lean-4

该论文确定了在独立非同分布噪声和两两非负相关噪声下，选择最大噪声分数所产生的“赢家偏差”的尖锐常数界，并将全部定理在 Lean 4 中形式化验证，同时在 448 个模型选择流程上验证了结论的实际意义。

A paper showing that a simple agentic harness (h1) with an efficient Lean 4 feedback interface achieves state-of-the-art formal theorem proving results on PutnamBench, FATE-X, and FormalConjectures, matching or beating specialized multi-step workflows and settling eight open problems. The authors argue that execution interfaces matter more than complex orchestration and warn against prescribing structured workflows before evaluating frontier models with efficient feedback.

A Purdue paper introduces a bounded, online step-level repair module for Lean 4 theorem provers that feeds compiler error messages to a pretrained repair model instead of discarding failed tactics, achieving up to a 32% relative gain in solve rate on the LeanDojo benchmark and nearly doubling performance on Lean Workbook.

开发者用 Lean 4 完整实现了 RealWorld（Medium 克隆）参考应用，前后端全部使用 Lean 编写，并借助社区库（HTTP 服务器、Postgres 驱动、JWT、HTML 渲染等）通过官方 API 与网站测试套件。文章以数学论文风格呈现，部分关键性质以定理形式在 Lean 中形式化验证。

The authors introduce Choir, an open, modular protocol for distributed multi-agent autoformalization that decomposes projects into GitHub-based tasks with deterministic trust-gate verification, supporting Lean 4, Isabelle, and Rocq; it includes a preprint and an open-source repo funded by DARPA's expMath program.

The paper introduces LeanPolish, a symbolic Lean 4 pipeline releasing 33k+ verified proof edits and failed attempts, showing that verified supervision can suffer from search artifacts and that iterating the symbolic compression pass beats neural hybrids on miniF2F while modestly improving whole-proof rewriting on PutnamBench.

华为 Lagrange 数学计算研究中心提出 Sage，一个四阶段分解生成管线加双重信号语义校正循环的自动形式化框架，将答案泄漏率从70.9%降至2.7%，在 Omni-MATH NP 上达到73.3% pass@4，并在新提出的 IMO-Unformalized 基准上零样本达到87.4%验证保真度。

OpenAI announced a formal proof for the Navier-Stokes equations using Lean 4, reducing the cost of formal verification from tens of thousands of person-hours to just 17 hours, highlighting AI's transformative role in mathematics and verification.

StochBench introduces a domain-specific benchmark of 450 graduate stochastic processes problems in Lean 4, evaluated with an AI agent achieving a 34.9% proof rate, to advance formal theorem proving in applied mathematics.

This paper introduces AViD Journal, a pipeline for automated novelty verification of mathematical theorems using Lean 4, evaluating it on withdrawn arXiv papers and highlighting challenges in formal verification.

MathCode is an AI-powered coding assistant that converts mathematical problems into Lean 4 theorems and attempts formal proofs, featuring a persistent REPL, theorem libraries, and agent-mode proving.

A research paper introducing a failure-triggered cascade approach to safely integrate machine learning into Lean 4's grind tactic, achieving improved efficiency and solving previously unsolvable proofs without regressions.

This paper presents FVSpec, a benchmark for AI-assisted formal verification that translates real-world property-based tests from Python into Lean 4 specifications using a multi-agent LLM pipeline, aiming to drive progress on formal verification of real-world software.

Aleph Prover has formalized OpenAI's disproof of Paul Erdős' planar unit problem in Lean 4 and released it as open source for independent validation, demonstrating AI's role in accelerating mathematical research with verifiable proof data.

This paper evaluates Claude Code in an agentic proving framework on the Clever benchmark for program verification, achieving over 98% success in specification generation and end-to-end verification, revealing that existing benchmarks may be insufficient for evaluating modern agentic provers.

OProver is a unified framework for agentic formal theorem proving in Lean 4 that iteratively improves proof generation through training with verified proofs and compiler feedback, achieving state-of-the-art results on multiple benchmarks.

TorchLean is a newly released Lean 4 framework that enables formal verification of neural network software, featuring typed tensors, verified autograd, PyTorch interoperability, and GPU execution. The release expands support to modern architectures like diffusion models, GPT-style transformers, and state-space models, bridging practical ML workflows with mathematical proof checking.

This paper introduces Discover and Prove (DAP), an open-source agentic framework for automated theorem proving in Lean 4 that tackles 'Hard Mode' problems where the answer must be discovered independently before formal proof construction. The work releases new Hard Mode benchmark variants and achieves state-of-the-art results while revealing a significant gap between LLM answer accuracy (>80%) and formal prover success (<10%).