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Regular degree-18 endpoint capacity verifier v1

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@AlecKriebel AlecKriebel released this 24 Jul 19:46
ramsey55-endpoint-capacity-v1
26d4fbb

Regular degree-18 endpoint capacity theorem and verifier

Superseded for packaging by
v1.0.1.
The mathematical result and frozen classifications are unchanged. Use
v1.0.1 for repeat-run and source-checkout reproducibility.

This compact release preserves the catalog-conditional exclusion of the
regular degree-18 endpoint
[
(e(A),e(H))=(85,128)
]
for a hypothetical ((5,5;43))-graph.

The reusable mathematical ingredient is a minimum-miss transversal-capacity
inequality. Applied to the two pinned published catalogs, it excludes 61,939
of 62,382 fixed-side pairs strictly. The remaining 443 equality cases are
eliminated by uniqueness of one size-six minimizer and a forced
high--high-edge contradiction. Conditional on the published catalog
completeness statements, every vertex of an 18-regular ((5,5;43))-graph
therefore lies in at most 84 triangles.

The attached archive is self-contained, standard-library-only, and independent
of the multi-gigabyte research history. It includes:

  • the standalone theorem and proof;
  • a focused primary-source novelty review;
  • the two byte-pinned source catalogs and their provenance;
  • the deterministic producer, independently written checker, and 17 tests;
  • the complete 62,382-line classification stream; and
  • a one-command verifier.

Run python3 verify_bundle.py from the extracted directory. The clean replay
completed in about 67 seconds with peak memory below 150 MB and returned
"valid": true.

Integrity identifiers:

  • source research checkpoint:
    b14f50dd3b048b2d0e51e6aabd63bb608662f053;
  • compact release commit:
    26d4fbbb2a5f0c3829507d9a38d80ec1fdf4e726;
  • bundle manifest SHA-256:
    17a02f86268dd7682813b263120f6f0dccca4bb97701c87248203aeb567af2be;
  • archive SHA-256:
    f73b9b3d61e4b831623c36a0bc99ee769cd6bb11a9699704e00ac6403853624d.

Scope: this closes only the ((85,128)) endpoint layer. It does not close the
remaining regular degree-18 layers, determine (R(5,5)), or improve the
current bound (43\le R(5,5)\le46). The focused novelty review found a
positive but moderate novelty signal, not proof of global priority.

Assets 3
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