# Lean formalization of the Stacks Project

Axiom released a Lean formalization of the Stacks Project, turning the roughly 7,500-page open reference that lays the foundations of modern algebraic geometry into a single machine-checked library of about 16 million lines of code. Algebraic geometry had lacked matching Lean infrastructure: a contemporary proof may invoke a long chain of theorems across commutative algebra, schemes, sheaves, cohomology and algebraic stacks before its core argument begins. The library keeps the original permanent tags so researchers and AI agents can import definitions and theorems directly, and the formalization surfaced dozens of statements needing local refinement.

Axiom released a Lean formalization of the Stacks Project, turning the roughly 7,500-page open reference that lays the foundations of modern algebraic geometry into a single machine-checked library of about 16 million lines of code. Algebraic geometry had lacked matching Lean infrastructure: a contemporary proof may invoke a long chain of theorems across commutative algebra, schemes, sheaves, cohomology and algebraic stacks before its core argument begins. The library keeps the original permanent tags so researchers and AI agents can import definitions and theorems directly, and the formalization surfaced dozens of statements needing local refinement.