Publication v8
Original question, distinct results, proof provenance, selected history and an explanatory schematic.
Formal proofs: Pinned Lean C/D nonexistence theorems are reported complete, with zero sorry and standard logical axioms. They are distinguished from the manuscript’s stronger detailed singular-flow construction; OpenMath has not executed the project.
AI-assisted work: OpenAI is the printed manuscript author and credits an internal multi-agent research-model workflow for the mathematical argument. The announcement and formal metadata credit GPT-6 Astra/Codex for formalization. Fefferman and CMI own the official statement and evaluation process; Lean, Mathlib and Formal Conjectures/Comparator contributors support the proof infrastructure. Alpöge and Buckmaster’s separately credited forced-Euler work is not this Navier–Stokes theorem.
Selected primary papers, exact formal declarations, project provenance and official descriptions checked on 13 October 2026.
Checked Oct 13, 2026 · independent review pending.
Forced whole-space breakdown reported · observed Oct 13, 2026
Source status dated Sep 8, 2026 · observed Oct 13, 2026
Every positive viscosity; compact smooth force, zero initial velocity, bounded kinetic energy.
Forced periodic breakdown reported · observed Oct 13, 2026
Source status dated Sep 8, 2026 · observed Oct 13, 2026
Every positive viscosity; smooth periodic data and forcing.
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
navier-stokes: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:v2navier-stokes:entry:lean-r3:v2navier-stokes:entry:lean-periodic:v2Charles L. Fefferman · 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
navier-stokes:entry:clay:v1navier-stokes:clay-two-dimensions:v1navier-stokes:clay-small-data:v1navier-stokes:clay-short-time:v1navier-stokes:clay-leray:v1navier-stokes:clay-partial-regularity:v1Clay Mathematics Institute · 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
navier-stokes:entry:clay-announcement:v1Di Kang; Bartosz Protas · metadata-link · Links and original OpenMath paraphrases only; upstream license governs external files.
No upstream full text is republished by this record. Rights / source terms
navier-stokes:kang-protas-lps:v1navier-stokes:kang-protas-energy:v1Terence Tao · metadata-link · Links and original OpenMath paraphrases only; upstream license governs external files.
No upstream full text is republished by this record. Rights / source terms
navier-stokes:tao-l3-criterion:v1Source-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.