No Verified Solution to Navier–Stokes; Millennium Prize Remains Open — E8 Intelligence Research

FINDING: No verified solution exists; OpenAI's 2026 claim is contested, and the Clay Millennium Prize remains open | MATH: ∂u/∂t + (u·∇)u = −∇p/ρ + ν∇²u + f, ∇·u = 0 | CONNECTION: None established — no geometric-harmony constants (0.382, 0.618, 0.786, 1.618, 2.618), base-60, or crystallographic/lattice structure appears in any cited source | DEPTH: 2 --- **1. Key mathematical insight or discovery** None confirmed. The corpus contains: - A **claim** (OpenAI, ~Sept 2026) of an AI-generated proof of 3D Navier–Stokes existence and smoothness. - A **rebuttal** (Stan Palasek) identifying a possible gap in that proof. - A **preprint** (arXiv:1806.10081v10) proposing a "new method" for global solutions — unrefereed, unverified, and not accepted by the Clay Institute. - **Expository content** (Numberphile, Lex Fridman/Terence Tao) explaining why the problem is hard: the singularity question is whether finite-time blow-up of ‖∇u‖_L∞ can occur from smooth finite-energy data. The mathematical Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com