Audit ten PR3114 departure obstructions with independent minors

[josecarlosgonzalezroque-design]

Change and mathematical scope

Independently reconstruct ten departure obstructions in Marius-Paul Dumitrean's #3114: the eight registers that cannot replace a (2,2) restore climb with (1,3), and departure-forced visits 69/444. On each pinned PR3042 provider word, 27 candidate frames split into 17 with no reader and 10 with explicit nonzero rational minors. The receipt also exposes null vectors showing why the restricted-row test loses rank.

One isolated package, research/rank7-departure-minor-audit/. Its separate implementation checks all 91 forced-coordinate identities against a 520-row non-target prefix, derives frame intervals through finite-set dataflow, and emits determinant witnesses without importing predecessor proof code, optimizers or certificates. The source proof and code were read first; independence means separate implementation, not a blind audit or a new lemma.

This is partial independent coverage of the fixed-A/B, fixed-end claim. The complete empty-restore optimum, remaining blocked/zero-sum/lift charges, physical invoice, supplier admission and selected cold replay remain outside scope. No new κ is claimed.

Task and overlap

• Base: canonical main 997e6a9ca7b4f95d50e366f61412fd640d72a88a, refreshed unchanged; priority revision 6.
• Card independent-moment, scope key c191650c0fa8d2fa514e, refined. The original card and bounded pivot are preserved in TASK.json.
• Claim reviewed: research: restore-only optimum for PR #3042's six-skip words (scoped exact negative, no new κ) #3114 at c88769c350977d9ed4f90fe5c652d582cfe2782a. Only the two frozen Conditional κ = 0.001729736166387916: six restore carrier/pivot skips (R1_E42, R2_E7) on PR2979's words and literal allocation #3042 words are computational inputs, with Git/SHA256 pins.
• test(research): independently audit the six restore skips #3050 already covers the restore-splice audit initially considered, so that duplicate was stopped. Contract PR3042's four-ADD restore block to three #3056 concerns a local contraction; Prove the complete restore-frame optimum of the six-skip words #3057/Prove the complete joint A/B/restore frame optimum #3065 concern frame optimization with fixed scalar order. The new coverage is an independently reconstructed set of ten explicit minors and associated failure witnesses.
• Handoff/start-here/active Discussion pages and targeted live PR searches were inspected. The offline helper had sparse local coverage and no remote cache; Discussion pagination and arbitrary code diffs were not exhaustive. research(rank7-coupled-586-588-carrier-fold): lower helpers 586 & 588 via coupled B+restore carrier folds (κ = 0.0017297760894) #3133 changes helper endpoints and B routing, outside this audit's fixed hypotheses.

Validation

CPython 3.12.14 on Windows, standard library only:

python3.12 -B scripts/research_package.py --package research/rank7-departure-minor-audit --check-only
python3.12 -B scripts/research_package.py --package research/rank7-departure-minor-audit
python3.12 -B scripts/check_research_commit.py --package research/rank7-departure-minor-audit

All pass. The registered replay checks both providers, exact receipt equality and eight behavioral test groups under optimized Python. Controls include a separate rational determinant algorithm, singular minors, corrupted bytes, empty restore, wrong coefficients, changed prefix, target feedback, singular scalar gates, inconsistent cut equality and a deleted required coordinate. The published commit's tree and all nine package/input file bytes match the tested local tree.

The selected baseline orientation command was attempted but stopped at the absent selected ASSEMBLY.json in this sparse checkout; no baseline PASS is claimed. The finite checks accompany the written inverse-column proof; they are not formal verification of the full theorem. Hosted CI has not been claimed.

Credit

Credit Marius-Paul Dumitrean for #3114's departure lemma, cases and original row-restriction control; dcharb78 for #3042; and the #2979/#3015/#2917/#2908/#2833 lineage. Nick Petalas's #3050/#3056/#3057/#3065 audits delimit overlap. Full attribution is in the package README; existing source archives are unchanged.

Prepared for josecarlosgonzalezroque-design with substantial OpenAI Codex assistance in analysis, implementation, testing and writing. No separate-agent, independent-human or proof-assistant review is claimed. New work is Apache-2.0.

Open next questions

See the package's next questions and TASK.json. The smallest follow-up toward the full claim is a separate reconstruction of the empty-restore optimum and remaining disjoint charging groups. For a changed A/B or helper-end word, first recompute the affected coordinates and frame intervals before reusing any witness.

Workflow feedback

The acceptance gate prevented duplicating #3050 once the broader search found it. Sparse checkout kept the bounded local audit small, but the offline overlap helper had limited coverage without a remote cache; that limitation is recorded explicitly.