FaithSieve is a Lean‑assisted framework that fine‑grains natural‑language mathematical proofs into local reasoning units, extracts typed proof obligations, and verifies them with formal evidence gated by semantic alignment. It introduces two expert‑verified datasets—ProofLoc‑Olympiad and ProofLoc‑University—to benchmark first‑error localization. On these benchmarks, FaithSieve outperforms direct‑judging baselines, achieving 81.43% and 84.5% exact first‑error accuracy respectively.
By Ziyu Wang, Qiming Dai, Yishan Wu, Zaiwen Wen
arXiv:2606. 26525v1 Announce Type: new Abstract: Auto-formalization is critical for scalable formal verification, but existing progress largely focuses on isolated statements, while theory-scale auto-formalization, which coherently translates hundreds of interdependent definitions, lemmas, and theorems, remains open due to challenges in consistency, faithfulness, scalability, and correctness.
By Yuming Feng, Frederick Pu, One An, Osbert Bastani, Li Zhang, Jiani Huang, Xujie Si, Ziyang Li
Magenta is a training‑free pipeline that bridges informal natural‑language mathematical problems and formal Lean 4 verification. Given a problem in plain text, it generates an answer, translates it into a Lean 4 statement, and constructs a machine‑checked proof. The system includes a statement judge to ensure the formalisation matches the original problem and an error‑attribution judge to guide corrections, achieving perfect accuracy on olympiad benchmarks and solving all six IMO 2026 problems when combined with K2‑Horizon‑7B.
By Joshua Ong Jun Leang, Haonan Li, Zheng Zhao, Xinyi Shang, Wenda Li, Zhengzhong Liu, Erix Xing, Shay Cohen, Eleonora Giunchiglia
arXiv:2609.35790v1 Announce Type: cross
Abstract: While neural theorem provers have achieved impressive milestones in formal mathematics, they largely operate on the assumption that faithful Lean 4 f...
By Thomas Hirtz, Farzad Jafarrahmani, Abdelmouksit Sagueni, Xiang Zhou, Wengping Deng, Liang Zhang
arXiv:2607. 12650v1 Announce Type: cross Abstract: Tool access alone does not make LLM empirical reasoning governable: accepted outputs need not descend from attested evidence, and accepted deductions need not hold up under formal scrutiny.
By Junyu Ren
arXiv:2606. 29493v1 Announce Type: new Abstract: Benchmarks for LLM-assisted theorem proving in Lean are often treated as intrinsically reliable because every solved instance comes with a machine-checked proof.
By Pawan Sasanka Ammanamanchi, Siddharth Bhat, Stella Biderman
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.
By Yiming Fu, Peixuan Liu, Zichen Wang, Kun yuan
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...
By Zelin Zhao, Bo Yuan, Yuchen Zhu, Jaemoo Choi, Yongxin Chen
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.
By Austin Letson, Leopoldo Sarra, Auguste Poiroux, Oliver Dressler, Paul Lezeau, Dhyan Aranha, Frederick Pu, Aaron Hill, Miguel Corredera Hidalgo, Julian Berman, George Tsoukalas, Lenny Taelman
arXiv:2607. 17352v1 Announce Type: new Abstract: Designing effective Lean proof agents is a central challenge in formal mathematical reasoning.
By Yuqing Li, Zeguan Wu, Yu Gan, Junyu Liu
CausalSmith is a framework that automates theoretical research in causal inference by integrating a Lean proof assistant with a self‑improving agentic pipeline. It uses Causalean, a Lean library of over 7,000 machine‑checked declarations, and a pipeline that selects topics, proposes results, formalizes statements, constructs proofs, and audits them against informal claims. The system’s artifacts and source code are publicly available on GitHub.
By Jiyuan Tan, Vasilis Syrgkanis
arXiv:2607. 22511v1 Announce Type: cross Abstract: Automating theoretical research is constrained not only by the generation of candidate results, but also by their reliable evaluation.
By Jiyuan Tan, Vasilis Syrgkanis