Audit Gaussian chirp domain and exact block budgets

[ineffyble]

The Gaussian chirp construction already replaces the broad upstream no-sort hypothesis with alpha^-2 <= theta <= 1/4 before inserting the new lemma. This research note / mathematical audit resolves the domain caveat in PR #371 at its pinned head and verifies the associated integer-window and sufficient-precision arithmetic. No new kappa is claimed.

The distinction has a concrete control: p=101, alpha=2, s=2, t=19 satisfies the old header, but the new E-window recipe would omit q_1=10 from a block computing only 0,...,7. The actual generated domain rejects this tuple. This is not a counterexample to the original slower theorem or to the restricted generated construction. PR #371's separate grid-rounding defect remains genuine; this audit does not incorporate its correction.

The new package includes written uniform arithmetic arguments, source and generated-manuscript SHA256 pins, a deterministic receipt, and two independent standard-library arithmetic implementations. The main command checks 21,773 parameter pairs, 968,049 generic correction-window cases plus forward-window residues, and seven negative controls. The second implementation checks 168,093 pairs and five controls using a different exact window-ceiling formula. Finite checks are explicitly distinguished from the written universal arguments and from a formal proof.

Base: 66849e1475c930fd7732b1a0067ffee7e1e95f60. Audited PR #371: 988ef67986c313445936fc7103908b6163b9d47e; its generator and upstream resampling file were checked byte-for-byte against the base. The accepted #626/#543 certificate remains unchanged. All additions are confined to research/gaussian-chirp-domain-audit/.

Validation passed:

python3 -B research/gaussian-chirp-domain-audit/verify.py
python3 -B research/gaussian-chirp-domain-audit/independent_budget_check.py
make selected-record-check
git diff --check

The first command prints PASS_SCOPED_GAUSSIAN_CHIRP_DOMAIN_AUDIT; the second prints PASS_INDEPENDENT_GAUSSIAN_BUDGETS pairs=168093 controls=5. Tested with Python 3.14.7. Gaussian tails, the internal error enclosure, transcendental approximation, packing, tape movement, Neumann evaluation and the full multiplication theorem remain outside the audit. This is scoped evidence for #371's review, not certification of the entire PR.

Assignment seed 64, adversarial mathematical audit. No pinned or other sprint coordination issue existed, so the claim is recorded locally. A final refresh of 500 open PRs found no overlapping audit; #479/#481/#489 address distinct Gaussian mechanisms.

Credit eumemic's fast-Gaussian construction, icekylinx's shifted enclosure, Artus Krohn-Grimberghe and PR #371's disclosed GPT-6 Pro/Codex rounding work, and Harvey–van der Hoeven's analytic algorithms. Contribution by Effy Elden (ineffyble), with substantial OpenAI Codex assistance including a separate AI source/arithmetic reviewer; no human peer review or formal verification is claimed. Apache-2.0 and predecessor notices are retained.

[Mister-Meeseeks]

Integrated at ee055dc44815497927ef618fc985b93c2dcbda2a in the 20-PR pilot, retaining your original commit, source notices and contributor credit.

Restricted generated Gaussian chirp domain and integer-window/precision arithmetic. Scoped source and arithmetic replay passed; #371 grid-rounding issue remains separate. Full analytic error/tape theorem outside scope.

The scoped package check passed at 14dd937d9e2d3e51092c0c35a8c2c9cdf8ba81f4. This is research integration; the selected κ and inherited theorem assumptions are unchanged. Review, evidence and attribution. Thank you for the contribution.