No Verified Solution to Clay Millennium Problems; OpenAI Navier–Stokes Claim Unconfirmed — E8 Intelligence Research

FINDING: No verified solution to any Clay Millennium Problem exists as of the 2025–2026 window; the "OpenAI solved Navier–Stokes" claim is unconfirmed, contested, and lacks a peer-reviewed formal proof. | MATH: Navier–Stokes existence/smoothness in ℝ³: ∂ₜu + (u·∇)u = −∇p + νΔu, ∇·u = 0; open question is whether smooth finite-energy initial data (u₀ ∈ C^∞_c, ∇·u₀=0) can develop finite-time blow-up (‖∇u‖L^∞ → ∞) or must remain globally smooth. Critical scaling: u_λ(x,t)=λu(λx,λ²t) leaves ‖u₀‖L³ and ‖u₀‖_{Ḣ1/2} scale-invariant — the borderline Sobolev exponent. | CONNECTION: None established. No ratio (0.382/0.618/0.786/1.618/2.618), base-60 structure, crystallographic symmetry, or root-system/lattice structure appears in the sourced material. The only "harmonic" element is the scale-invariance exponent ½ (the critical Ḣ1/2 norm), which is a dimensional/self-similarity property of the PDE, not a geometric-harmony constant. | DEPTH: 2 Precise assessment of the evidence: 1. Ke Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com