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Prove sharp Walsh rounding error with one interleaved integer shear (No new κ) - #6146
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Mister-Meeseeks merged 1 commit intoOct 28, 2026
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Prepared for @CubeJerry with substantial OpenAI Codex assistance. No new kappa; credits and scope are in the research package.
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Prove sharp error h*(|m|+3)/4 for two distinct normalized real Walsh stages with one exact integer shear: all 12 directed pairs, every integer m, all grid inputs. A unit shear raises 3h/4 to h. Written parity proof and 24 affine witnesses answer PR6140's open question beyond PR6129's pure-stage law; neither predecessor is incorrect. No new κ.
Base: 721c038 (canonical main re-fetched 2026-10-28 14:59 UTC).
Published: 2331c10; complete tree a077fc07d6cf85ab8fff180f6459645cb4a29811 matches the tested tree. Only the new 11-file package changes.
Context pins: PR6129 f496734; PR6140 1c97110. Exact document blobs/SHA256, proof, seed 83, domain, stopping rule and source credits are in the package.
Reproduce (Python 3.12, standard library):
python3.12 -B scripts/research_package.py --package research/walsh-interleaved-shearExpected: PASS_WALSH_INTERLEAVED_SHEAR in normal/-O modes, PASS_WALSH_SHEAR_ARTIFACT_CONTROLS, then PASS_REGISTERED_RESEARCH_PACKAGE.
Executed: independent integer and rational/dense-matrix engines compare complete vectors on 196608 residue cases; 24 witnesses, 2051 signed rounding cases, 768 period/coefficient cases, 2916 reversed-axis cases. Sixteen semantic/domain/certificate controls and four actual-CLI artifact corruptions reject. Certificate regeneration is byte-identical. Metadata, committed bytes/modes/source ancestry, official export integrity and Git-free optimized export replay pass; all exported bytes/modes stay unchanged. CPython 3.12.14, Linux x86_64.
Scope: real grid, two distinct axes, one integer off-diagonal shear, exact pre-round arithmetic and sufficient range. More stages, complex/nonintegral/multiple shears, overflow, physical costs and an actual selected caller remain unproved. All five selected framework assumptions remain. No selected cold replay, hosted CI, human review or formal proof-kernel acceptance claimed. Coordination claim/result recorded locally; Discussion posting unavailable.
Prepared for @CubeJerry with substantial OpenAI Codex assistance. Credit Nick Petalas (#6129/#5912), Josie Elliston (#6140), CubeJerry (#6119), Vlado Vojdanovski (#1673), Sricharan Vagvala (#1631), repository tooling and retained lineage. Apache-2.0.
Research package, proof and exact pins