Independent audit: nonlinear dirty restoration and exact PR628 leaf count

[0xkilgore]

Change and mathematical scope

Independent verification; no new κ. PR628's balanced dirty commutator allows 4*n*n primitive calls. This standalone audit proves the exact count C(n)=3*q*n-2*q*q, where q=2^floor(log2(n)), with sharp supremum 9*n*n/8. The exact count can replace the conservative allowance in the inherited execution-error budget; asymptotic precision and pass orders remain unchanged. At n=62, it accounts for 3904 calls instead of the allowance of 15376.

An independent free-term interpreter checks the pinned recursive dispatcher with arbitrary deterministic nonlinear leaf functions. A separate free noncommutative algebra checks the ideal linear product without assuming factor commutation. The written induction confirms exact source/scratch restoration, target independence and inverse-word ordering under the stated primitive contract. No defect was found in this scoped obligation. A concrete example distinguishes exact scratch restoration from independence of the output increment from initial dirt, corroborating PR628's caveat.

The subject is Chafik Boukhalfa's #628 at 0768f97d06c623b8211e651543c66135796b62bf; its dispatcher and notice are retained byte-for-byte for offline replay. Base commit: 66849e1475c930fd7732b1a0067ffee7e1e95f60. Source pins, predecessor credit, track/seed 62, bounded coverage, overlap review and the completed local claim are in research/dirty-commutator-audit/.

This adds evidence distinct from #628's dense rational accuracy tests. It does not re-audit rounded leaf accuracy, coefficient preparation, bit/tape costs, routing, full-transform composition or multiplication. No selected pointer, existing generator, or upstream/ file changes. No priority or formal theorem certification claim is made.

Validation

python3 -B research/dirty-commutator-audit/verify.py --check

Expected: PASS for 64 symbolic factor counts, 10,000 exact recurrence cases, seven instruction/interface rejection controls, and a nonlinear dirt counterexample.

The same check passes under optimized Python and from a relocated standalone package with isolated imports. Corrupt vendored input and corrupt expected-certificate controls both fail under isolated optimized Python. The unchanged selected-record integrity check and staged whitespace check pass. Python 3.14.7/macOS, standard library only; no remote CI or repository-wide regenerating suite pass is claimed.

The finite symbolic checks support the separate written all-n proof; they are not a formal proof of the multiplication theorem. Prepared for @0xkilgore with substantial OpenAI Codex assistance, including a separate mathematical reviewer. Apache-2.0; PR628's attribution and assistance notice are preserved.

[Mister-Meeseeks]

Thank you @0xkilgore. This contribution is now retained on main in the scoped 100-PR review and contributor credits.

Contribution: Independent nonlinear dirty-restoration audit and exact leaf count.

Review and limits: Exact scratch restoration differs from output-increment independence from initial dirt. The symbolic/count argument preserves that distinction and changes no asymptotic order.

The complete original source, notices and relevant execution evidence are retained through the pinned source archive. The review distinguishes fresh local runs, source-bound historical Linux CI and prior exact-head review; it does not claim 100 fresh full mathematical audits. Closing this historical PR as reconciled. This preserves parallel and cumulative credit without replacing the selected frontier or promoting priced research targets to completed constructions.

Reviewed head: e0e546fd01b396478c68b6b6c5a16d87515983ba. Publication: 64039f1bd3b6a523b96083fd858ad040a75e3030.