{"data":{"event":{"id":"85b36745-6f8b-4b76-82f3-9749a33356bc","slug":"openai-internal-navier-stokes-singularity","title":"OpenAI reports a forced Navier–Stokes singularity matching Clay C and D","short_summary":"On 8 September 2026 OpenAI published a 166-page writeup and Lean formalization arguing that a smooth, finite-energy 3D Navier–Stokes flow starting from rest, under a smooth force, blows up in finite time. That is Clay statements C and D, which have been part of the official Millennium Problem since Fefferman’s formulation. The search model was an unreleased internal system; GPT-6 Astra did the Lean step. Clay wrote on 11 September that the problem has “apparently been settled,” with formal evaluation still to come.","full_description":"OpenAI reports that after rumors on 1 September 2026 that other researchers had resolved Millennium problems, it launched a multi-agent evaluation of an internal model still in training and more capable than GPT-6 Astra. About 10,000 concurrent agents ran on Navier–Stokes; OpenAI says they reached a resolution on 5 September after roughly 88 hours, then Astra spent about 17 hours on Lean formalization (complete 6 September).\n\nThe claimed theorem is finite-time blowup for an initially smooth fluid at rest, with a smooth force and bounded energy. That matches Fefferman’s official statements C and D. Clay gives solvers four ways to resolve the problem and explicitly grants “reasonable leeway”; C and D are not a later loophole. OpenAI has not resolved the famous unforced A/B question, which remains open. A valid C or D proof is still a resolution of the Clay problem on Clay’s own terms. OpenAI says it will not claim the prize.\n\nThe Clay Mathematics Institute wrote on 11 September that the Navier–Stokes problem has “apparently been settled,” while stressing that formal evaluation and credit will take time. Nature quoted Navier–Stokes specialist Luis Martínez Zoroa calling the result “truly remarkable.” That is not peer review, but it is more than a lab press release.\n\nTristan Buckmaster alleges OpenAI moved after learning of his work with Levent Alpöge. The live dispute is over priority, timing, and whether unpublished interactions could have influenced the process—not, at present, a strong claim that the theorem is false. OpenAI says the proofs differ (forced Navier–Stokes versus their forced Euler/IPM/Boussinesq program), that it did not see their manuscripts, and that an investigation found Buckmaster’s Codex prompts could not have influenced the search model. Hodge, Birch–Swinnerton-Dyer, Riemann, Yang–Mills, and P vs NP are not recorded as solved.\n\nUpdate (2026-09-08): On the Navier–Stokes Millennium Prize Problem. We’re sharing an AI-generated solution to the Navier–Stokes Millennium Prize Problem, including a writeup and a formal proof in Lean.\n\nUpdate (2026-09-18): AI cracked the Navier–Stokes challenge. What does that mean for physics?. AI cracked the Navier–Stokes challenge. What does that mean for physics?\n\nUpdate (2026-09-08): On the Navier–Stokes Millennium Prize Problem - OpenAI. On the Navier–Stokes Millennium Prize Problem  OpenAI","ledger_type":"benefit","primary_domain_id":"23d935bb-b857-4b2b-9471-d568bb848a66","event_status":"provisional","event_date":"2026-09-08T00:00:00.000Z","discovery_date":"2026-09-08T00:00:00.000Z","first_published_date":"2026-09-08T00:00:00.000Z","last_reviewed_date":"2026-09-08T00:00:00.000Z","geographic_scope":"International","affected_population":"Mathematical fluid-dynamics and Millennium Prize communities","base_impact_tier":4,"base_score":"30.00","attribution_multiplier":"0.9000","evidence_multiplier":"0.7000","realization_multiplier":"0.9000","durability_multiplier":"0.9500","current_event_score":"16.159500","confidence_level":"medium","score_explanation":"Base impact is Historic (tier 4, 30 pts): if the claim is true, an AI system apparently settling one of the six remaining Millennium Prize Problems is a once-in-a-generation contribution to knowledge, not a civilizational welfare event. Uncertainty lives in the multipliers, not the tier. Evidence 0.70 reflects a complete manuscript, Lean formalization, Clay’s 11 September “apparently been settled” note, and specialist commentary, still short of completed CMI evaluation or independent reconstruction. Realization 0.90 is a public proof plus machine-verifiable formalization; community acceptance would be 1.0. Durability 0.95 treats a correct theorem as effectively permanent—a fatal flaw would be an evidence or retraction issue, not a decay problem. Search credit stays with the unreleased system (0.85 share, attribution 0.90); Astra’s Lean pass is 0.15 at attribution 0.60. Follow-up ingest: added a follow-up source. Follow-up ingest: added a follow-up source. Follow-up ingest: added a follow-up source.","methodology_version_id":"d7881163-fb23-4e71-8625-bac1a8662c0f","original_methodology_version_id":"d7881163-fb23-4e71-8625-bac1a8662c0f","published_at":"2026-09-08T00:00:00.000Z","created_at":"2026-09-13T21:33:49.339Z","updated_at":"2026-09-22T16:00:56.591Z","flags":["Priority contested","Clay review pending","Unforced A/B remains open"],"domain_name":"Mathematics","domain_slug":"mathematics","methodology_version":"0.1"},"contributions":[{"id":"5568fb4f-823b-45e2-9f17-456f8e748374","event_id":"85b36745-6f8b-4b76-82f3-9749a33356bc","model_id":"8b0780ab-3f59-4f88-8ee4-00662f49a002","role_description":"Unreleased multi-agent system OpenAI says produced the analytic Navier–Stokes singularity.","attribution_multiplier":"0.9000","credit_share":"0.8500","contribution_score":"13.735600","attribution_rationale":"OpenAI attributes the proof search to an internal model significantly more capable than GPT-6 Astra, not to the public Astra release.","attribution_confidence":"medium","first_used_date":"2026-09-01T00:00:00.000Z","model_version_if_known":null,"review_status":"approved","created_at":"2026-09-13T21:33:49.339Z","model_slug":"openai-internal-research-system-2026-09","model_name":"OpenAI Internal Research System — 2026-09","identity_class":"internal_unreleased","is_internal":true,"family_name":"GPT-6","family_slug":"openai-gpt-6","organization_name":"OpenAI","organization_slug":"openai"},{"id":"8086203d-f410-4263-8591-09e1a6b67d0f","event_id":"85b36745-6f8b-4b76-82f3-9749a33356bc","model_id":"0f0d18fc-d3f1-4551-9eaf-a13f1f93b1a5","role_description":"Named release used for the 17-hour Lean formalization and verification pass after the internal system produced the analytic argument.","attribution_multiplier":"0.9000","credit_share":"0.1500","contribution_score":"2.423900","attribution_rationale":"OpenAI credits Astra with Lean formalization, not with finding the Navier–Stokes argument.","attribution_confidence":"medium","first_used_date":"2026-09-05T00:00:00.000Z","model_version_if_known":null,"review_status":"approved","created_at":"2026-09-13T21:33:49.339Z","model_slug":"gpt-6-astra","model_name":"GPT-6 Astra","identity_class":"named_release","is_internal":false,"family_name":"GPT-6","family_slug":"openai-gpt-6","organization_name":"OpenAI","organization_slug":"openai"}],"sources":[{"id":"ffe16364-a994-4b47-bbe8-da381e53f63a","event_id":"85b36745-6f8b-4b76-82f3-9749a33356bc","url":"https://openai.com/index/navier-stokes-solution/","canonical_url":"https://openai.com/index/navier-stokes-solution/","source_type":"developer_announcement","publisher":"OpenAI","author":null,"publication_date":"2026-09-08T00:00:00.000Z","retrieved_at":"2026-09-13T21:33:49.339Z","title":"On the Navier–Stokes Millennium Prize Problem","excerpt":null,"content_hash":null,"source_reliability_class":"low","is_primary_source":true,"is_independent":false,"is_peer_reviewed":false,"archived_url":null,"created_at":"2026-09-13T21:33:49.339Z"},{"id":"47538920-ce73-4ab8-9c9f-a1177a2df3fe","event_id":"85b36745-6f8b-4b76-82f3-9749a33356bc","url":"https://www.nature.com/articles/d41586-026-02842-5","canonical_url":"https://www.nature.com/articles/d41586-026-02842-5","source_type":"journalism","publisher":"Nature","author":null,"publication_date":"2026-09-08T00:00:00.000Z","retrieved_at":"2026-09-13T21:33:49.339Z","title":"OpenAI claims huge maths breakthrough on a famed ‘Millennium Problem’","excerpt":null,"content_hash":null,"source_reliability_class":"medium","is_primary_source":false,"is_independent":true,"is_peer_reviewed":false,"archived_url":null,"created_at":"2026-09-13T21:33:49.339Z"},{"id":"d62e9486-bdd3-4216-b562-11f6e2527eec","event_id":"85b36745-6f8b-4b76-82f3-9749a33356bc","url":"https://techcrunch.com/2026/09/08/openai-fought-dirty-on-career-making-math-problem-says-nyu-mathematician/","canonical_url":"https://techcrunch.com/2026/09/08/openai-fought-dirty-on-career-making-math-problem-says-nyu-mathematician/","source_type":"journalism","publisher":"TechCrunch","author":null,"publication_date":"2026-09-08T00:00:00.000Z","retrieved_at":"2026-09-13T21:33:49.339Z","title":"OpenAI fought dirty on career-making math problem, says NYU mathematician","excerpt":null,"content_hash":null,"source_reliability_class":"medium","is_primary_source":false,"is_independent":true,"is_peer_reviewed":false,"archived_url":null,"created_at":"2026-09-13T21:33:49.339Z"},{"id":"ca8ff3b4-dfce-4126-bc9f-baaa08852448","event_id":"85b36745-6f8b-4b76-82f3-9749a33356bc","url":"https://openai.com/index/navier-stokes-solution","canonical_url":"https://openai.com/index/navier-stokes-solution","source_type":"developer_announcement","publisher":"OpenAI News","author":null,"publication_date":"2026-09-08T00:00:00.000Z","retrieved_at":"2026-09-17T03:01:02.181Z","title":"On the Navier–Stokes Millennium Prize Problem","excerpt":"We’re sharing an AI-generated solution to the Navier–Stokes Millennium Prize Problem, including a writeup and a formal proof in Lean.","content_hash":null,"source_reliability_class":"medium","is_primary_source":false,"is_independent":true,"is_peer_reviewed":false,"archived_url":null,"created_at":"2026-09-17T03:01:02.181Z"},{"id":"9102db94-ff6f-4435-a414-79d48c3dd44c","event_id":"85b36745-6f8b-4b76-82f3-9749a33356bc","url":"https://news.google.com/rss/articles/CBMiXEFVX3lxTE9WeUdwVDNOQkR0VFo3SjJHY1BFdUFCMzhsTGhKbUh6ZVBYTDQzRHlTdGtVYlVzbmVnbWh5X2NZMUU5R2p4STNaVVY1M3FoWnczS0UyNDBDOUhJNTQ3?oc=5","canonical_url":"https://news.google.com/rss/articles/CBMiXEFVX3lxTE9WeUdwVDNOQkR0VFo3SjJHY1BFdUFCMzhsTGhKbUh6ZVBYTDQzRHlTdGtVYlVzbmVnbWh5X2NZMUU5R2p4STNaVVY1M3FoWnczS0UyNDBDOUhJNTQ3?oc=5","source_type":"journalism","publisher":"Frontier lab development news","author":null,"publication_date":"2026-09-08T00:00:00.000Z","retrieved_at":"2026-09-22T16:00:56.519Z","title":"On the Navier–Stokes Millennium Prize Problem - OpenAI","excerpt":"On the Navier–Stokes Millennium Prize Problem  OpenAI","content_hash":null,"source_reliability_class":"medium","is_primary_source":false,"is_independent":true,"is_peer_reviewed":false,"archived_url":null,"created_at":"2026-09-22T16:00:56.519Z"},{"id":"bfc1a078-8199-40c0-a159-698459f9b059","event_id":"85b36745-6f8b-4b76-82f3-9749a33356bc","url":"https://www.claymath.org/news/navier-stokes-announcement/","canonical_url":"https://www.claymath.org/news/navier-stokes-announcement/","source_type":"other","publisher":"Clay Mathematics Institute","author":null,"publication_date":"2026-09-11T00:00:00.000Z","retrieved_at":"2026-09-13T21:33:49.339Z","title":"Navier-Stokes Announcement","excerpt":null,"content_hash":null,"source_reliability_class":"medium","is_primary_source":false,"is_independent":true,"is_peer_reviewed":false,"archived_url":null,"created_at":"2026-09-13T21:33:49.339Z"},{"id":"b9f34a87-7028-4347-b878-3f5080bfe38c","event_id":"85b36745-6f8b-4b76-82f3-9749a33356bc","url":"https://www.nature.com/articles/d41586-026-02922-6","canonical_url":"https://www.nature.com/articles/d41586-026-02922-6","source_type":"peer_reviewed","publisher":"Nature","author":null,"publication_date":"2026-09-18T00:00:00.000Z","retrieved_at":"2026-09-18T19:01:00.019Z","title":"AI cracked the Navier–Stokes challenge. What does that mean for physics?","excerpt":"AI cracked the Navier–Stokes challenge. What does that mean for physics?","content_hash":null,"source_reliability_class":"medium","is_primary_source":false,"is_independent":true,"is_peer_reviewed":true,"archived_url":null,"created_at":"2026-09-18T19:01:00.019Z"}],"claims":[{"id":"6fdb6614-86ce-4830-87a2-46aa06180e83","event_id":"85b36745-6f8b-4b76-82f3-9749a33356bc","claim_text":"OpenAI published a paper and Lean artifact claiming finite-time blowup for forced 3D incompressible Navier–Stokes with smooth data and bounded energy, corresponding to Clay statements C and D.","claim_type":"outcome","claim_status":"supported","confidence_score":null,"created_at":"2026-09-14T02:21:25.209Z","updated_at":"2026-09-14T02:21:25.209Z"},{"id":"242a182e-e003-4388-8fc2-c7fdeaee3e2b","event_id":"85b36745-6f8b-4b76-82f3-9749a33356bc","claim_text":"Clay statements C and D, which permit a smooth external force, are official Millennium Problem formulations. A valid C or D proof resolves the Clay problem on Clay’s own terms even while unforced A and B remain open.","claim_type":"significance","claim_status":"supported","confidence_score":null,"created_at":"2026-09-14T02:21:25.209Z","updated_at":"2026-09-14T02:21:25.209Z"},{"id":"972dd11f-e1e5-49ce-b424-39a57b466143","event_id":"85b36745-6f8b-4b76-82f3-9749a33356bc","claim_text":"The unforced Clay statements A and B remain open.","claim_type":"significance","claim_status":"supported","confidence_score":null,"created_at":"2026-09-14T02:21:25.209Z","updated_at":"2026-09-14T02:21:25.209Z"},{"id":"77c0e382-b6ee-4237-ac16-562a2777d9bf","event_id":"85b36745-6f8b-4b76-82f3-9749a33356bc","claim_text":"The Clay Mathematics Institute has awarded the Millennium Prize or completed its evaluation.","claim_type":"significance","claim_status":"disputed","confidence_score":null,"created_at":"2026-09-14T02:21:25.209Z","updated_at":"2026-09-14T02:21:25.209Z"},{"id":"dd1f7398-b492-4fec-9a97-c6807bea01ce","event_id":"85b36745-6f8b-4b76-82f3-9749a33356bc","claim_text":"GPT-6 Astra produced the Navier–Stokes proof.","claim_type":"attribution","claim_status":"disputed","confidence_score":null,"created_at":"2026-09-14T02:21:25.209Z","updated_at":"2026-09-14T02:21:25.209Z"},{"id":"22c494c5-34e8-425b-82bb-18c6120696a7","event_id":"85b36745-6f8b-4b76-82f3-9749a33356bc","claim_text":"Priority and provenance are settled; unpublished interactions could not have influenced OpenAI’s process.","claim_type":"attribution","claim_status":"disputed","confidence_score":null,"created_at":"2026-09-14T02:21:25.209Z","updated_at":"2026-09-14T02:21:25.209Z"},{"id":"bd4a989f-7d45-477f-ac75-7071866b7281","event_id":"85b36745-6f8b-4b76-82f3-9749a33356bc","claim_text":"Hodge, Birch–Swinnerton-Dyer, Riemann, Yang–Mills, or P vs NP have been solved in the same week.","claim_type":"significance","claim_status":"disputed","confidence_score":null,"created_at":"2026-09-14T02:21:25.209Z","updated_at":"2026-09-14T02:21:25.209Z"}],"revisions":[{"id":"f2239578-079b-4b70-b489-3b92d7e55ed7","event_id":"85b36745-6f8b-4b76-82f3-9749a33356bc","model_id":null,"previous_score":"0.000000","new_score":"1.125400","previous_factors":{},"new_factors":{"evidence":0.45,"base_score":10,"durability":0.65,"attribution":0.9,"realization":0.45},"change_reason":"Imported September 2026 mathematics events under methodology 0.1 credit-unit rules.","trigger_type":"editorial_import","trigger_source_ids":null,"reviewer_id":null,"review_status":"published","created_at":"2026-09-13T21:33:49.339Z"},{"id":"b2cd5716-3e50-4e7a-9fd0-371b3512d54e","event_id":"85b36745-6f8b-4b76-82f3-9749a33356bc","model_id":null,"previous_score":"1.125400","new_score":"15.351600","previous_factors":{},"new_factors":{"flags":["Priority contested","Clay review pending","Unforced A/B remains open"],"evidence":0.7,"base_score":30,"durability":0.95,"attribution":0.9,"realization":0.9},"change_reason":"Rescored Navier–Stokes as Historic/provisional: base tier is importance-if-true; Clay C/D is an official formulation; 11 September Clay note and specialist commentary raise evidence; math realization and durability no longer double-count uncertainty.","trigger_type":"editorial_import","trigger_source_ids":null,"reviewer_id":null,"review_status":"published","created_at":"2026-09-14T02:21:25.209Z"},{"id":"fe5e3130-a002-45f3-bc47-90f5167a1f29","event_id":"85b36745-6f8b-4b76-82f3-9749a33356bc","model_id":null,"previous_score":"15.351600","new_score":"16.159500","previous_factors":{"tier":4,"evidence":0.7,"base_score":30,"durability":0.95,"attribution":0.9,"realization":0.9},"new_factors":{"tier":4,"models":["8b0780ab-3f59-4f88-8ee4-00662f49a002","0f0d18fc-d3f1-4551-9eaf-a13f1f93b1a5"],"evidence":0.7,"base_score":30,"durability":0.95,"attribution":0.9,"realization":0.9},"change_reason":"Ingest update: added a follow-up source.","trigger_type":"ingest_update","trigger_source_ids":["ca8ff3b4-dfce-4126-bc9f-baaa08852448"],"reviewer_id":null,"review_status":"published","created_at":"2026-09-17T03:01:02.228Z"},{"id":"513b72bf-3365-40e8-8861-31dffdc915a2","event_id":"85b36745-6f8b-4b76-82f3-9749a33356bc","model_id":null,"previous_score":"16.159500","new_score":"16.159500","previous_factors":{"tier":4,"evidence":0.7,"base_score":30,"durability":0.95,"attribution":0.9,"realization":0.9},"new_factors":{"tier":4,"models":["8b0780ab-3f59-4f88-8ee4-00662f49a002","0f0d18fc-d3f1-4551-9eaf-a13f1f93b1a5"],"evidence":0.7,"base_score":30,"durability":0.95,"attribution":0.9,"realization":0.9},"change_reason":"Ingest update: added a follow-up source.","trigger_type":"ingest_update","trigger_source_ids":["b9f34a87-7028-4347-b878-3f5080bfe38c"],"reviewer_id":null,"review_status":"published","created_at":"2026-09-18T19:01:00.095Z"},{"id":"1acdb732-0b06-4b73-bf66-0addd5b7de71","event_id":"85b36745-6f8b-4b76-82f3-9749a33356bc","model_id":null,"previous_score":"16.159500","new_score":"16.159500","previous_factors":{"tier":4,"evidence":0.7,"base_score":30,"durability":0.95,"attribution":0.9,"realization":0.9},"new_factors":{"tier":4,"models":["8b0780ab-3f59-4f88-8ee4-00662f49a002","0f0d18fc-d3f1-4551-9eaf-a13f1f93b1a5"],"evidence":0.7,"base_score":30,"durability":0.95,"attribution":0.9,"realization":0.9},"change_reason":"Ingest update: added a follow-up source.","trigger_type":"ingest_update","trigger_source_ids":["9102db94-ff6f-4435-a414-79d48c3dd44c"],"reviewer_id":null,"review_status":"published","created_at":"2026-09-22T16:00:56.606Z"}],"secondary":[{"name":"Physics","slug":"physics"},{"name":"Computer Science","slug":"computer-science"}]},"methodology_version":"0.1"}