The σ-Cascade: Navier–Stokes as Coherence Failure in a Closed Dynamical System

Reframes the Navier–Stokes existence and smoothness Millennium problem as a competition between two operators: the σ-operator (nonlinear advection via vortex stretching, which concentrates coherence defects into smaller scales) and the kernel operator (viscous diffusion, which redistributes energy toward equilibrium). Shows that in 2D the ½-operator is stable (enstrophy conservation locks the cascade), while in 3D the σ-cascade is free. The Hou–Chen proof of 3D Euler blowup (2023) demonstrates that without viscosity, σ wins. Conjectures 3D Navier–Stokes blowup: viscous diffusion is critical (not supracritical) and cannot overcome the structurally stable σ-cascade. Connects to Tao’s supercriticality barrier and the Beale–Kato–Majda and Caffarelli–Kohn–Nirenberg regularity results.