Repository navigation
Exact dirty-fanout source counts over finite associative rings - #5310
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Outdated suggestions cannot be applied.This suggestion has been applied or marked resolved.Suggestions cannot be applied from pending reviews.Suggestions cannot be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 extends the finite-commutative source-count criterion to every finite associative unital ring. The minimum is zero for zero demand, one for a nonzero principal left demand ideal, and two otherwise. It gives restoring constructions and a noncommutative left-versus-right ideal discriminator. 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 #5300.
CPython 3.12.14 registered normal and optimized replays passed: 1,825 demand lists across six ring/row contexts, including 120 nonprincipal demands and 38 elementary source orbits. Both print
PASS_FINITE_RING_INSERTIONS; 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 39990770611. 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.
Price one concrete noncommutative realization, including native coefficients and movement. Source preparation, native operations, precision, movement, and supplier/outer admission remain separate obligations.
Credit lee-phys's PR #5139 and pinned finite-commutative proof, Nick Petalas's PR #4916 and noncommutative gate contract, Ross Richardson's PR #3121, and Ali Romman's Discussion #5266 and Discussion #5269. Their ideal invariant, restoring echo, matrix-ring case and model retain their credit. No general ring-theory priority is claimed.
Prepared by Ali Romman with substantial OpenAI Codex assistance; Apache-2.0.