{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"1dbd5c6c451f99eebc78a6cb9ef3be42d6971c80168f534f9dfd140b789b030e","created":"2026-10-03T07:18:06Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"d851847d42582d41a3e03845a77a7b5fefc94579ea6c5da87ec973cd04db8967","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"yes-no","assisted_by":[],"external_id":"mathph.fluid-singularities.forced-ns-blowup","kind":"well-posed","literature_status":"contested","n":"1","parents":[],"plain":"A machine-generated proof announced in September 2026 claims that a viscous fluid pushed by a smooth outside force can develop infinite velocity at one point in finite time. Whether the proof is correct decides two of the four official versions of the Clay problem.","posed_since":"2000","precise":"For $\\nu > 0$, do there exist smooth divergence-free u_0 with $\\mid d^a u_0(x)\\mid \\le C_{a,K} (1+\\mid x\\mid)^{-K}$ and smooth f with $\\mid d_x^a d_t^m f\\mid \\le C_{a,m,K} (1+\\mid x\\mid+t)^{-K}$ for which no smooth finite-energy solution of forced 3D Navier-Stokes exists on $R^3 x [0, \\infty)$ (Clay statement C; statement D is the periodic version)? The OpenAI construction claims such a blowup; its structure, as abstracted by Constantin, Ignatova and Vicol (arXiv 2609.20803), is Type II with an anisotropic angular mean and exact axisymmetry in a core collapsing to the singular point. Answer: independent verification or a located error.","problem_ref":null,"references":"","settled_by":"A line-by-line check of the manuscript and of any accompanying formal proof, including a check that the formal definitions match the Clay statement.","status_note":"Announced by OpenAI on 7-8 September 2026 (dates as reported by Petrillo and Glimm, arXiv 2609.23868); Constantin, Ignatova and Vicol (arXiv 2609.20803) proved rigidity constraints on constructions of its type; no independent verification as of 2026-10-01.","title":"Finite-time Navier-Stokes blowup driven by a smooth force","topic_ref":"56471002f5ad6f04f20e12861588794aa7901ecb598d7f960b48900e00132b59"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"44f79cd1c9082f171fff98ae365ec052b4a25f99639d31d5afd79a743b81edb5","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"6fffbc937832c85544bf746ecd1e820fac400f5ec55196f60e9d96d9da2852fb","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"2m5tKL-pZLLEuG8TJfv_1GtPjbmW6sa52EUv8s7R0l_6fN-2Y0ZZ5gYv6-oD4PNtw-oZCmRGQzWlq2NpGtEvDw"},"schema":"pubphys.envelope/1"},"record_hash":"44f79cd1c9082f171fff98ae365ec052b4a25f99639d31d5afd79a743b81edb5","leaf_index":1617}