Dynamic Transversal Decoherence (DTD) and the 3D Navier–Stokes Regularity Problem: A Structural Program with Technical Closure

This project presents a structured research program addressing the global regularity problem for the three-dimensional incompressible Navier–Stokes equations via the mechanism of Dynamic Transversal Decoherence (DTD). The work develops a geometric–microlocal framework that reduces potential singular behavior to the persistence of angular coherence in the vorticity direction field. The program is organized modularly, culminating in a technical closure consisting of gap-closing lemmas and fully detailed appendices. The present repository includes: the complete DTD structural framework, paradifferential and microlocal reductions, a hypocoercive mechanism for transversal angular decay, and a set of technical appendices (A–C) addressing curvature coercivity, hypocoercive corrections, regularization, and passage to the limit. The results are formulated under standard assumptions compatible with Leray–Hopf weak solutions and rely only on time-integrability of the Lipschitz norm of the velocity field and absence of spatial concentration. This project is intended as a technical preprint and research program.