Navier–Stokes Millennium Problem Still Open; OpenAI Solution Claim Unverified — E8 Intelligence Research

FINDING: No verified solution exists; the Navier–Stokes Millennium Problem remains open. The "OpenAI solution" is an unverified claim (dated 2026, i.e., speculative/future-dated content), and no peer-reviewed proof has been accepted by the Clay Mathematics Institute. | MATH: The problem concerns the 3D incompressible Navier–Stokes equations: ∂u/∂t + (u·∇)u = −(1/ρ)∇p + ν∇²u + f, with ∇·u = 0. The question: given smooth, divergence-free initial data u₀ ∈ C^∞ with finite energy (or Schwartz class), do smooth solutions exist for all time t > 0, or can finite-time blow-up (singularity) occur? | CONNECTION: No geometric-harmony constants (0.618, 1.618, etc.) appear in the problem statement itself. The relevant structural quantities are: the Reynolds number Re = UL/ν (dimensionless ratio governing turbulence onset), the Kolmogorov microscale η = (ν³/ε)^(1/4), and energy-cascade scaling exponents. Vorticity stretching term (ω·∇)u in the vorticity equation ω_t + (u·∇)ω = (ω·∇)u + ν∇²ω is the s Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com