Independent finite-field verification of a Hankel seed certificate for hyperbolicity cones

Independent reconstruction of Appendix A's prescribed finite calculation over F7 in OpenAI's Hyperbolicity Cones Without Semidefinite Lifts. At the printed point and tangent, the seed has rank 20 and its L restriction determinant 6. All ten weight blocks give ranks (G1,G2,D,border)=(136,84,302,623). All 24 displayed determinant values, 21 corner entries, six direct bordered minors and two signed-pivot examples agree. The primary implementation uses sorted monomial-index tuples and standard-library modular elimination. A separately tasked AI reviewer independently used exponent vectors and SymPy DomainMatrix over GF(7). All 42 canonical matrix fingerprints agree. The implementations share mathematical formulas and certificate JSON for expected minor/basis data; the reviewer independently transcribed the weights, point, pivots and tangent. Twenty-eight tests pass in each Python mode, with ten deliberate rejection runs. No discrepancy was found in this finite ingredient. This is finite computational verification and scoped AI review, not a kernel proof or human peer review. The characteristic-zero lifting, simultaneous real-form/genericity argument, real PSD deformation and final nonliftability theorem remain outside scope. A raw integer principal minor has determinant -1, illustrating why the printed point cannot simply be called an explicit real PSD witness; this is not a source counterexample. No global novelty or complete theorem-verification claim is made. All 28 pinned public packet files are unchanged in this archive. Source commit: 1581d4cbdd69a0faf34b2089614fe2a814316a6a. Contribution commit: 565237779f37c244b633546974444d4cee3eaeaf. First documented public disclosure: 2026-10-25T18:46:24Z in PR #42. Upstream review is pending at archival publication; submission and DOI do not establish acceptance or human peer review. Alexander Richard Towell, ORCID 0000-0001-6443-9897, with substantial OpenAI Codex assistance. OpenAI supplied the source construction and certificate data. Pico's original whole-family classification and contribution process are credited; the overall not-finite classification is retained. Classical methods and dependency authors retain credit. A DOI supplies a persistent citation and archive, not certification of correctness, novelty, human review or legal priority.