Strong permanent inequalities for complex two- and three-chord seven-cycle supports
Scott Schubr, Luminary Oddities LLC

Contents
  Strong_Permanent_Multichord_Seven_Cycles.pdf  Complete paper
  manuscript/main.tex                       Editable LaTeX source
  certificate.json                          Exact integer mathematical supplement
  verify_certificate.py                     Exact standard-library verifier
  MANIFEST.sha256                           SHA-256 checksums of the reader files

Read the paper for the analytic lemmas and the exact theorem hypotheses.
The strongest support is C7 with chords 03,15,26; the two-chord 03,15
subgraph inherits matching-loss/50. The crossing 03,14 placement has the
stronger analytic matching-loss/12 bound. The claim is for these supports
and subgraphs, not unrestricted Chollet. Missing edges and singular PSD
endpoints are included. The coefficient 1/50 is not claimed optimal.

Verification (Python 3.9 or newer, no third-party packages)
  python -B verify_certificate.py
  python -B -O verify_certificate.py
Both commands must exit with code zero and print PASS. They write no files.
An optional first argument selects another certificate file. The verifier
reconstructs graph cycles and matchings, convex weights, pair eligibility,
charges and an exact integer/rational polynomial identity. It requires
323 positive integer terms and exactly zero polynomial residual. It does
not replace the analytic cycle estimates and normalization proofs in the
paper. No solver, floating arithmetic, network or private files are needed.

Certificate conventions
Edges use the order in equation (1) of the paper. Cycles are sorted by
length then lexicographically by edge-index list. Mixtures are exact
rational strings. A term's integer_coefficient multiplies the monomial
specified by its ten exponents, and the star slacks at listed vertices
(with multiplicity). The identity is 350 F = sum of these 323 terms.
All other definitions and the target F are given in the paper.

Rebuild the paper with a standard LaTeX installation containing amsmath,
amssymb, amsthm, booktabs, geometry and hyperref. For example:
  tectonic --outdir build manuscript/main.tex
Or run pdflatex twice with a chosen output directory. Compilation is
separate from the exact mathematical certificate check. PDF creation
metadata can differ between builds; compare text, formulas and layout.

The earlier cycle/single-chord paper is cited as the predecessor. This
package contains a self-contained new multichord paper and its necessary
mathematical evidence. AI assistance is disclosed in the manuscript.
