MATH-PROGRAMME/pr-430/PRVSR-LIVE-PR430-cd967335c55b-20260813115252/
Report generation or archive failure remains advisory and non-blocking.