Theorem · version 3
There exists smooth compactly supported divergence-free initial velocity on ℝ³ whose unforced incompressible Euler solution has a positive finite maximal smooth lifespan T*, with limsup as t ↑ T* of ‖∇u(t)‖∞ infinite and infinite.
The 2026 manuscript’s smooth-data theorem; the source-reported formal proof is under mathematical assessment.
This source presents a theorem with a proposed proof. Its wording does not establish acceptance or independent mathematical review.
Proposed
Compact smooth data on ℝ³; finite maximal lifespan and derivative/vorticity blowup.
Finite Time Blowup for the Euler Equation · Theorem 1.1 and Section 1.1 →
Source dated Sep 8, 2026 · Observed Oct 13, 2026
Complete formal proof reported externally
This formal theorem supplies compact support, a maximal lifespan 0 < T* ≤ 1 in the all-order Sobolev class, bounded energy before breakdown, infinite C¹ limsup and divergent integrated vorticity. The project reports only standard logical axioms and self-assessed correspondence. It is not an OpenMath execution.
Statement match: Linked by OpenMath · independent review separate · checked Oct 13, 2026
Euler.exists_compact_smooth_euler_singularityCommit f9e8bc5b38b6e212696e8a30e3e91517af887bbd
In this problem · publication v8 · Selected context
Primary formulation · Proposed
Relationship not independently reviewed. This concerns its use in this problem.
In this problem · publication v9
Primary formulation · Proposed
Relationship not independently reviewed. This concerns its use in this problem.
The manuscript states smooth compactly supported unforced Euler data with finite maximal lifespan.
paraphrase · OpenMath supplies its own mathematical paraphrases and links; proof text is not republished.
OpenAI · Preprint · Publication date Sep 8, 2026
Source revision: 2026-09-08. Observed Oct 13, 2026.
OpenAI attributes the argument to its internal research model. Bibliographic authorship is printed as OpenAI; individual human preparation and checking roles are not inferred.
The exact endpoint gives compact smooth nonzero data, a finite positive maximal Sobolev lifespan, bounded energy, infinite C¹ limsup and divergent integrated vorticity.
paraphrase · OpenMath supplies its own mathematical paraphrases and links; proof text is not republished.
The project reports complete main-result formalizations, zero sorry counts and only standard logical axioms at the listed endpoints.
paraphrase · OpenMath supplies its own mathematical paraphrases and links; proof text is not republished.
OpenAI · Project documentation · Publication date Sep 8, 2026
Public formal source; execution and statement correspondence are separate checks.
Exact proof source inspected. This digest identifies this file only, not a project build, theorem correspondence or independent reproduction.
Source revision: f9e8bc5b38b6e212696e8a30e3e91517af887bbd. Observed Oct 13, 2026.
The project metadata names GPT-6 Astra with Codex for formalization and marks alignment review as self-assessed. Lean, Mathlib and independent statement/Comparator infrastructure have separate supporting roles.
Euler nonexistence and compact-data proofs: f9e8bc5b38b6e212696e8a30e3e91517af887bbd.
Statement versions and problem publication versions are separate. A new publication can update context or sources while retaining the same statement.
Assessments retained in these publication records. Earlier statement versions retain their own source histories.
Proposed
Compact smooth data on ℝ³; finite maximal lifespan and derivative/vorticity blowup.
Source dated Sep 8, 2026 · Observed Oct 13, 2026 · Source passage →