Axiom released a Lean formalization covering the entire Stacks Project. The project spans about 16 million lines of machine-checked code. The Stacks Project is a roughly 7,500-page open-source reference for modern algebraic geometry.
Library access and structure
The formalization lets researchers and AI agents import definitions and theorems directly into new proofs. Permanent Stacks tags link every Lean declaration to the original text. A side-by-side website shows the Stacks Project pages next to the corresponding Lean code.
A different kind of project
Axiom previously released a Lean formalization of the Classification of Finite Simple Groups on October 27, 2026. That project focused on a single landmark theorem. The Stacks Project instead provides a reusable foundational library with thousands of interlocking definitions and lemmas.
Faithfulness and repairs
Axiom used coordinated swarms of AI agents to translate, prove, and integrate theorems in parallel. The system identified dozens of statements that needed local refinement. Agents identified missing hypotheses, built counterexamples, and found alternative routes to main results.
The formalization is open source and kept in Axiom's own repository. It remains independent from the upstream Stacks Project. Axiom invites mathematicians, Lean developers, and AI agents to examine the library and build new mathematics on it.