No Progress Found: Navier-Stokes Global Regularity Remains an Open Problem — E8 Intelligence Research

FINDING: No new mathematical insight or discovery; the search returns only expository videos and a single unverified arXiv preprint claiming a solution. The core problem remains open: whether 3D Navier-Stokes equations with smooth initial data always yield smooth solutions globally in time. MATH: The Navier-Stokes equations for incompressible flow: ∂u/∂t + (u·∇)u = -∇p + ν∇²u + f, ∇·u = 0 Key unknown: existence of smooth (C∞) velocity field u(x,t) for all t>0 given smooth initial data. The critical threshold for blow-up involves the vorticity ω = ∇×u and the strain tensor S. No proven constants or ratios emerge from the search. CONNECTION: None found. The problem is analytic, not geometric. No ratios (0.382, 0.618, etc.), no base-60, no crystallographic symmetry. The equations are continuous and Euclidean, not discrete or harmonic. DEPTH: 1 — The search yields no original mathematical content. The arXiv preprint (1806.10081v10) is not peer-reviewed and has no known acceptance; i Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com