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Navier–Stokes Millennium Prize problem: finite-time breakdown with smooth forcing
OpenAI claims to construct a smooth finite-energy solution of the three-dimensional incompressible Navier–Stokes equations, starting from a fluid at rest and driven by smooth forcing, that develops a finite-time singularity. The construction is claimed both on R^3 and in the periodic setting, thereby establishing statements C and D of Fefferman's official Clay formulation. If the correspondence between the released proof/formalization and the Clay statements survives independent review, this resolves the Navier–Stokes Millennium Prize problem. It does not establish finite-time blow-up for the unforced Navier–Stokes equations; the Clay resolution comes through the smooth-forcing alternatives C/D.
Exact FrontierDelta
Prior state unknown→proved
Scope and record
Occurred: Sep 5, 2026
Delta type: SOURCE CLAIM
Assumptions: VibeMathed verification: lean-verified. Publication: preprint. AI contribution: ai-discovered. VibeMathed editorial classifications, scores, notes, relations, and dataset structure are CC BY 4.0. Source statements and linked content retain their own rights.
Canonical aliases: Navier–Stokes Millennium Prize problem: finite-time breakdown with smooth forcing · Navier–Stokes (Clay C/D)
Confidence: Not scored
Registry verification: lean verified · preprint · candidate
Attribution
VibeMathed
registry · event recorded by
Unnamed internal OpenAI model
model · ai model contributor · OpenAI
Artifacts and verifiers
formal registration · pending
Artifact ↗Compute record
No linked compute attempts recorded.
Lineage and corrections
OpenAI claims to construct a smooth finite-energy solution of the three-dimensional incompressible Navier–Stokes equations, starting from a fluid at rest and driven by smooth forcing, that develops a finite-time singularity. The construction is claimed both on R^3 and in the periodic setting, thereby establishing statements C and D of Fefferman's official Clay formulation. If the correspondence between the released proof/formalization and the Clay statements survives independent review, this resolves the Navier–Stokes Millennium Prize problem. It does not establish finite-time blow-up for the unforced Navier–Stokes equations; the Clay resolution comes through the smooth-forcing alternatives C/D. parent of this event
VibeMathed record: Navier–Stokes Millennium Prize problem: finite-time breakdown with smooth forcing evidence for this event
Navier–Stokes Millennium Prize problem: finite-time breakdown with smooth forcing evidence for this event
Formal Conjectures' original, which the statement matches byte for byte evidence for this event
Navier–Stokes Millennium Prize problem: finite-time breakdown with smooth forcing parent of this event
This event attributed to Unnamed internal OpenAI model
Fefferman's official Clay problem description evidence for this event
Navier–Stokes existence and smoothness evidence for this event
OpenAI's comparator challenge statement for (C) and (D) evidence for this event
The Lean development and comparator configuration evidence for this event
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