Alphabeta MathHow 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.
Current public status of the three-dimensional Navier–Stokes problem
Remark
As checked on 2026-10-23, the Clay Mathematics Institute lists the three-dimensional Navier–Stokes existence-and-smoothness problem among its Active problems. In its announcement dated 2026-09-11, CMI said it contemplated an announcement that the problem had apparently been settled and that the evaluation process was deliberately unhurried. This remark records CMI's public status only: it does not assess or accept the announced proof, and this batch's two-dimensional periodic theorem makes no claim about three-dimensional Navier–Stokes or unrestricted three-dimensional Euler regularity.
Remark references
Facts & Assumptions
Given: This is a dated report of the public status displayed by the Clay Mathematics Institute, checked on 2026-10-23.
The CMI's current Millennium Prize Problems page lists “Navier–Stokes Equation” under “Active problems.”
In a notice dated 2026-09-11, CMI describes its response to an announcement that the Navier–Stokes problem has “apparently been settled” and says the evaluation process is “deliberately unhurried.”
Proof
The checked CMI list places Navier–Stokes Equation under its Active problems heading. This supports the first dated status sentence and states only the institution's public classification.
The CMI notice is dated 2026-09-11 and describes an announced result as apparently settling the problem while saying evaluation is deliberately unhurried. Its qualification reports an announcement under evaluation; it does not certify the proof. The remark preserves that qualification and limits the batch's result to two-dimensional periodic Navier–Stokes.
Dependency tree · 0 levels
Nothing. This result depends on no other item in the library.