arXiv AI By Bodla Krishna Vamshi, Haizhao Yang

Reward-Oracle MCTS for Formal Theorem Proving: Sample-Efficient Search and the Need for Kernel-Level Proof Auditing

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Pythagoras-Prover: Advancing Efficient Formal Proving via Augmented Lean Formalisation

arXiv:2606. 12594v1 Announce Type: new Abstract: Modern Lean theorem provers achieve strong performance only with substantial training and inference compute, driven in part by scarce verified proof data and the long reasoning traces of formal proof search, making both supervised fine-tuning (SFT) and sampling expensive.

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Stellar Colosseum: A Many-Agent Harness for Long-Horizon Research in Mathematics and Theoretical Computer Science

Stellar Colosseum is a model‑agnostic harness designed to improve long‑horizon research in mathematics and theoretical computer science by allocating inference across multiple agents. It explores alternative strategies before constructing proofs, uses a readiness gate to decide when a route is mature enough to decompose, represents proof plans as interdependent subproblems, and routes verifier findings back to the relevant part of the argument. The workflow generates candidates in parallel, attacks them with targeted falsification, and combines candidates and critiques into a single research artifact through overlapping random‑sample tree aggregation, and has been integrated into Google Antigravity's Teamwork framework as the Long Proof pattern. Demonstrations show that, when paired with Gemini 3.1 Pro, Stellar Colosseum achieves 71.0% accuracy on the TCS‑Bench theorem‑proving benchmark and solves 218 of 222 Codeforces problems.

By Honghao Lin, David P. Woodruff, Yuan Deng, Jieming Mao, Song Zuo, Vahab Mirrokni
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LEVER: Adaptive Cost-Aware Proof Search Over AND/OR Graphs

LEVER is a new proof‑search algorithm that lets users program the objective over correct proofs and optimizes it during search. It scores partial proofs on an AND/OR graph, combining achieved objective values with predictions for open subgoals, so the objective guides search before a proof is complete. On the PutnamBench in Lean 4, LEVER reduces computational cost by 34 % and raises the solve rate from 80 % to 96 %, while also improving topical impurity and approaching refactoring for proof length.

By Nihal Jain, Shuangjie Yao, Begum Cicekdag, Zhuo Zhang, Suman Jana