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Public story · 2026-08-04 · high
OpenAI shipped Lean 4 code alongside the results so a computer, not a referee, can check the math.
Why now: OpenAI posted the repo on August 1, three days before this coverage on August 4.
OpenAI posted Lean 4 proofs for ten math and computer science results on August 1, per GitHub.
That's the shift the Solution Hacking paper says AI evaluation needs: a claim only counts if something besides a human grader can confirm it. The repo had drawn 459 stars and 41 forks by August 4, per GitHub.
The proofs accompany OpenAI's paper Ten advances in mathematics and theoretical computer science.
The results include an improved sphere-packing bound reaching the Cohn-Elkies threshold, formalized in SpherePacking.lean. Permanent.lean sets a lower bound of n⁴/log n for an arithmetic formula computing the permanent. NonSoficGroup.lean and ConnesRigidity.lean cover two more of the ten claims.
This breaks from how math papers normally get vetted, where a PDF stands alone until reviewers work through the argument by hand. Publishing the Lean certificates next to the paper lets anyone run OpenAI's own checker over the argument instead of taking the abstract on faith.
Each link below shares sources, entities, or timing with this story.
LLM uses OpenAI / Shared entities / Earlier coverage
Linked by a graph relationship (LLM uses OpenAI); both cover August, Lean, OpenAI, PDF; earlier August coverage from 2026-08-02.
OpenAI uses Claude Code / Shared entities / Same source domain / Earlier coverage / Tension
Linked by a graph relationship (OpenAI uses Claude Code); both cover GitHub, OpenAI; reported by the same outlet (github.com).
Microsoft competes with OpenAI / Shared entities / Same source domain / Earlier coverage
Linked by a graph relationship (Microsoft competes with OpenAI); both cover GitHub, OpenAI; reported by the same outlet (github.com).
TCS partners with Anthropic / Shared entities / Same source domain / Earlier coverage
Linked by a graph relationship (TCS partners with Anthropic); both cover GitHub, Shipping; reported by the same outlet (github.com).
OpenAI released Codex / Shared entities / Same source domain / Earlier coverage
Linked by a graph relationship (OpenAI released Codex); both cover OpenAI, PDF; reported by the same outlet (github.com).
TCS partners with Anthropic / Shared entities / Same source domain / Earlier coverage
Linked by a graph relationship (TCS partners with Anthropic); both cover GitHub, Lean; reported by the same outlet (github.com).
Linked by a graph relationship (TCS partners with Anthropic); both cover GitHub, Lean; reported by the same outlet (github.com).
Linked by a graph relationship (TCS partners with Anthropic); both cover GitHub, OpenAI; reported by the same outlet (github.com).