ProofCouncil: An LLM Agent for Solving Open Mathematical Problems
Researchers introduced ProofCouncil, an LLM agent with an author-critic architecture designed to solve open mathematical problems. It was submitted to the FirstProof challenge, where it autonomously tackled 6 out of 10 problems and received referee evaluations.
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OpenProver: Open-source LLM-driven theorem proving with Lean 4 verification
OpenProver is an open-source system for LLM-driven automated theorem proving (ATP) that integrates Lean 4 formal verification. It uses a Planner-Worker-Verifier architecture to decompose mathematical problems into parallel workers, with a whiteboard scratchpad and repository for intermediate findings. The system is fully open-source and offers reproducible evaluation through automatic formal verification of generated proofs.
Danus: open-source framework for mathematical reasoning with fact-graph memory
Danus is a new open-source framework that orchestrates mathematical reasoning agents using a fact-graph memory system. A main agent (Claude Code) directs a swarm of autonomous codex workers to prove statements, with a cold-start verifier as the sole authority on correctness. Verified results accumulate in a content-addressed fact graph, and a strategy loop decomposes problems and steers the swarm.
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GPT-5.6 Sol Ultra produces proof of the Cycle Double Cover Conjecture
On July 10, 2026, a user on X (__eknight__) shared a PDF hosted on OpenAI's CDN containing a prompt that led GPT-5.6 Sol Ultra to produce a proof of the Cycle Double Cover Conjecture, a long-standing open problem in graph theory. The post on Hacker News garnered 755 points, indicating significant community interest. The prompt and resulting proof are available via OpenAI's CDN link.
Hypothesis Evolution Protocol proposed for auditable AI scientist agents
A new arXiv paper introduces the Hypothesis Evolution Protocol (HEP), a framework to make LLM-based AI scientists auditable by structuring hypothesis generation, testing, and belief updates in a transparent, logged process. The protocol aims to address the lack of auditability in current autonomous scientific agents.