MaxProof: Scaling Mathematical Proof with Generative-Verifier RL and Population-Level Test-Time Scaling

Authors:Jiacheng Chen, Xinyu Zhang, Shunkai Zhang, Yanmohan Wang, Lin Li, Tiancheng Qin, Qin Wang, Zhengmao Zhu, Tianle Li, Jingyang Li, Zehan Li, Binyang Jiang, Jin Zhu, Han Ding, Fei Yu, Chenyu Du, Zijian Song, Jiayuan Song, Zhi Zhang, Yunan Huang, Weiyu Cheng, Pengyu Zhao, Yu Cheng View PDF HTML (experimental) Abstract:We present MaxProof, a population-level test-time scaling framework for competition-level mathematical proof in the MiniMax-M3 series. M3 first trains three proof-oriented capabilities -- proof generation, proof verification, and critique-conditioned proof repair -- using a defense-in-depth generative verifier engineered for low false-positive rate. These capabilities are merged into a single released M3 model. At test time, MaxProof treats the model as a generator, verifier, refiner, and ranker, searches over a population of candidate proofs, and returns one final proof through tournament selection. With MaxProof test-time scaling, the M3 model reaches 35/42 on IMO 2025 and 36/42 on USAMO 2026, exceeding the human gold-medal threshold on both.

Subjects: Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Computation and Language (cs.CL) Cite as: arXiv:2606.13473 [cs.LG]   (or arXiv:2606.13473v1 [cs.

LG] for this version)   https://doi.org/10.48550/arXiv.2606.13473 arXiv-issued DOI via DataCite (pending registration) Submission history From: Jiacheng Chen [view email] [v1] Thu, 11 Jun 2026 15:27:06 UTC (2,912 KB)