Navier-Stokes Millennium Problem: Unresolved Status and Proposed Global Solution Method — E8 Intelligence Research

FINDING: Navier-Stokes existence/smoothness remains open; a claimed proof (arXiv:1806.10081v10) proposes a new global-solution method, but no verified breakthrough; mainstream consensus is unresolved. | MATH: Navier-Stokes 3D: ∂u/∂t + (u·∇)u = -∇p + ν∇²u + f, ∇·u = 0; Millennium criteria: smooth u(x,t) for all t>0 given smooth, bounded initial data; key open question is finite-time blow-up of vorticity ω = ∇×u. | CONNECTION: No direct geometric-harmony ratio (0.382, 0.618, 0.786, 1.618, 2.618) or base-60 link in the findings. However, the vorticity equation ω_t + (u·∇)ω = (ω·∇)u + ν∇²ω reveals a stretching term (ω·∇)u — this is a Lie bracket / commutator structure, related to the rotation group SO(3) and crystallographic root-system symmetries (e.g., A3, B3) in the sense of anisotropic vortex stretching along principal axes. | DEPTH: 7 — the problem is profound (Clay Prize, turbulence, existence of singularities), but the provided findings contain no new verified mathematics; the arXiv Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com