Audit selected bootstrap stock fit: conditional factor-16 coefficient extension

[ToikY]

Change and mathematical scope

The selected fourteen bootstrap cutoffs leave unused slack in PR1965’s stock-fit proof. This package independently reproduces all seven native and seven conservative stage records/headrooms, then proves that the same cutoffs suffice for σ_j ≤ 2^(H_j+1) under the same uniform stock-envelope hypothesis—16 times its original sufficient cap 2^(H_j−3). The ceiling term is retained: k ≤ e/4 + 1 < e/2 for e ≥ 8. This is a conditional fit lemma and independent arithmetic audit; actual selected stock coefficients remain uncomputed, with no new κ or frontier change.

H is the largest integer log bound admitted by the original guard. That guard is sufficient, rather than necessary for borrowed-stock fit. The README gives the proof and a source boundary: the explicit 57,604 increment belongs to the m=120/four-halving historical candidate; it is not automatically a selected m=73 reserve recurrence. PR185’s completed inner borrowing and its 252 caveat are retained.

Task and overlap

Card independent-moment, independent-verification; scope changed from moment enclosures to one selected assembly stock-fit implication because the selected endpoints already have independent audits. Chooser nonce fe06ff840e600bace63d0bd7005f2525, revision3, scope key c191650c0fa8d2fa514e/selected14-stock-fit. Base 4d3248d. Package: research/selected-bootstrap-stock-audit/. Claim: #1166 (comment).

Nearest predecessor: Josie Elliston’s #1965 at c9819a9, following #1956 at f800395. Its README and receipt are retained unchanged; its checker is neither imported nor executed. The existing pr1407-complex-moment-audit-seed39 package covers selected/pending endpoint arithmetic. This package adds the conditional factor-16 proof and explicit reserve-source boundary; it credits the fourteen headrooms to #1965.

Entry census468 open PR bodies, refreshed433 at 2026-10-14T16:19:53Z, plus direct coordination-board reads. No duplicate extension found in this bounded, non-atomic coverage; no novelty guarantee is claimed. At refresh main808a7815 had the same selected record and guidance.

Validation

Python3.12, standard library only.

python3 -I -B research/selected-bootstrap-stock-audit/verify.py
python3 -I -O -B research/selected-bootstrap-stock-audit/test_verify.py
python3 -B scripts/research_package.py --package research/selected-bootstrap-stock-audit

PASS: fourteen integer-rational reconstructions, separate Fraction closed-form oracle, maximal-H inequalities, seven semantic controls, seven focused test groups with relocated optimized source/manifest/receipt and no-overwrite checks, registered source/metadata replay, and all24 repository onboarding tests. The verifier uses integer pairs and cross products, without predecessor functions, Fraction, float or numerical log/exp. A separate agent reviewed the proof/source reading. Hosted CI and independent human acceptance are not established at submission. No full cold supplier replay or Lean/compiler build was run; frozen inputs and the selected result are unchanged.

Credit

Josie Elliston (Claude Code) supplied #1956’s carry audit and #1965’s split, sufficient guard and headrooms. Rohan Arun supplied PR185/PR387 and the selected PR1094 assembly; Jeremy Kothe supplied PR1087. Eumemic’s finite bit accounting and the retained PR185/PR384 lineage supply the examined contracts. Earlier fixed-allowance checks by Tekalign and Wronskode are credited. Prepared for ToikY with substantial OpenAI Codex assistance and separate arithmetic/source review; no human review claim. Apache-2.0; predecessor attribution retained.

Open next questions

Derive selected per-level row divisors, depth constants and actual uniform σ_j at the real atom widths before comparing them with either cap. Audit any additional “sufficiently large width” condition and H2 uniformity. Maintainers must choose the complete proof wording between #1956 and #1965; this PR changes neither. The README and TASK.json give first steps and blockers.

[Mister-Meeseeks]

Batch review at c3bd90d9a8d9202c063700ae443e83825780e056.

Merged to main, preserving the original contributor commits and package attribution.

Reviewed scope: Independent integer-pair arithmetic reproduces fourteen headrooms and proves a sufficient factor16 stock-cap extension. The written proof retains an unknown selected stock coefficient and rejects importing the historical m120 reserve coefficient into the selected m73 supplier. This corroborates and narrows #1965; no full outer-proof adoption.

The pinned scoped command passed; the batch ledger contains its command, input hashes, environment and log. This incorporates the research/tooling contribution and does not change the selected κ or discharge the inherited multiplication-theorem assumptions.

Batch review, attribution and evidence. Thank you for the contribution.