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Regular degree-18 endpoint capacity theorem and verifier v1.0.1

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@AlecKriebel AlecKriebel released this 24 Jul 22:28
ramsey55-endpoint-capacity-v1.0.1
b6d7f1a

Regular degree-18 endpoint capacity theorem and verifier v1.0.1

This corrected packaging 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 mathematical result and all frozen classifications are unchanged from
v1.0. The packaging is hardened so that the one-command verifier works both
from a Git checkout and after repeated runs: it ignores only Git's private
.git metadata and interpreter-generated __pycache__/*.pyc or .pyo files,
while continuing to reject every other unlisted file. The deterministic
archive builder applies the same exclusions.

The reusable ingredient is a minimum-miss transversal-capacity inequality.
Applied to the two byte-pinned published catalogs, it excludes 61,939 of
62,382 fixed-side pairs strictly. Equality rigidity eliminates the remaining
443 pairs. Conditional on the published catalog completeness and extremal-edge
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 and a separately implemented checker;
  • the complete 62,382-line classification stream;
  • 17 focused semantic tests; and
  • a one-command clean-room verifier.

Run python3 verify_bundle.py from the extracted directory. The final replay
returned "valid": true, reproduced every frozen artifact byte-for-byte, and
passed all 17 tests.

Integrity identifiers:

  • source research checkpoint:
    b14f50dd3b048b2d0e51e6aabd63bb608662f053;
  • compact release commit:
    b6d7f1a87382d63debeb8c96c76caa230e44331d;
  • bundle manifest SHA-256:
    7aac9cf56dad8787bef798dc7507ca437ec2e662645d77f7ddaf565932e671fe;
  • normalized archive SHA-256:
    de541d6c7ed8be496784397ea0ee3f1b12c2b93cdbc42ba908160095c1d79cc4.

The archive was rebuilt twice and was byte-identical. It contains no .git
metadata or generated Python cache files.

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.

Version v1.0 remains mathematically valid when used as a clean extracted
archive, but v1.0.1 supersedes it for source-checkout and repeat-run
reproducibility.

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