Publication v8
Original question, distinct results, proof provenance, selected history and an explanatory schematic.
Formal proofs: The pinned project reports both a detailed compact-data finite-lifespan theorem and a separate global bounded-energy nonexistence theorem, with zero sorry and standard logical axioms. Their statements were compared; independent review and external build remain pending.
AI-assisted work: OpenAI is the printed author of the unforced Euler manuscript and credits its internal research-model workflow. GPT-6 Astra/Codex is credited for the later formalization. Beale, Kato and Majda own the older continuation criterion. The announcement separately recognizes Levent Alpöge and Tristan Buckmaster’s Anthropic-assisted forced-Euler result; it is not the same unforced theorem. Individual mathematical checking roles are not inferred from formal code.
Selected primary papers, exact formal declarations, project provenance and official descriptions checked on 13 October 2026.
Checked Oct 13, 2026 · independent review pending.
Smooth unforced Euler singularity reported · observed Oct 13, 2026
Source status dated Sep 8, 2026 · observed Oct 13, 2026
Compact smooth data on ℝ³; finite maximal lifespan and derivative/vorticity blowup.
OpenAI · metadata-link · Original source license and document rights apply.
OpenMath supplies its own mathematical paraphrases and links; proof text is not republished. Rights / source terms
euler-regularity:entry:paper:v1OpenAI · metadata-link · Original source license and document rights apply.
OpenMath supplies its own mathematical paraphrases and links; proof text is not republished. Rights / source terms
fluid-regularity:entry:announcement:v1OpenAI · metadata-link · Original source license and document rights apply.
OpenMath supplies its own mathematical paraphrases and links; proof text is not republished. Rights / source terms
fluid-regularity:entry:lean:v2euler-regularity:entry:lean-singularity:v2euler-regularity:entry:lean-nonexistence:v2J. Thomas Beale, Tosio Kato, Andrew Majda · metadata-link · Original source license and document rights apply.
OpenMath supplies its own mathematical paraphrases and links; proof text is not republished. Rights / source terms
Source-linked pilot import; independent mathematical review remains pending.
Reviewed reader correction: preserve assertion history, exact citations and scoped assessments; task evidence names its exact Claim target.
Reviewed reader correction: preserve assertion history, exact citations and scoped assessments; task evidence names its exact Claim target.
Reviewed reader correction: preserve assertion history, exact citations and scoped assessments; task evidence names its exact Claim target.
Reviewed reader correction: preserve assertion history, exact citations and scoped assessments; task evidence names its exact Claim target.
Reviewed reader correction: preserve assertion history, exact citations and scoped assessments; task evidence names its exact Claim target.
Reviewed reader correction: preserve assertion history, exact citations and scoped assessments; task evidence names its exact Claim target.
Reviewed reader correction: preserve assertion history, exact citations and scoped assessments; task evidence names its exact Claim target.
Reviewed reader correction: preserve assertion history, exact citations and scoped assessments; task evidence names its exact Claim target.