{"data":{"event":{"id":"bae41473-78a3-4e22-987e-9ac84658623a","slug":"openai-internal-astra-ten-advances-2026-08","title":"GPT-6 Astra posts ten Lean-certified advances across math and TCS","short_summary":"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.","full_description":"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 scored as one Historic cluster because the theorems would have been Major or Historic as independent discoveries; bundling them in one paper is not a 10-point ceiling. It is not the September Navier–Stokes search system, which OpenAI described as more capable than Astra. Independent reconstruction of the full set remains incomplete, so the event stays provisional.","ledger_type":"benefit","primary_domain_id":"23d935bb-b857-4b2b-9471-d568bb848a66","event_status":"provisional","event_date":"2026-08-01T00:00:00.000Z","discovery_date":"2026-08-01T00:00:00.000Z","first_published_date":"2026-08-01T00:00:00.000Z","last_reviewed_date":"2026-10-28T00:00:00.000Z","geographic_scope":"International","affected_population":"Mathematics and theoretical computer science research communities","base_impact_tier":4,"base_score":"30.00","attribution_multiplier":"0.9000","evidence_multiplier":"0.6000","realization_multiplier":"0.9000","durability_multiplier":"1.0000","current_event_score":"14.580000","confidence_level":"medium","score_explanation":"Ten Lean-certified advances across long-open problems are a Historic cluster (tier 4). Publication format is not a scoring ceiling. Search credit is GPT-6 Astra (0.90). Evidence is a lab paper plus a public Lean repo, not journal peer review or full independent reconstruction (0.60). Realization is machine-verifiable posted proofs (0.90). Correct theorems are permanent (1.00).","methodology_version_id":"8745541b-0f8e-4d5a-9b47-5291d3813a8d","original_methodology_version_id":"d7881163-fb23-4e71-8625-bac1a8662c0f","published_at":"2026-08-01T00:00:00.000Z","created_at":"2026-09-13T22:56:05.431Z","updated_at":"2026-10-28T20:22:47.621Z","flags":["Independent reconstruction pending"],"domain_name":"Mathematics","domain_slug":"mathematics","methodology_version":"0.2"},"contributions":[{"id":"276920a9-bdfd-495b-bcb4-d5ddbca8288c","event_id":"bae41473-78a3-4e22-987e-9ac84658623a","model_id":"0f0d18fc-d3f1-4551-9eaf-a13f1f93b1a5","role_description":"GPT-6 Astra, still in development on 1 August 2026, generated the ten arguments; humans helped prepare manuscripts; the same model produced Lean certificates.","attribution_multiplier":"0.9000","credit_share":"1.0000","contribution_score":"14.580000","attribution_rationale":"The 1 August post attributes the results to an internal version of Astra. 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