Overview
Public Lean 4 repository (github.com/openai/ten-proofs) containing machine-checkable certificates for openai-astra’s ten mathematics/TCS advances announced August 1, 2026. Apache-2.0; Lean 4.32.0 + mathlib.
Key Results Covered
Sphere packing, binary/spherical codes, arithmetic circuit complexity, non-sofic groups, Connes rigidity, quantum parallel repetition, closest vector problem, Ehrhart volume, multicolor Ramsey, extremal Erdős problems.