Finite-time Navier-Stokes blowup driven by a smooth force
In plain words
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.
Precise statement
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.
What would settle it
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 in the literature
Unverified 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.