AXLE: A Cloud Infrastructure for Lean 4 Theorem Proving Utilities
For researchers and engineers building AI for mathematics, AXLE provides scalable, multi-tenant Lean 4 infrastructure with per-request isolation and multi-version support, enabling high-throughput proof verification and manipulation.
AXLE is a cloud service for Lean 4 proof manipulation and verification that has served over 500 million requests and supported a 12/12 score on the 2025 Putnam competition, addressing the need for scalable, correct tooling in AI-driven mathematics.
We present AXLE (Axiom Lean Engine), a cloud service for Lean 4 proof manipulation, extraction, and verification. Recent progress in AI for mathematics -- reinforcement learning pipelines, agentic proving workflows, dataset curation -- demands Lean 4 tooling that scales to millions of requests while remaining correct and robust; existing infrastructure offers parallel compilation but not scalable proof verification, higher-level proof manipulation, multi-version support, or per-request isolation at the throughput modern AI workflows require. AXLE provides 14 Lean 4 metaprogramming tools spanning strict proof verification, declaration metadata extraction, semantic source manipulation, deterministic proof repair and simplification, and lemma extraction. The service runs as a multi-tenant cloud deployment with per-request isolation and concurrent support for multiple Lean 4 and Mathlib versions, accessible via a Python SDK, command-line interface, web UI, MCP server, and raw HTTP API. AXLE is publicly available and free to use at https://axle.axiommath.ai and via the axiom-axle PyPI package, with no local Lean 4 installation required. It has served over 500 million requests to date and is the underlying infrastructure for Axiom Math's proving efforts, including its 12/12 score on the 2025 Putnam competition.