No Verified Solution to Any Clay Millennium Problem; 2025–2026 AI Navier–Stokes Claims Unverified — E8 Intelligence Research

FINDING: No verified solution to any Clay Millennium Problem exists as of the search window; the 2025–2026 "AI solved Navier–Stokes" claims are unverified, contested, and partly plagiarism-disputed, while the only arXiv item is a self-published (v23) preprint, not peer-reviewed. MATH: - Navier–Stokes (3D, incompressible): ∂u/∂t + (u·∇)u = −(1/ρ)∇p + ν∇²u, ∇·u = 0 Clay statement requires proof of global regularity OR finite-time blow-up from smooth finite-energy data. - Critical scaling: u_λ(x,t) = λu(λx, λ²t). NS is *supercritical* in 3D — the energy norm ‖u‖_{L²} scales as λ^{−1/2}, so energy methods cannot close the gap. This scaling deficit is the structural obstruction, not a missing trick. - Vorticity form: ∂ω/∂t + (u·∇)ω = (ω·∇)u + ν∇²ω. The vortex-stretching term (ω·∇)u is the sole source of possible singularity. - Beale–Kato–Majda criterion: blow-up at T* ⟺ ∫₀^{T*} ‖ω(·,t)‖_{L^∞} dt = ∞. - Prodi–Serrin regularity class: u ∈ L^p_t L^q_x with 2/p + 3/q ≤ 1, q > 3. The expon Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com