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

arXiv: https://arxiv.org/abs/2607.23614 · HTML: https://mlsanity.com/paper/2607.23614/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 38 references that are in the map.
- First posted on arXiv 26 Jul 2026.

## Builds on (most cited first, 18 of 18)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Reflexion: Language Agents with Verbal Reinforcement Learning](https://mlsanity.com/paper/2303.11366/) (2023)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (2023)
- [Large Language Models Cannot Self-Correct Reasoning Yet](https://mlsanity.com/paper/2310.01798/) (2023)
- [Teaching Large Language Models to Self-Debug](https://mlsanity.com/paper/2304.05128/) (2023)
- [LeanDojo: Theorem Proving with Retrieval-Augmented Language Models](https://mlsanity.com/paper/2306.15626/) (2023)
- [Theoretical Physics Benchmark (TPBench) -- a Dataset and Study of AI Reasoning Capabilities in Theoretical Physics](https://mlsanity.com/paper/2502.15815/) (2025)
- [Probing the Critical Point (CritPt) of AI Reasoning: a Frontier Physics Research Benchmark](https://mlsanity.com/paper/2509.26574/) (2025)
- [Quiver Mutations, Seiberg Duality and Machine Learning](https://mlsanity.com/paper/2006.10783/) (2020)
- [HepLean: Digitalising high energy physics](https://mlsanity.com/paper/2405.08863/) (2024)
- [Unsupervised Machine Learning Techniques for Exploring Tropical Coamoeba, Brane Tilings and Seiberg Duality](https://mlsanity.com/paper/2309.05702/) (2023)
- [Learning to Disprove: Formal Counterexample Generation with Large Language Models](https://mlsanity.com/paper/2603.19514/) (2026)
- [Formalization of QFT](https://mlsanity.com/paper/2603.15770/) (2026)
- [PhysProver: Advancing Automatic Theorem Proving for Physics](https://mlsanity.com/paper/2601.15737/) (2026)
- [Generative AI for Brane Configurations and Coamoeba](https://mlsanity.com/paper/2411.16033/) (2024)
- [Axioms for physical reasoning: codifying the Seiberg--Witten solution in Lean](https://mlsanity.com/paper/2607.06379/) (2026)
- [Grading the Unspoken: Evaluating Tacit Reasoning in Quantum Field Theory and String Theory with LLMs](https://mlsanity.com/paper/2604.14188/) (2026)

## Abstract (arXiv)

We present DualityCert, a symbolic verifier for candidate Seiberg-duality claims in four-dimensional N=1 quiver gauge theories. The verifier evaluates 't Hooft anomaly matching, superpotential R-charge consistency, central-charge matching, and a bounded chiral-ring proxy. A claim that passes receives a consistency certificate, which states that no tested inconsistency was found, not that the duality is proven. We use the verifier as a repair environment for language-model agents, which receive a deliberately broken claim and must edit it until it certifies. On a preregistered benchmark of 145 broken claims, with the analysis fixed before the first confirmatory model call, verifier-gated retry improves final repair success over a single attempt by +8.3 percentage points (pp) on deepseek-chat and +7.1 pp on qwen-plus (Holm-adjusted p<0.002). Under an equal budget of eleven attempts, the stop-first strategy portfolio underperforms independent verifier-filtered resampling by 10.3 percentage points on deepseek-chat but outperforms it by 14.7 points on qwen-plus, reversing the ordering of the two tested verifier-exploitation policies across the two confirmatory models. On qwen-plus, category-level verifier feedback is worth +8.7 pp over content-free retry, and interpretable obligation identities alone are worth +6.4 pp over structurally identical masked feedback. Neither effect is detected on deepseek-chat. Separately, a preregistered MiniMax-M2.5 extension again finds an iteration gain and independent verifier-filtered resampling outperforming the strategy portfolio. Which policy is better thus differs between the two models, while every winning policy uses the same cheap certificate. The verifier, benchmark, protocol, and all per-attempt records are released.