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Nearest coefficient rounding attains quadratic closed-word error - #5308
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Mister-Meeseeks merged 1 commit intoOct 23, 2026
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This scoped lower construction answers the deterministic-rounding question in PR #5153. Nearest rounding of a fixed rational shear coefficient produces error proportional to the square of the exact prefix envelope. It applies to unchanged emitted words; a compiler can remove the symbolic zero loops. The complete kappa calculation is unchanged.
Proof and scope, exact checker, replay declaration, and source provenance are pinned to the reviewed commit. Base: canonical main
ff3cc58e370d0f678e529246f8c73e8094e18fcf, priority revision 7.The initial proof and standalone check are in Discussion #5294.
CPython 3.12.14 registered normal and optimized replays passed: 288 cases, 6,876 prefixes, 96 small-error cases and four controls. Both print
PASS_DETERMINISTIC_CLOSED_WORD; the launcher printsPASS_REGISTERED_RESEARCH_PACKAGE. All five package files match their committed bytes, and the base is an ancestor of the package commit.Use Python 3.12 and the standard library. No external runtime inputs or third-party Python packages are required. Hosted planning and the registered package replay passed on this exact head in run 39990269905. No predecessor scientific suite, selected cold replay, native replay, compiler, Lean or Docker build was run. The optional full-history preflight is unavailable in this shallow checkout. Finite checks corroborate the written proof; they do not constitute independent human or proof-kernel acceptance.
Test which exact coefficient relations a production storage policy preserves. Source preparation, native operations, precision, movement, and supplier/outer admission remain separate obligations.
Credit Nick Petalas's PR #5153 for the open deterministic-policy question and the retained sharp-power context, ywz65's PR #2701 for the simultaneous-error theorem, and Vlado Vojdanovski's PR #1673 for the Toeplitz precision interface. Prepared by Ali Romman with substantial OpenAI Codex assistance; Apache-2.0. No independent human or proof-kernel acceptance is claimed.