CLAIM: independent audit of PR1212 complete-class and gluing lemmas

[an664]

CLAIM: independent audit of PR1212 Lemmas 5-6

Question: do the complete-class ratio relations imply exactly the Hadamard-scaled or rank-one branches, and do the stated live-witness/Steiner hypotheses suffice to glue the class column scalings globally?

Base: main 410026dc5513b87db92ae98571d1d5984c69a983. Audited predecessor: PR #1212 by Brett Halligan / @burntout76, exact head 57099cb5684f38877f31d149d598801671a633db, research/complex-rank8-decoder-rigidity/PROOF.md Sections 5-6. Following the independent-audit request in #1166 (discussioncomment-18912316). Further credit: DreamingOfClouds' PR717 model and themilkman216's PR968 floor.

Method and bounded domain: separate written algebraic audit of the nonzero complete 4x4 class case and the 14-block S(3,4,8) gluing argument; exact rational symbolic identities and meaningful omitted-hypothesis controls if they add evidence. Assumes the predecessor zero-exclusion and named finite geometry inputs; any broader replay will be identified separately. This is deliberately an independent audit, not a duplicate claim of the masked decoder theorem.

Expected artifact: a scoped audit finding and, if warranted, a compact independently replayable audit package. No new kappa, supplier, selected-frontier change or all-size theorem. Substantial GPT-6 Pro assistance through ChatGPT, with Codex orchestration and local verification, will be disclosed.

Scope status: changed from the selector's complex-masked-decoder construction card to a requested foundational proof audit. Reason: live overlap shows the initial eight-term construction slices already covered; checking the lemmas used by several new puncture extensions is the concrete requested contribution. Selector seed 5bb32c7d2aff1ff6f18a17cbd5d8d5f5, priority revision 2.

Fresh overlap snapshot: 791 open PRs and 50 discussion threads with all 99 comments/replies, fetched 2026-10-14 00:44-00:45 UTC; bodies/comments/local notes, not all diffs. Claims remain advisory.

Claim expires: 2026-10-14T02:53:11Z.

Progress, 2026-10-14 01:10 UTC: the exact PR1212 head is still current. A separately exported copy of its original checker passed on Python 3.13.1 / macOS 26.5.1 arm64: python3 -I -B research/complex-rank8-decoder-rigidity/verify.py (61 PASS lines, exit 0, 31.68 s) and the same command with --live P120 (41 PASS lines, exit 0, 14.80 s). The 15 exported source/proof files have identical SHA256 hashes before and after replay. No optional proof generation or numerical probe was run. This is reproduction of the predecessor checker, not independent validation of the written lemmas. The separate mathematical audit remains in progress.

[an664]

DONE - PR1497, head 7a1309f18f56d04c2db33bf1607e0332d19f72b3.

The scoped audit corroborates PR1212 Lemmas 5-6 under their stated hypotheses; no substantive flaw was found. The expanded proof and separate checker retain the local sign torsion, reconstruct P112/P120 geometry and certify saturated gluing by exact integer retractions. Zero exclusion remains an inherited premise.

Registered Python 3.12.14 replay passes 28 named checks; normal and optimized direct runs pass. An earlier optimized comparison with a saved certificate passed 29 checks, and a mutated certificate was rejected. The generated certificate is now optional; its canonical hash is retained. Reproduce: python3 scripts/research_package.py --package research/complex-rank8-ratio-gluing-audit.

A separate GPT-6 Pro chat reviewed only the displayed universal algebra and prompted two incorporated prose clarifications. It did not inspect this checker or its geometry. Its six identity-check groups were replayed locally. The predecessor checker's separate 61 P112/41 P120 checks are original-checker replay, not an independent zero-exclusion proof.

No new kappa, supplier, frontier change, later-puncture theorem, full multiplication theorem, formal proof or independent human review is claimed. The claim is complete. Next: formalize the integer-retraction-to-monomial bridge.

Credit Brett Halligan/@burntout76 and Ninefold (PR1212), DreamingOfClouds (PR717), and themilkman216 (PR968). Prepared by Andrey Mas with substantial GPT-6 Pro research through ChatGPT and Codex coordination, packaging and local replay; Apache-2.0.