lean4

This paper introduces a compiler-guided adaptive proof search framework for context-dependent theorem proving in Lean 4, using cross-model synergy to improve proof success rates while reducing computational cost.

MathForm introduces a framework for mathematical autoformalization using knowledge retrieval and verification-guided refinement, yielding the FormalVerse dataset and an 8B model that outperforms specialized baselines.

PULSE is a new executable contract language for spatiotemporal knowledge graph engineering, providing a typed runtime with role-based write effects, safety properties verified in Lean 4, and trace parity across large datasets.

OpenAI used an internal model, Astra, to solve ten mathematical problems that had stalled for over a decade, spending under $2,000 per problem and releasing Lean 4 formalizations and a paper. The results prompt reflections on AI's role in mathematics.

This paper identifies a fundamental issue in top-k explanations for graph neural networks: automorphisms in input graphs cause non-unique explanations, as the model cannot distinguish symmetric elements. The authors provide a criterion to detect such arbitrariness and verify it using automated reasoning in Lean 4, showing the problem is widespread in molecular datasets.

A DSL based on Google Zanzibar's datalog language for Lean4 to represent and evaluate knowledge bases, manageable under git and without heavy external dependencies.

A formally verified 3D mesh intersection implementation in Lean 4 that requires reviewing only 93 lines of specification, trusting the Lean checker rather than 1000+ lines of AI-generated code. It demonstrates a novel approach to reducing human review effort while ensuring correctness.

This paper presents the design and end-to-end formal verification of IEEE-754 binary32 and bfloat16 arithmetic for ARCH HDL, a hardware description language intended for AI model generation. The operators are proven correctly rounded using a hybrid approach combining exhaustive SMT equivalence checking and Lean 4 proofs, with synthesizable SystemVerilog output.

This article presents Demonstrandum, a verification-first multi-agent AI mathematics pipeline that produces mechanically checkable artifacts, including refutations and proofs of conjectures with Lean 4 kernel verification.

OpenProver is an open-source system for LLM-driven automated theorem proving using Lean 4, featuring a Planner-Worker-Verifier architecture and both autonomous and interactive modes. It enables reproducible evaluation and human-AI synergy in mathematical proof search.

A formalization of combinatorial game theory in Lean 4, covering games, nimbers, and surreal numbers, based on Conway's work.

This paper presents an experience report on a verification pipeline that uses AI provers (Aristotle and Aleph) alongside symbolic extraction tools and formal cryptographic libraries to produce machine-checked correctness proofs for Rust cryptographic code in Lean 4, with case studies from the Ethereum Foundation's zkEVM project.

Introducing Leanstral 1.5, a 119B parameter (6B active) open model for formal proof engineering in Lean 4, achieving 100% on miniF2F, state-of-the-art scores on PutnamBench and FATE benchmarks, and discovering previously unknown bugs in open-source repositories.

Automated theorem proving is evolving from niche tools like Lean 4 into systems aided by machine learning that can solve real mathematical problems, such as verifying a counterexample to an Erdős conjecture.

Mistral AI releases Leanstral 1.5, an updated Lean 4 formal proof engineering model optimized for automated theorem proving and autoformalization, with 119B total parameters and 6.5B active parameters.

This paper uses evolutionary game theory to model competition between a harm-minimizing AI agent and an approval-seeking (RLHF) agent in a community, analyzing conditions for adoption and welfare outcomes. The results show that while a self-audited agent can fixate, it is not sufficient to prevent community harm, and alignment and timeframe are critical.

Ansatz is a Clojure library that implements Lean 4's Calculus of Inductive Constructions kernel, enabling Clojure programmers to write dependently typed, verified code with proofs compatible with Mathlib and compile to JVM bytecode.

This paper proposes a complete architectural specification of safe AGI based on closed reentry loops, providing formal proofs, machine verification in Lean 4, and Python code. It argues that this architecture mathematically guarantees self-modeling, self-preservation, and safe goal-directed behavior, contrasting with current feedforward approaches.

This paper evaluates the robustness of proof autoformalization models in Lean 4 under global and local perturbations, finding that current LLM-based models are sensitive to perturbations and often fail to faithfully reflect local changes.

This paper presents an agent pipeline for formalizing a numerical analysis textbook in Lean 4 and introduces a quality audit framework that evaluates semantic correctness and library reuse beyond kernel acceptance, revealing common unfaithful formalization patterns.