The proof note uses the same established structural results as the dimension 9 and 10 packages:
- Hwang's positive-maximizer theorem for the Dittert functional.
- Cheon and Wanless's exclusions of partly decomposable maximizers and of a complete zero set consisting of one proper rectangle.
- Li's cut characterization of doubly superstochastic matrices.
- Hwang's permanent minimum at the barycenter of a staircase face.
- Minc's averaging theorem for the doubly stochastic face with two independent prescribed zeroes.
- The van der Waerden permanent theorem and equality case.
Full citations are in the proof note. The support-stationarity equation, large-column support argument, and grouped line-sum deficit argument are proved directly there.
The primary and independent standard-library programs check:
- the two-zero equalization and permanent bound;
- both safe marginal intervals;
- all six large-column support cases on the remaining interval;
- seven grouped subset-deficit inequalities and their localization checks;
- all 21 proper tight cuts, including the six exceptional one-dimensional cores; and
- all staircase-face barycenter counts used in those arguments.
The independent program imports no primary-verifier code and reconstructs the key polynomials from exact values. No floating-point number is used in a proof decision; printed decimal approximations are diagnostic only.
These materials are an exact computer-assisted working proof, not a claim of
completed journal peer review. The repository now has working-proof packages
for every dimension 4 <= n <= 16; the n=6,7 entry is an attributed
reconstruction of Hongyuan Lu's source argument. See the root
PROOF_STATUS.md for the complete all-dimensions source map and review status.