CK degree-zero descent: publication release

8 September 2026. Publication edition 1. AI-assisted FPRD Lab manuscript; internally audited, not externally peer-reviewed or author-endorsed.

Contents

Result and scope

The packet proves the CK comparison intersection equality for the standard right-tetrahedron/left-edge Laurent presentation and thereby establishes the assertion of Chen-Kricker Conjecture 5.27 in that presentation. The actual PP ambient-image target is used.

The source’s contradictory “left ideal” phrase is disclosed prominently, along with the inverse-generator shorthand. No theorem about the altered left/two-sided closure is asserted. CK supplies the named trace-intertwining theorem; this work makes that existing comparison invertible.

The original six-root peripheral-action extension and Panitch-Romo Conjecture 7.1 remain open. No first-priority claim or claim of a major Dehn-filling breakthrough is made.

Read

CK-degree-zero-descent-publication.pdf: 13-page readable paper.
CK-degree-zero-descent-publication.html: standalone offline reading edition, with embedded KaTeX fonts.
CK-degree-zero-descent-publication.md: canonical editable source.
CK-degree-zero-descent-publication.tex: generated LaTeX source.
hostile-publication-audit.md: independent internal mathematical reconstruction and attempted failure modes.
source-and-priority-ledger.md: fresh primary-source and bounded-priority record.

Reproduce the exact mathematics

With Python 3 and no third-party packages:

python3 verify-ck-pbw.py
python3 verify-ck-weyl-legacy.py
python3 validate-release.py

The PBW verifier is newly implemented for the publication audit; the legacy Weyl verifier is retained unchanged from ATTACK. Neither imports the other. The general theorem is the written grading-and-intersection proof, not an exhaustive computer search or a proof-assistant formalization.

The checked outputs are verification-pbw-output.txt and verification-weyl-output.txt. The new checker verifies all twelve fixed orientation-preserving tetrahedral symmetries; it enumerates no manifolds, triangulations, slopes or skein configurations.

Rebuild reading editions

Requires Node.js, KaTeX, pandoc and XeLaTeX:

node render-publication.mjs /absolute/path/to/katex

The rendering script creates the PDF, generated LaTeX, offline HTML and Site-ready publication-content.json from the same Markdown source, and throws on any math-rendering error. KaTeX’s MIT license accompanies its embedded fonts/CSS. Toolchain versions can affect binary output; the manifest identifies this release’s exact bytes. The script fixes the PDF source date; it does not promise cross-platform bitwise reproducibility.

To record outputs and rebuild the manifest and archive after deliberate source changes:

python3 build-release.py
python3 validate-release.py

Do not treat a rebuild as a new mathematical audit. If the paper changes, repeat the relevant algebra, source and visual checks before updating its review status.

Source integrity

source-snapshots.json lists five freshly downloaded primary PDFs and their SHA-256 hashes. The PDFs themselves are not redistributed. An unversioned author-hosted URL can later change; a different hash denotes a different snapshot. The ledger records exactly which statements were used.

Provenance of the earlier ATTACK inputs:

129e79103a5e3266541bb1e7122e158ab9f8c6c54686b6428306e5581404f558  FPRD-CK-injectivity-and-GY-PP-bridge-candidate-2026-09-08.md
7ef14dca2f226d68042de2f4194dbbe36df582f31a43baab63e26bb7b5fea714  gy-pp-bridge-attack-candidate.zip
273a44f5f2480c8bbf8d8bd4b36d6cf1bd32b29729052f418d976d074bb0854d  verify-ck-weyl-legacy.py

Integration

publication-metadata.json supplies the publication and four theorem records. publication-content.json supplies HTML with math spans for the existing Site renderer. integration-snippets.json supplies conservative public status text. FPRD-research-loop-state-proposed.md is the proposed replacement handoff, not evidence that a deployment has happened.

The mathematical auditor did not edit the Site, use Sites/Library tools or contact authors. Deployment and preservation belong to the parent Site workflow. Retain earlier evidence packets as historical dependencies.

Integrity files

SHA256SUMS.txt covers every payload file. The ZIP includes those payload files and the manifest. ARCHIVE-SHA256.txt and archive-validation.txt sit alongside, rather than inside, the archive to avoid self-referential hashes. The archive checker verifies CRCs, exact member names, all member hashes and agreement with the release files.