Anandkumar et al.: unforced 3D Euler singularity candidate (PINN)
Vintage: 2026-09. Issuer blog dated Sep 7, 2026; X announce Sep 8. Evidence in 2026-09-08-x-morning-buckmaster-alpoge-ai-fluid-proofs-openai-credit. Keep as candidate / partial formalization. Unforced Euler ≠ Clay unforced Navier–Stokes; also ≠ Buckmaster–Alpöge with forcing.
Anandkumar et al.: unforced 3D Euler singularity candidate (PINN)
One-line summary: anima-anandkumar reported a PINN-found unforced 3D Euler singularity candidate on R^3 (blog 7 Sep 2026). Tao (via her cite) notes rigorous stability demonstration still lacking. Contrasts with buckmaster-alpoge-forced-blowups.
The insight
A parallel AI-for-fluids track on the unforced Euler equations in free space — PINN approximate self-similar blowup, then spline refinement for certified bounds. The clip’s grain is candidate, not a finished Lean-checked theorem and not the Clay NS prize. Do not collapse into Buckmaster–Alpöge (smooth forcing) or into “Navier–Stokes solved” discourse.
Evidence
All bullets are from 2026-09-08-x-morning-buckmaster-alpoge-ai-fluid-proofs-openai-credit.
- From 2026-09-08-x-morning-buckmaster-alpoge-ai-fluid-proofs-openai-credit (@AnimaAnandkumar, 2026-09-08): “We have found stable singularity on 3D Euler!” linking Stable Singularity of the Euler Equations on R^3 without forcing (dated Sep 7, 2026; authors Adarsh Ganeshram, Valentin Duruisseaux, Anima Anandkumar per X news cluster / Tao note).
- From the same source (issuer blog): PINN finds approximate self-similar blowup on free space without boundary or forcing; refine with splines for certified bounds; transport-field study for linear damping; contrasts with Buckmaster–Alpöge with forcing.
- From the same source (@AnimaAnandkumar): Tao Mastodon acknowledgment amplified. Tao (via Anima’s cite) notes rigorous stability demonstration still lacking.
What this source does not establish
- Not Clay unforced Navier–Stokes.
- Not a Lean-checked finished proof in this clip (PINN + spline bounds; stability still lacking per Tao-via-Anima).
- No person pages for Ganeshram, Duruisseaux, or Tao.
- Paper-body beyond the issuer blog not separately fetched as a PDF.
- No ticker.
Contradictions / tensions
- Unforced candidate vs forced Lean results vs OpenAI unforced Euler. Same news window, different objects. Afternoon OpenAI unforced Euler is openai-unforced-euler — issuer writeup, not this PINN candidate. Not collapsed.
- “Stable singularity” headline vs Tao note that rigorous stability demonstration is still lacking.
Open questions
- Does a later formalization close the stability gap Tao flagged?
- How do certified spline bounds compare to the Buckmaster–Alpöge Lean statements (different equations / forcing)?