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.
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.
arXiv:2606. 09450v1 Announce Type: new Abstract: LLMs have recently achieved strong results on formal proving benchmarks.
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...
LeanGraphSearch is a graph‑based retrieval method for the Lean 4 theorem prover that builds a dependency graph from Mathlib’s forward dependencies and traverses it to find supporting lemmas via multi‑hop chains. By linking each declaration to its premises, propagating relevance through a graph‑ranking algorithm, and re‑ranking candidates against the original query, it improves recall by up to 12% over LeanSearch v2 on MathlibQR and increases coverage of complete annotated proof routes on MathlibMPR by up to 3.7%. When integrated into an iterative proving loop, LeanGraphSearch raises pass rates at 8, 16, and 32 reflection turns by as much as 40% compared to a vanilla prover and up to 10% compared to LeanSearch v2, demonstrating higher accuracy‑cost efficiency.
The paper introduces a compiler-guided adaptive proof search framework for Lean 4 theorem proving, addressing the challenge of context-dependent proofs in real-world projects. It balances exploration and exploitation by generating diverse starting points via dual-model generation and resampling when stagnation occurs, while refining promising states using compiler-grounded pairwise comparison. Experiments on seven Lean 4 projects from miniCTX‑v2 demonstrate that the method improves average pass rates by 12.8 percentage points within a pass@32 budget and reduces LLM calls by 21.9 % compared to pass@k baselines.
arXiv:2609.39544v1 Announce Type: new Abstract: Recent achievements in AI-assisted mathematics require intensive interaction of agents with proof assistants to generate machine-checked proof certific...
arXiv:2606. 03743v1 Announce Type: new Abstract: While Large Language Models (LLMs) have shown strong performance in generating formal proofs, their outputs often remain less readable, modular, maintainable, and reusable than proofs in mature formal mathematics libraries.
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.
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.
arXiv:2605.22875v2 Announce Type: replace Abstract: Long-horizon mathematical reasoning fails less often because a model cannot produce a valid next step than because an agent fails to maintain and e...
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. 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.