DUALITYCERT: Verifier-Gated Language-Model Repair of Broken Duality Claims in Quantum Field Theory

Language-model agents in mathematics can search against a proof assistant; theoretical physics offers no such target. We ask what verification remains available without one, on the problem of deciding whether two quantum field theories describe the same physical system. DUALITYCERT decomposes such a duality claim into obligations that can each be decided in isolation — anomaly matching, superpotential R-charge conditions, central charges, and a bounded chiral-ring proxy — and issues a certificate stating that no tested inconsistency was found, not that the duality holds. Because the duality is an explicit move on the gauge theory, the same machinery labels its own benchmark: positives are dual by construction, and a negative is kept only when some obligation actually fails, so each carries the obligation that rejected it. On 145 such claims, in a preregistered study, allowing five verifier-gated attempts rather than one improves final-certificate rates on all three models tested (+8.3, +7.1, +11.5 percentage points), while the ordering of two budget-matched exploitation policies reverses sign between models (−10.3, +14.7, −9.0). Interpretable feedback beats content-free retry on one model of the three.