ProofCouncil is an LLM-based mathematical agent built around an author-critic architecture for solving open problems. In the second batch of the FirstProof challenge, its submissions to 6 of 10 problems were judged correct or requiring at most minor revisions, reportedly the strongest result among participating teams. On 30 additional open problems collected from researchers, 21 solutions received human feedback: 5 were judged completely correct, 2 were promising pending final verification, and 8 contained useful partial progress. The authors also release the agent-building library used to develop ProofCouncil.
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