Dynamic Certificate Closure for Navier–Stokes: A Conditional Branch-Reduction Framework for Singular Cascades

This manuscript presents Dynamic Certificate Closure, a conditional branch-reduction framework for the three-dimensional incompressible Navier–Stokes regularity problem. The framework organizes a hypothetical singular cascade through scale-critical velocity-pressure mass, pressure gauge behavior, frame normalization, frequency loss, and concentration channels. The paper does not claim an unconditional proof of global regularity. Instead, it audits the reduction architecture and identifies two terminal profile regimes that must be excluded: a bounded ancient suitable weak Navier–Stokes critical profile, and an unbounded degenerate amplitude-normalized stationary Euler/Reynolds concentration profile. Regularity follows within the framework only if both terminal gates are closed. This work is intended as a structured reduction and proof-audit document for future analysis of singular cascades, scale-critical compactness, and terminal profile exclusion in the Navier–Stokes problem.