Strong permanent inequalities for three-row bipartite and triangle-free supports
Scott Schubr, Luminary Oddities LLC

The PDF is the reader-facing paper. manuscript/main.tex is its complete editable
LaTeX source. Compile it with a current TeX distribution supporting amsmath,
amssymb, amsthm, geometry, booktabs and hyperref, for example:
  pdflatex -output-directory manuscript manuscript/main.tex
Run LaTeX again to resolve references. Tectonic is an alternative compiler.

The three-row theorem is analytic. For the two finite supplements, Python 3.10+
with its standard library is sufficient. From this directory run:
  python -B verify_nonadjacent_certificate.py
  python -B classify_trianglefree.py
Both programs print their results and write no files. They may also be run with
python -O -B. The first checks the exact 119-term positive integer identity,
38 matchings, six cycles, mixture coefficients and triple matching budget.
The second enumerates all labelled triangle-free seven-vertex graphs, tests
maximality and exhaustive degree-preserving isomorphisms to six representatives.
The manuscript proves the analytic reductions; code output alone is not the proof.

nonadjacent_certificate.json supplies the exact polynomial identity. All rational
mixtures are strings and are parsed exactly. No optimizer, numerical tolerance,
third-party graph library or private research file is required.

The triangle-free corollary explicitly uses one previously published theorem:
Strong permanent inequalities for complex two- and three-chord seven-cycle
supports, first edition, cited with its public archive link in the bibliography.
Its adjacent-doubled pentagon result is a credited dependency, not a new result
or a claim that this ZIP contains that earlier paper's complete certificate.

Scope: arbitrary complex phases, missing edges and singular/zero-diagonal PSD
endpoints in the stated classes. No K4,4 or unrestricted Chollet claim.
AI tools assisted drafting and verification; this is not external peer review.

MANIFEST.json records the public payload inventory and SHA-256 identities.
SHA256SUMS records the payload and manifest hashes; it omits itself.
Private assessments, correspondence, privacy gates and release records are not
part of this public supplement.
