Corrected Dynamic Certificate Closure for the Three-Dimensional Navier--Stokes Regularity Problem

This manuscript develops a corrected Dynamic Certificate Closure (DCC) framework for the three-dimensional incompressible Navier–Stokes regularity problem. The approach introduces a detector-based structure that partitions critical activity into velocity, pressure, transport, dissipation, and localization channels. Active density domination is established through a corrected detector family that includes uncaptured velocity mass, primary dissipation detection, endpoint energy variation, annular pressure decomposition, and terminal defect analysis. The framework reduces the regularity problem to a single explicitly stated analytic gate, termed Persistent Critical Activity Collapse. The manuscript presents the reduction architecture, detector system, terminal contradiction mechanism, and supporting compactness structure, while identifying the remaining theorem required for a complete regularity proof. This work is presented as a research framework and finite reduction program for further mathematical investigation.