Border-strip Lorentzianity counterexamples

This repository verifies an infinite straight-column family of counterexamples to Conjecture 5.3 in:

Candice X. T. Zhang, Newton polytopes of immanants of some combinatorial matrices, arXiv:2604.06615v2.

The smallest convenient certificate uses the column $(1^{10})$, $\theta=(10)$, and ten variables. The Hessian of $\partial_1^8 N(E_{(1^{10})}^{(10)})$ has exact inertia $(2,8,0)$.

Run the three independent exact checks:

python3 verify_column_family.py
python3 verify_from_jacobi_trudi.py
python3 verify_full_expansion.py

The first starts from the published border-strip power-sum formula and literally expands the four required coefficients. The second starts from the Jacobi--Trudi definition and independently enumerates the contributing permutations. The third expands $E_{(1^{10})}^{(10)}$ completely in ten variables (all monomials, no coefficient shortcut), builds the full Hessian of $\partial_1^8 N(E_{(1^{10})}^{(10)})$, and computes its exact inertia from the characteristic polynomial; it also confirms that the same polynomial in nine variables still satisfies the Hessian condition, so the failure genuinely requires the tenth variable.

The proof is in paper/main.tex; COLUMN_FAMILY_PROOF.md is a compact derivation.

The compiled note is counterexamples-border-strip-E-polynomials.pdf.

Every push runs all three checks in CI, and every tag v* publishes a GitHub release containing the verification log and SHA-256 checksums of the scripts that produced it.

The verification scripts are released under the MIT license in LICENSE-CODE.