Repository navigation
Whole ordered Schur normal form for the H=1 primary component - #5348
Merged
Mister-Meeseeks merged 1 commit intoOct 23, 2026
Merged
Mister-Meeseeks merged 1 commit into
Mister-Meeseeks merged 1 commit into
Conversation
This file contains hidden or bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment
Add this suggestion to a batch that can be applied as a single commit.This suggestion is invalid because no changes were made to the code.Suggestions cannot be applied while the pull request is closed.Suggestions cannot be applied while viewing a subset of changes.Only one suggestion per line can be applied in a batch.Add this suggestion to a batch that can be applied as a single commit.Applying suggestions on deleted lines is not supported.You must change the existing code in this line in order to create a valid suggestion.Outdated suggestions cannot be applied.This suggestion has been applied or marked resolved.Suggestions cannot be applied from pending reviews.Suggestions cannot be applied on multi-line comments.Suggestions cannot be applied while the pull request is queued to merge.Suggestion cannot be applied right now. Please check back later.
This enabling proof gives an explicit normal form for the entire ordered Schur residual when I-H is nilpotent. It proves exact sector-capacity conditions and removes all sector00 factor data by an explicit coordinate map, even when the original splits are inequivalent. The sharp-sector criterion remains a cited premise. 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.CPython 3.12.14 registered normal and optimized replays passed: 2,577 candidate factor pairs, 360 complete-domain residual intertwiners, 11 padded basis changes, 16 higher-block fixtures and five controls. Both print
PASS_UNIPOTENT_ORDERED_SCHUR; 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 40001909184. 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.
Prove a source-bound general-H gluing statement before using primary-component normal forms to identify arbitrary ordered residual states. Source preparation, native operations, precision, movement, and supplier/outer admission remain separate obligations.
Credit @ssafwann's PR #5267 supplies the nilpotent-H comparison, exact sector equations and explicit full-rank extension specialization in its proof. @MatShep's PR #4762 supplies the arbitrary factor-system extension and realizability theorem in its proof, extending codyw912's argument. @petalas's PR #4746 sharp-sector criterion is used in exactly the form stated and credited in the pinned nilpotent proof. @aliromman's PR #5287 already determines the whole central class in its proof; it leaves the ordered pair open. The broader Schur and normalizer lineage retains its source credit. Basis extension and nilpotent Jordan methods are classical.
Prepared by @aliromman with substantial OpenAI Codex assistance; Apache-2.0.