A Finite Certificate for the Positive n=9 Vasc Inequality

arXiv:2606.06136v1 Announce Type: cross Abstract: We prove the positive-real n=9 case of the Vasc cyclic inequality. The proof was obtained with human-guided assistance from the AI agent MechMath Agent Team: the human-readable part reduces the rational inequality to a homogeneous polynomial inequality, fixes a cyclic maximum, and parametrizes each sorted fixed-maximum cone by cumulative gaps; the finite part is a certificate covering all 8!=40320 sorted cones. MechMath Agent Team generated the certificate verification workflow through Python tool calls, including the case split, verification programs, and terminal classifications. The published certificate has 36815 coefficient leaves, 2236 ordinary Polya multiplier leaves, and 1269 AM-GM midpoint overlay leaves. Human authors audited the mathematical reductions and verification logic, and a separate artifact contains the certificate, an independent verifier, and a from-source rebuild route.

Source: arXiv cs.AI | 2026-06-06