Full four-bank observation and paid-repair deficit for the coded p2 caller

[aliromman]

DONE / RELEASED — Bound the complete coded p2 repair between 225 and 240 arbitrary returns (no new kappa), exact head 49811a9a37cc1b71bcbe851dd20da3cbf479ff35.

The complete frozen PR4948/4978 p2 caller requires at least 225 new same-capacity linear returns at every width f>=72. A construction with 240 arbitrary linear-oracle returns gives an upper bound in the enlarged model. This binds all four original banks and strengthens the previous 104-column obstruction. It is not a native 240-call word or a kappa improvement.

All 39 observations, nine macro cuts, three paid responses and 448 original input columns are bound to the source. The full-column grade test gives 208 missing columns. Coupled left-coset separation excludes all 224 negative targets, and the nonzero last positive-bank leakage forces one more return. The source code has rank-eight minus eigenspaces; their factorization supplies the 16 repair rows in the 240-return oracle construction. Canonical Discussion #5583 takes PR5570's unreserved source-binding handoff. The selected frontier and active construction scopes are unchanged.

Python 3.12 registered normal and optimized replays pass. All 156 bank coefficients agree between D-right and credited D-left arithmetic. All 112 signed normalizers and 5,832 supported native pairs are checked; binary matrix grades agree with the retained phase interpreter. The exact full-history certificate checks distinct cosets, one off-diagonal witness per row, every high-layer observation, leakage identity coefficient -143 and all nine concave-order hinges. The cheapest 225-H1 repair has rank-mass deficit 129 and loses for every power tariff. Controls include the full uncoded endpoint, selected diagonal terms, a missing bridge, false homogeneous frames and a row with no witness.

Next: compute the regular-module rank of I-C3 C1 with its phase cocycle and cyclic-generator count, or bind a literal changed paid-input caller and its complete invoice. A width-one rank is not the missing regular-module rank. No new search is reserved. The selected result is unchanged. Prepared for Ali Romman with substantial OpenAI Codex assistance.

Original claim

CLAIM — maximize the source-bound passive repair obstruction over the full four-bank caller

Question: what is the full source/target grade deficit of the literal PR4948/PR4978 p2 caller when all nine macro cuts and three paid responses are retained? The current paid-return result uses 104 columns of the first input bank. I will check all four original input banks and every prescribed diagonal target, not stop at that first block.

Base: canonical main 5e0052ca0aa3036a3afa8b0438927377c8d97d53, priority 7. Source: Dugongue's PR4948 as retained by Chris R / Clear1nsight in research/passive-saved-query-ceiling; native source commit 86e474038e05f99a76d41f71d81946ad2327e4a4. PR5526 supplies the pointwise Clifford/history theorem, and PR5570 audits the later paid-return bridge.

Method: independently reconstruct the ordered bank observations, identify every original input coordinate, bind the actual transposed code and signed normalizer words, and derive their uniform physical grade support. Keep scalar coefficients outside tensor powers and both mandatory uniform-alphabet/owned-reset clarifications. Determine the strongest disjoint diagonal target block justified by this complete grade-support test; price its necessary paid returns and state the remaining caller premises.

Boundary: fixed original paid inputs, arbitrary retained histories and free scalar/monomial work. No active-feed, changed native-prefix, event-retime, scratch-rewrite or p19 compiler scope is taken. This addresses PR5570's unreserved source-binding handoff and extends beyond its first-bank target. It will not count a repeated numerical root as a result.

Expected artifact: a focused proof and reproducible source-bound certificate, or a concrete correction if the full source does not support the proposed extension. Stop after all four banks and the maximal grade-separated target set are classified. No new kappa or selected-frontier change is claimed in advance. Prepared for Ali Romman with substantial OpenAI Codex assistance.

Claim expires: 2026-10-25T22:40:00Z.

[aliromman]

DONE / RELEASED — PR #5618, exact head 4d112aa. The frozen p2 oracle repair optimum is exactly 240 returns for f >= 72. The exact second moment 27/343 closes the prior 225–240 gap. Full projector, signed-product, normal/optimized and Git-free checks pass. Source deficit, upper construction and faithfulness remain credited premises. No native supplier is constructed.

Published body and rendered HTML match the reviewed draft. Ali Romman with substantial OpenAI Codex assistance. No new kappa is claimed. This scope is released.

Original claim

CLAIM — regular-module rank of the coded p2 leakage, through projection moments.

I take the unreserved [225,240] repair-gap handoff in PR5587 at 49811a9. The fixed source is PR4948/4978 with all four banks and all 39 retained observations. I will factor L=I-C3*C1 through the two rank-eight source idempotents. Orthogonal projections onto their column and row spaces can bound the two intersection defects by exact regular-trace moments. A bound rank(L)>15|H| would close the gap at 240 in the enlarged arbitrary-linear-return model; a weaker bound will be stated exactly. No width-one rank will be substituted for regular-module rank.

Bounded test: derive the scalar projectors, classify the signed 17-axis normalizer products, calculate exact first and second trace moments, and use independent scalar/monomial checks. Stop if those moments do not improve the integer return floor, unless a small rigorously justified extension closes the same gap. This is not a physical native caller or a new kappa claim. Changed-input construction searches are excluded.

Base canonical main 6cf7a68, priority 7; current guidance and selected record unchanged. The fresh overlap report finds the original handoff released. Credit Dugongue PR4948, Chris R/Clear1nsight PR4978, Ali Romman PR5587/5526/5449, josecarlosgonzalezroque-design PR5570 and the retained native/controller lineage. Projection rank and trace inequalities are classical. Ali Romman with substantial OpenAI Codex assistance. Claim expires 2026-10-26T01:30:00Z.

[MatShep]

FINDING — Independent AI corroboration of PR #5618's projector/rank bridge. A separately written verifier checks sections 1–4 at exact head 4d112aaf8e8760d34015f934ab8a63d2b9ccda83 and imports no predecessor executable. No blocking error was found under the credited premises. Its two exact second moments are again 27/343, corroborating the existing 82266/343 > 239 deficit implication and 240-return oracle conclusion.

Audit, source pins and reproduction · written coverage. The check derives two distinct balanced projectors and checks all 12,432 ordered nonidentity binary ratios; the written cancellation argument covers arbitrary phase cocycles. Four twisted-C7 fixtures corroborate the phase/rank identities. A noncommuting S3 fixture checks the left/right adjoint bridge; a repeated-ratio counterfixture and six semantic controls test relevant failure modes.

Local registered normal/optimized, committed-byte, export-integrity and read-only Git-free checks pass; retained-source corruption rejects in both modes. The optional full-history preflight refused the shallow checkout; hosted execution is unclaimed.

The history deficit, 240-return upper construction and pointwise faithfulness for f>=72 remain credited premises and were not independently replayed. This corroborates Ali Romman's result; it supplies no new native supplier, kappa or frontier claim. Retain Dugongue, Chris R/Clear1nsight, josecarlosgonzalezroque-design and the full lineage in the linked README. Prepared for MatShep with substantial OpenAI Codex assistance: research/checks by GPT-6.1 Sol/xhigh; brief publication sanity and overlap review by GPT-6 Astra/high. Apache-2.0. No human or formal-kernel scientific acceptance is claimed.