{"data":{"event":{"id":"4cb49466-0bb5-4b74-8091-1f91cdfc2cd8","slug":"ganeshram-duruisseaux-anandkumar-euler-pinn-candidate","title":"A Caltech PINN finds a candidate unforced 3D Euler blowup profile","short_summary":"On 9 September 2026 Ganeshram, Duruisseaux, and Anandkumar posted evidence of a numerically stable, approximately self-similar finite-time singularity for unforced 3D Euler on R³, found with a physics-informed neural network. Terence Tao called it a promising candidate, not a closed proof.","full_description":"In the same week as OpenAI’s Navier–Stokes claim and the Buckmaster–Alpöge forced-blowup papers, Adarsh Ganeshram, Valentin Duruisseaux, and Anima Anandkumar released two arXiv manuscripts (2609.10867, 2609.10860). Using a physics-informed neural network with a self-similar ansatz, they report an approximate singular Euler profile at the critical blowup rate 1/2, plus a framework that would prove nonlinear stability if a large finite set of constants can be certified. Tao’s 7 September note, updated after the preprint, treats this as a significant advance on the mainstream self-similar approach and as relatively AI-light: the PINN searched for a profile; literature review and partial Lean work were secondary. This is not Clay Navier–Stokes, not unforced Euler as a theorem, and not GPT-6 Astra or GPT-5.6 Sol. Credit stays with the documented PINN system so those named LLM releases are not given the search.","ledger_type":"benefit","primary_domain_id":"23d935bb-b857-4b2b-9471-d568bb848a66","event_status":"provisional","event_date":"2026-09-09T00:00:00.000Z","discovery_date":"2026-09-09T00:00:00.000Z","first_published_date":"2026-09-09T00:00:00.000Z","last_reviewed_date":"2026-09-09T00:00:00.000Z","geographic_scope":"United States","affected_population":"Mathematical fluid-dynamics research community","base_impact_tier":2,"base_score":"3.00","attribution_multiplier":"0.4000","evidence_multiplier":"0.5000","realization_multiplier":"0.3500","durability_multiplier":"0.5500","current_event_score":"0.115500","confidence_level":"medium","score_explanation":"A published unforced-Euler candidate profile is notable mathematics (tier 2), not a closed theorem or a Millennium solution. The PINN materially located the ansatz (0.40). Evidence is arXiv plus expert commentary from Tao (0.50). Realization remains a candidate pending constant certification (0.35).","methodology_version_id":"d7881163-fb23-4e71-8625-bac1a8662c0f","original_methodology_version_id":"d7881163-fb23-4e71-8625-bac1a8662c0f","published_at":"2026-09-09T00:00:00.000Z","created_at":"2026-09-13T21:33:49.339Z","updated_at":"2026-09-13T21:33:49.339Z","flags":[],"domain_name":"Mathematics","domain_slug":"mathematics","methodology_version":"0.1"},"contributions":[{"id":"453146c9-b33b-4144-8639-8ca596808a6c","event_id":"4cb49466-0bb5-4b74-8091-1f91cdfc2cd8","model_id":"30586362-d468-429c-923e-785e52410cc5","role_description":"Physics-informed neural network used to locate an approximately self-similar unforced 3D Euler blowup profile.","attribution_multiplier":"0.4000","credit_share":"1.0000","contribution_score":"0.115500","attribution_rationale":"The authors and Tao attribute profile search to the PINN; general-purpose LLMs were secondary and are not named as the search model.","attribution_confidence":"medium","first_used_date":"2026-09-09T00:00:00.000Z","model_version_if_known":null,"review_status":"approved","created_at":"2026-09-13T21:33:49.339Z","model_slug":"ganeshram-duruisseaux-anandkumar-pinn","model_name":"Ganeshram–Duruisseaux–Anandkumar PINN","identity_class":"named_release","is_internal":false,"family_name":"PINN","family_slug":"caltech-pinn","organization_name":"California Institute of Technology","organization_slug":"caltech"}],"sources":[{"id":"b5ed6d76-2d79-48c6-ba52-11cf6a50b370","event_id":"4cb49466-0bb5-4b74-8091-1f91cdfc2cd8","url":"https://arxiv.org/abs/2609.10867","canonical_url":"https://arxiv.org/abs/2609.10867","source_type":"preprint","publisher":"arXiv","author":null,"publication_date":"2026-09-09T00:00:00.000Z","retrieved_at":"2026-09-13T21:33:49.339Z","title":"Stable Singularity of the Euler Equations on R³","excerpt":null,"content_hash":null,"source_reliability_class":"medium","is_primary_source":true,"is_independent":true,"is_peer_reviewed":false,"archived_url":null,"created_at":"2026-09-13T21:33:49.339Z"},{"id":"b0e7a09c-d80e-4e5a-af14-86161985a870","event_id":"4cb49466-0bb5-4b74-8091-1f91cdfc2cd8","url":"https://arxiv.org/abs/2609.10860","canonical_url":"https://arxiv.org/abs/2609.10860","source_type":"preprint","publisher":"arXiv","author":null,"publication_date":"2026-09-09T00:00:00.000Z","retrieved_at":"2026-09-13T21:33:49.339Z","title":"Stability Framework for the Singularity of the Euler Equations on R³","excerpt":null,"content_hash":null,"source_reliability_class":"medium","is_primary_source":true,"is_independent":true,"is_peer_reviewed":false,"archived_url":null,"created_at":"2026-09-13T21:33:49.339Z"},{"id":"894d20e6-90df-4923-b512-5ed37f3ccfe0","event_id":"4cb49466-0bb5-4b74-8091-1f91cdfc2cd8","url":"https://terrytao.wordpress.com/2026/09/07/finite-time-blowup-with-smooth-forcing-term-for-the-incompressible-porous-medium-boussinesq-and-incompressible-euler-equations/","canonical_url":"https://terrytao.wordpress.com/2026/09/07/finite-time-blowup-with-smooth-forcing-term-for-the-incompressible-porous-medium-boussinesq-and-incompressible-euler-equations/","source_type":"other","publisher":"Terence Tao","author":null,"publication_date":"2026-09-07T00:00:00.000Z","retrieved_at":"2026-09-13T21:33:49.339Z","title":"Finite time blowup with smooth forcing term for IPM, Boussinesq, and incompressible Euler","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"}],"claims":[{"id":"28f014ec-bdb4-4791-9874-9378d4f6c50d","event_id":"4cb49466-0bb5-4b74-8091-1f91cdfc2cd8","claim_text":"The authors posted numerical evidence of a stable approximate self-similar finite-time singularity for unforced 3D Euler on R³, found with a PINN.","claim_type":"outcome","claim_status":"supported","confidence_score":null,"created_at":"2026-09-13T21:33:49.339Z","updated_at":"2026-09-13T21:33:49.339Z"},{"id":"1f9c39e8-5d64-4370-a16c-ba452498dc4c","event_id":"4cb49466-0bb5-4b74-8091-1f91cdfc2cd8","claim_text":"This closes a rigorous proof of unforced 3D Euler blowup or the Clay Navier–Stokes problem.","claim_type":"significance","claim_status":"disputed","confidence_score":null,"created_at":"2026-09-13T21:33:49.339Z","updated_at":"2026-09-13T21:33:49.339Z"},{"id":"9c16007a-e85c-4d3a-9b99-e7699f3c9728","event_id":"4cb49466-0bb5-4b74-8091-1f91cdfc2cd8","claim_text":"GPT-6 Astra or GPT-5.6 Sol produced the candidate profile.","claim_type":"attribution","claim_status":"disputed","confidence_score":null,"created_at":"2026-09-13T21:33:49.339Z","updated_at":"2026-09-13T21:33:49.339Z"}],"revisions":[{"id":"7520e3f9-8f84-487a-ad7b-e3ee4510c46f","event_id":"4cb49466-0bb5-4b74-8091-1f91cdfc2cd8","model_id":null,"previous_score":"0.000000","new_score":"0.115500","previous_factors":{},"new_factors":{"evidence":0.5,"base_score":3,"durability":0.55,"attribution":0.4,"realization":0.35},"change_reason":"Imported September 2026 mathematics events under methodology 0.1 credit-unit 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