Borromean Triads, the Ring Lemma, and Spectral Non-Dispersal

This preprint introduces a conditional regularity framework for the 3D incompressible Navier–Stokes equations based on spectral localization and geometric control of vorticity direction. Key contributions include:- The Ring Lemma, bounding vorticity direction gradients by shell frequency- A Spectral Non-Dispersal (SND) condition- A Global Summation Lemma under SND- Global regularity of an augmented Navier–Stokes system with targeted operators No claim is made regarding unconditional regularity of the classical Navier–Stokes equations. One open problem remains: whether SND holds dynamically for all Leray–Hopf solutions.