DONE: independent R437 bad-class pivot and high-lift audit (#4584)

[mihir-s-05]

Status: DONE / 2026-10-22T08:15:14Z / priority revision 7. Focused PR #4584, exact head cc304c09c48103c20e7c0e2634b22d0aa19aa38a. Claim released.

The scoped proof audit found no gap in #4176 NUMERICAL.md §3 under its declared split-projector, invertible fixed-chart, complete uniform low-cover and unit-weight premises. The new argument connects the low-field principal minors to both literal binary pivot routines, including the full-ring Schur/endpoint condition. Exact finite checks agree; this is author-checked work with an independently written arithmetic reference, not independent human or formal-kernel acceptance. It adds no κ and makes no selected-frontier change.

Public artifact: proof, verifier, receipt and source pins.

Evidence:

• 25,008 exhaustive field/rank cases, checking signed complementary minors, pivot ratios and all diagonal unit weights.
• All 3,888 GL2 lifts modulo 9 and 139,968 lift/unit-weight combinations.
• 61 fixtures through both literal binary Word/Ring routines, plus 20 synthetic 64-dimensional source classifications.
• Controls reject nonunit pivots, a missing intermediate-minor condition, a false split rank, singular preparation and related premise mutations.
• Registered ordinary/optimized replays, metadata/source pins and 14-file committed-byte preflight pass. Official export/integrity checks and Git-free ordinary/optimized exported-byte replays pass. Deliberately changed source and scientific receipt both reject; all 15 exported files are restored byte-identically. Hosted CI is still separate/pending.

Reproduce with Python 3.12:

python3.12 -B scripts/research_package.py --package research/r437-bad-class-pivot-audit

Remaining obligations / handoff:

1. Independently reconstruct Integrate the R437 carrier compiler, numerical invoice and paid local caller #4176's actual split-projector and chart inventory, including COPY's single chart application. First compare generated bases/ranks/charts with independent rational arithmetic; this needs the full source closure and a separately budgeted compiler replay.
2. Bind cover multiplicities and unit ancestry to one actual original-root request and its paid fallback. Start with nonzero high digits through Callback and selected_page; encoded ancestry, stock and the complete physical cost boundary remain open here.

Canonical main was refreshed and unchanged at f626db5c3a3d781d8f7695038776c621651f75e1. Final overlap snapshots covered 358 open PRs and 3,489 Discussion records with complete pagination; sparse local coverage was 35/5,860 notes. James Reed's earlier finite receipt audit is credited and complemented. The selected baseline was attempted but stopped at an omitted sparse package; no baseline pass is claimed. No full selected replay or optional full-history preflight was run.

Credit Chris R / Clear1nsight (#4176/#3950), unpaidmoon (#4147), ai-nanachi, Ali Romman, Sagar Thakrar, Rohan Arun, Jose Manuel / jmbarrancoml, David Arias, Nick Petalas, ywz65 and the retained source/normal-form lineage. Prepared for mihir-s-05 with substantial OpenAI Codex assistance; Apache-2.0.

Original claim: posted before computation for this same bounded question, expiring 2026-10-22T09:51:00Z. The work is now complete within that scope; no continuation claim remains.

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