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A strong Chollet inequality for all simple graph Laplacians (v1)

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@mxym mxym released this 08 Oct 09:39
Immutable release. Only release title and notes can be modified.
laplacian-chollet-general-v1
1336b63

This release packages a complete traditional proof of the strong Chollet inequality for every finite simple undirected unweighted graph, together with its independent mathematical review and final-copy check.

Let L_G be the graph Laplacian and S any vertex subset. With degrees taken in the original graph G, the theorem is

per(L_G[S] ∘ L_G[S]) <= per(L_G[S]) product_{v in S} deg_G(v).

The empty permanent and empty product are both 1. In particular,

per(L_G ∘ L_G) <= per(L_G) product_v deg_G(v) <= per(L_G)^2.

The statement includes all principal submatrices, disconnected graphs, isolated vertices, singular Laplacians, and the empty principal matrix. It proves the all-graph strong and self-Chollet statements posed in Section 6 of Pant–Singh, Structural Classes for Chollet's Permanent Conjecture, arXiv:2604.24192v2, and strengthens the strong statement to every principal submatrix. It does not assert a theorem for arbitrary Hermitian PSD matrices or arbitrary weighted graph Laplacians.

The quantified proof explicitly imports Lieb's block permanent inequality and Edmonds' matching-polytope theorem. It handles cycle and bridge cases and closes under vertex coalescence. All bounded exact computations in the package are auxiliary diagnostics, not proof premises. The independent audit and final-copy gate record the complete mathematical review and the final text's binding to the reviewed candidate. This is independent AI mathematical review, not external human peer review, Lean verification, or certification of historical priority.

Version binding:

All 16 original source files were downloaded from this fixed commit and checked against their SHA-256 digests and byte counts. The source archive retains the supplied directory layout, full proof, frozen candidate, final-copy diff, complete audit, and diagnostic scripts/results byte-for-byte. It is newly generated Release packaging with sorted entries, fixed tar mtime and uid/gid of zero, and fixed gzip mtime; two serializations produced identical bytes. Its archive hash is recorded in the separate Release asset checksum list, not in the original source manifest.

Uploaded asset Bytes SHA-256
2026-10-08-laplacian-chollet-general-v1.tar.gz 26154 c699adeb376b0d2609216138fae299ae33cd363b8d85925d81e09c72629c870d
proof.txt 11538 1ca73b56a67af220a63cb8599678fe5aca757403d766bdf2c961eaa18e99f70a
MANIFEST.json 6419 dd85fc03ef3405be0f2b9cf262c1905970a420219696bccc313b90544a796d42
SHA256SUMS 1551 7418250e1029eb7ab973c89acdfc42173e35e53dfab0ca56ac1c193e3e952e16
SHA256SUMS_ASSETS 346 fcfc46f8d1914079a37d4d77eea4642f131285674229bf2bb5141241a3310355

proof.txt, MANIFEST.json, and SHA256SUMS are unchanged original source files. The original SHA256SUMS uses paths relative to the extracted package root. SHA256SUMS_ASSETS is a separate flat-filename checksum list for the archive and these three attached original files; it excludes itself to avoid recursion. GitHub's automatically generated repository source archives are separate from these five uploaded assets.

The complete proof can be read without running any program. For optional bounded diagnostics, use Python 3.10 or later in a writable extracted copy:

tar -xzf 2026-10-08-laplacian-chollet-general-v1.tar.gz
cd laplacian-chollet-general
python3 -B source/verify.py
python3 -B laplacian_chollet_independent_audit_20261008/check_exact.py
sha256sum --check SHA256SUMS

Keep the supplied directory layout and run without -O; the programs use assertions and regenerate their adjacent JSON files. The frozen source package records previous executions of this publication layout that reproduced the supplied diagnostic results byte-for-byte. This Release task verified source and archive bytes; it did not rerun those mathematical diagnostics.

After publication, GitHub's immutable-release mechanism locks the tag/commit binding and uploaded assets. Its signed release attestation can be checked with a current official GitHub CLI:

gh release verify laplacian-chollet-general-v1 --repo mxym/math
gh release verify-asset laplacian-chollet-general-v1 ./2026-10-08-laplacian-chollet-general-v1.tar.gz --repo mxym/math

The same verify-asset command applies to each attached file. This is GitHub platform signature and timestamp evidence for the packaged bytes; the unchanged source documents do not assert an author-held signing key. No new license or personal authorship assignment is added.

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