arXiv:2603. 02668v2 Announce Type: replace Abstract: We present SorryDB, a dynamically-updating benchmark of open Lean tasks drawn from 78 real world formalization projects on GitHub.
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.
arXiv:2608.28639v1 Announce Type: new Abstract: Formal theorem proving with large language models remains challenging due to the difficulty of navigating large proof search spaces efficiently. Existi...
SkillEvoLean introduces a mutation‑enhanced skill evolution framework for Lean theorem provers, jointly refining a high‑level solving policy and its reference knowledge. The method combines progressive updates from successful and failed proof trajectories with mutation‑based exploration when no complete proof is found, sampling mathematical concepts to generate new skill candidates. Evaluations on MiniF2F, PutnamBench, IMO 2025, and USAMO 2026 show significant proof success improvements over baseline approaches.
arXiv:2607. 14582v1 Announce Type: new Abstract: Existing LLM-based theorem provers have achieved impressive results on formal mathematics benchmarks, yet they remain confined to acting as autonomous agents that prove a stated proposition.
arXiv:2607. 17352v1 Announce Type: new Abstract: Designing effective Lean proof agents is a central challenge in formal mathematical reasoning.
arXiv:2606. 09450v1 Announce Type: new Abstract: LLMs have recently achieved strong results on formal proving benchmarks.
arXiv:2607. 11307v1 Announce Type: new Abstract: Full-proof autoformalization bridges extensive mathematical proofs in natural language with formally validated reasoning, offering a pathway to elevate the ceiling of verifiable mathematical reasoning.
LLMs have recently achieved strong results on formal proving benchmarks. However, existing evaluations remain heavily concentrated on competition-style problems and often fail to capture how models behave on longer, more dependency-rich mathematical developments.
ProofEvolve is a neuro‑symbolic framework that evolves formally verified symbolic proof structures alongside neural models to expand the knowledge boundary in automated theorem proving. The neural component proposes variation operators such as decompositions, repairs, and schema recombinations, while the Lean kernel verifies every proof transition, ensuring formal soundness. Across three competition‑level Lean benchmarks, ProofEvolve achieves the highest average solve rate among evaluated proof systems.
arXiv:2606. 03303v1 Announce Type: new Abstract: Large Language Models (LLMs) exhibit strong informal mathematical reasoning but struggle to generate mechanically verifiable proofs in formal languages like Lean.
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.