Consensus State
Under Active Dispute
Priority Risk
High
Lean Verifiability
42%
Millennium Compliant
No (Smooth Forcing)
Active Case & Research Track
Case NS-2026-AI-1
“Today, Levent Alpöge and I have made public three results: finite-time blowup with smooth forcing for incompressible porous media, for Boussinesq, and for 3d incompressible Euler. We believe we also have blowup for hypo-dissipative Navier-Stokes... unlike the above, the Lean verification has not yet finished.” — Tristan Buckmaster
Fluid Equations & Counterexample Matrix
Select model equation to probe singularity
| Model PDE | Dissipation / Viscosity | Forcing Term | Lean 4 Formalization | Singularity Status |
|---|
Lean 4 Proof Verification Pipeline
2 of 5 Verified
Each milestone below represents a required mathematical component in establishing finite-time blowup for incompressible flow. Click toggles to simulate independent proof check completion.
Priority Norms & Attribution Audit Flags
Audit evidence weights
Academic Controversy & Priority Audit Report
Deterministic Verification Docket • Ref: DOCKET-NS-BLOWUP-OPENAI
Target Claim ID:
ns-blowup-openai
Primary Proponent:
OpenAI / Agentic AI Agents
Independent Rival:
Tristan Buckmaster & Levent Alpöge (Anthropic)
Consensus Status:
Under Active Dispute
Priority Risk Index:
High
Verifiability Score:
42
Lean Formalization:
Incomplete for Navier-Stokes / Complete for related Euler/Boussinesq
Navier-Stokes Governing Equation Analysis:
∂tu + (u • ∇)u = -∇p + ν Δu + f(x,t), ∇ • u = 0
Blowup Criterion (Beale-Kato-Majda): ∫0T ||ω(•, t)||L∞ dt = ∞
Current inspection: Claimed blowup utilizes non-autonomous smooth forcing f(x,t) ≠ 0. Clay Millennium Prize formulation requires smooth evolution with f = 0 (unforced Navier-Stokes) or globally smooth autonomous forcing.
AUDIT COMMITTEE VERDICT SUMMARY
The OpenAI agentic proof constructs a finite-time blowup using computer-generated ODE/PDE enclosure scripts, but controversy persists regarding uncredited prompt provenance derived from Tristan Buckmaster's prior Codex interactions. Full Lean 4 verification of the viscous dissipation step remains pending peer review.
Durable Artifact Handoff
Ready for Export
/* Click "Export Verification JSON" to generate official signed payload */
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navier-stokes-audit-ns-blowup-openai.json