Alphabeta MathResearch frontier status and calibrated model evidence
About this page
Pipeline-generated
How statement and proof provenance work
The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.
- Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
- AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
- AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.
These labels describe origin, not correctness: citations and verification chips remain separate evidence.
1 · Prerequisites
None. This page is self-contained.
2 · Logical flowchart
3 · Items
Remark
Research status for the Navier–Stokes regularity frontier
Remark
Evidence scope for calibrated and learned fluid models
Sources
- Charles L. Fefferman, ‘Existence and Smoothness of the Navier–Stokes Equation,’ in The Millennium Prize Problems (Clay Mathematics Institute, 2006)
- Clay Mathematics Institute, Navier-Stokes Equation, current Millennium Prize Problem page
- Clay Mathematics Institute, Navier-Stokes Announcement, 11 September 2026
- OpenAI, On the Navier–Stokes Millennium Prize Problem, 8 September 2026
- OpenAI, Finite Time Blowup for Navier–Stokes, 2026 preprint
- Alexander Bastounis, Fabian Circelli, and Anders C. Hansen, Navier-Stokes lost in translation: Why Lean verification of AI autoformalisation does not guarantee correct natural language proofs, arXiv:2610.08144v1 (6 October 2026)
- Karthik Duraisamy, Gianluca Iaccarino, and Heng Xiao, Turbulence Modeling in the Age of Data, Annual Review of Fluid Mechanics 51 (2019), 357–377
- DongHun Yeo, A Summary of Industrial Verification, Validation, and Uncertainty Quantification Procedures in Computational Fluid Dynamics, NIST IR 8298 (2020)
- Noelle Selin, ESD.864 Lecture 3: Verification and Validation, MIT OpenCourseWare (12 February 2013)