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Benefit Ledger · provisional · Mathematics

GPT-6 Astra posts ten Lean-certified advances across math and TCS

On 1 August 2026 OpenAI released a paper and Lean repo of ten results from GPT-6 Astra, then still in development, spanning sphere packing, codes, non-sofic groups, Connes rigidity, circuit lower bounds, quantum parallel repetition, CVP hardness, Ehrhart volume, and Erdős problems 183, 146, and 180.

1 Aug 2026Tier 3 MajorMethodology 0.1

Current score

+1.42

10 base · Major (tier 3 of 5, 10 pts)
× 0.9000 attribution · Primary causal contribution
× 0.4500 evidence · External expert evaluation
× 0.5000 realization · Experimentally validated
× 0.7000 durability
Event-level product before credit split: 1.42

A bundle of long-open theorems with Lean certificates is major (tier 3), not Historic, until independent reconstruction. Search credit is GPT-6 Astra, including the in-development snapshot (0.90). Evidence is a lab paper plus a public Lean repo, not journal peer review (0.45). Realization is posted proofs, not community-standard theorems (0.50).

What happened

OpenAI says the arguments were generated by Astra while the system was still in development, then prepared as manuscripts with the same model and formalized in Lean (openai/ten-proofs; the project reports zero sorries). Pre-release and public Astra are the same named release. The ten items are: high-dimensional sphere-packing bounds down to the Cohn–Elkies threshold; exponentially improved binary and spherical code bounds; an explicit finitely presented non-sofic group; a counterexample to Connes’s rigidity conjecture; permanent arithmetic-circuit and formula lower bounds including Ω(n^4/log n) for formulas; exponential parallel repetition for general two-player quantum games; polynomial-factor CVP hardness; the sharp Ehrhart volume inequality in every dimension; a superexponential lower bound resolving Erdős 183 on multicolor triangle Ramsey numbers; and resolutions of the compactness and degeneracy conjectures (Erdős 146 and 180). This is one documentary event, not eleven, because the results share a date, model, paper, and repo. It is not the September Navier–Stokes search system, which OpenAI described as more capable than Astra. Community reconstruction is incomplete, so the cluster is Major and provisional rather than Historic.

Model attribution

GPT-6

GPT-6 Astra, still in development on 1 August 2026, generated the ten arguments; humans helped prepare manuscripts; the same model produced Lean certificates.

The 1 August post attributes the results to an internal version of Astra. Pre-release and public Astra are scored as the same named release.

Attribution 0.9000 · Credit share 100% · OpenAI

Claims

  • Independent reconstruction has placed all ten results beyond expert dispute.

    significance · disputed

  • OpenAI released ten Lean-accompanied results from GPT-6 Astra on 1 August 2026, including a non-sofic group, a Connes rigidity counterexample, and Erdős 183/146/180.

    outcome · supported

Sources

primary sources

other sources

Secondary domains: Computer Science

Revision history

  • 13 Sep 2026 · 0.00 1.42

    Imported events under methodology 0.1.