Strong permanent inequalities for complex positive semidefinite cycle and single-chord supports
Scott Schubr, Luminary Oddities LLC
22 October 2026

This paper proves the strong self-conjugate permanent inequality
  per(A o conjugate(A)) <= per(A) product_i A_ii
for complex Hermitian positive semidefinite matrices supported on cycles of length at least four, or on theta graphs with path lengths 1,b,c, where b,c>=3 and b+c>=7. It also proves the corresponding hereditary block-closure result using the credited known one-point mechanism.

The result allows arbitrary phases, unequal edge magnitudes, singular matrices, and missing edges. It does not resolve unrestricted Chollet or the unrestricted Bapat-Sunder inequality. The paired consequence requires each input to meet a proved self-domain.

The paper contains analytic proofs. No computational certificate or external code is needed to verify the stated theorems. The accompanying TeX source compiles with standard LaTeX packages (amsmath, amssymb, amsthm, mathtools, geometry, hyperref). References and exact theorem hypotheses appear in the paper.

Archive contents:
  Strong_Permanent_Cycles_and_Single_Chords.pdf - complete paper
  manuscript/main.tex - complete editable source and bibliography
  README.txt - these reader instructions
  MANIFEST.sha256 - SHA-256 identities of the three files above

To rebuild with a standard LaTeX installation, run the following command twice
from the extracted archive directory:
  pdflatex -interaction=nonstopmode -halt-on-error manuscript/main.tex
The rebuilt document is main.pdf. Alternatively, run:
  tectonic manuscript/main.tex
No BibTeX step, external data, or accompanying code is needed.

The manifest excludes its own checksum. A checksum comparison verifies file
identity; mathematical correctness rests on the arguments in the paper.
