research: prove P104 whole-fiber coverage and helper-sharing gate

[Clear1nsight]

PR3954 rejects the full proposed two-axis P104 scaffold, but leaves changed coverage and helper ownership open. This study proves that pruning whole 104-port row/column calls cannot rescue its unchanged conditional profile, and identifies exactly what a sparse changed-profile candidate still owes.

For a row calls and b column calls, whole-word support touches N=104(a+b)-ab data pairs and leaves 104(a+b)-2ab one-sided endpoints. Without a replacement completion, the retained two-shear endpoint is incidence-closed only for the empty set or all 208 calls. Even granting all touched initial rank credits and zero new boundary overhead, the unchanged profile has excess 160(a+b)+ab>0 for every nonempty mask. Reducing helper-owner inventory does not change this numerator while the named all-role endpoint and per-call progress hypotheses are retained.

The new asymmetric-profile four-corner criterion distinguishes a sparse relaxation from a completed caller. A hypothetical excess 100 per axis gives a two-call relaxed excess -7, but leaves 206 dangling endpoints; the full closed caller has excess 9,984. No changed profile, legal shared-helper schedule, native physical completion, supplier or new kappa is claimed. The selected frontier is unchanged.

Adds only research/p104-coverage-gate/ (10 files). PROOF.md states the conditional progress assumptions, physical-boundary obligations and reopening criteria. This is a changed, user-assigned refinement of p104-side-correction, priority 6. Credit is retained for Rohan Arun's #1972 word, #1991 native realization, #3882/#3894/#3940 corrections and caller context, #3954 scaffold/gate, and the distinct #3045 private-COPY and #3943/#3956 consumer/adapter studies. Substantial OpenAI Codex multi-agent assistance is disclosed.

Validation at final head f7572974ac7fbcd21fd71c73b64bca0c8487aed6, tree 1edafdb794cafae16bfdb2ae9304b97bf0b13670, Python 3.12.3:

• Registered metadata and replay pass: canonical-source native recount, all 11,025 count masks, separate explicit 21,844-mask/operator/rational-corner checker, and seven optimized-mode tests including six actual CLI receipt/source mutations.
• Exact committed bytes and source-history availability pass for all 13 declared package/input files; all declared source history is canonical main 20ecf2891d80b5acf18d980b2164fb44ea7faa90.
• Committed export integrity and read-only Git-free replay of all three commands under -O pass; all 14 exported files retain their bytes and read-only modes. Archive SHA256: 7c0d2e2b997d1e01d697599ef8fb4dd5504d89570433f8f1edf8268eb22d99ac.

The initial cold export caught copied read-only fixture permissions in destructive tests. The second commit restores write permission only on private temporary copies. Scientific inputs, proof and result are unchanged. Final-head hosted CI passes, as recorded below; no human/kernel or selected cold review is claimed.

python3.12 -B scripts/research_package.py --package research/p104-coverage-gate
python3.12 -B scripts/check_research_commit.py --package research/p104-coverage-gate --check-source-history

Canonical investigation. Main and live overlap refreshed before publication; scoped claims preserved. Entry checks covered all 662 open PR bodies including drafts over seven pages, the repository helper and bounded live Discussions; the latest-100 delta found distinct P112 PR3960, updated PR3577 and sibling boundary PR3961. Full Discussion/closed/diff coverage is unclaimed.

Open next question: supply a changed partial-port word or paid completion for each dangling endpoint, with actual chart/encoded owners and a favorable full bill; or exhibit a changed translated-progress law. A sparse rank pass alone does not supply a caller. Full credit, source pins and precise blockers are in README/PROOF/TASK. Prepared by Clear1nsight with substantial OpenAI Codex assistance; Apache-2.0. No merge, closure or selected-frontier change.

Upstream run39214483909 passes on first attempt at exact final head f757297, tested at merge36ad0688b5a89889af1a261b59efdf3619e8f675 against unchanged main20ecf2891d80b5acf18d980b2164fb44ea7faa90. Planning, all three registered commands and committed-input preservation pass on Python3.12.15. The logs confirm all11,025 count pairs,21,844 explicit masks and all seven optimized test groups with six actual CLI mutations. Sibling #3961 addresses the encoded boundary, and #3965 audits literal private-copy retirement. The three scopes remain separate; no supplier admission or frontier change follows from execution success.