A Local Monotonicity Reduction of the 3D Navier–Stokes Regularity Problem to a Single Remaining Barrier

This paper introduces a scale-invariant local monotonicity framework for thethree-dimensional incompressible Navier–Stokes equations. The analysis systematically neutralizes all classical obstructions to localmonotonicity arising from advective flux, pressure nonlocality, and localizationerrors. As a result, the global regularity problem is reduced to a single explicitlocal condition: the behavior of a monotonicity functional in the limit ofvanishing scales. In particular, all mechanisms traditionally associated with singularity formationare resolved within the proposed framework except for one precisely identifiedremaining barrier. This manuscript is intended as a reduction and structural paper and has beensubmitted to Communications in Mathematical Physics.