A Geometric Observable for Nonlinear Activation in Fluid Flows (OSJ)

This work introduces a geometric regularization framework (OSJ) for the convective term in the three-dimensional Navier–Stokes equations. The approach is based on a spectral–geometric observable that detects helical torsion concentration and dynamically decouples critical geometric configurations from the nonlinear transport mechanism. We formulate a geometric instability lemma and derive a BKM-type criterion expressed in terms of the OSJ observable, providing a sufficient condition under which the convective contribution of the critical set becomes dynamically negligible. The analysis does not eliminate singular structures but renders their influence observable and controllable through geometric regularization. The framework offers a new perspective on blow-up mechanisms in Navier–Stokes, emphasizing geometric alignment, helicoidal instability, and spectral localization. This work is intended as a theoretical contribution and preprint for further mathematical scrut iny.