TEBAC Navier–Stokes Program V: Clay-Compatible Global Regularity Assembly — Final Closure Upgrade

This preprint is the fifth module of a modular TEBAC approach to the three-dimensional incompressible Navier--Stokes regularity problem on the periodic torus\[ T^3= R^3/(2π Z)^3.\] The preceding modules establish the periodic Leray--Stokes--Galerkin foundation, the vorticity-to-shell decomposition, the critical resonance absorption mechanism, the terminal axial-envelope packing closure, and the cutoff-uniform critical \(H1/2\)-Stokes estimate for Galerkin approximants. The purpose of the present module is to perform the final Clay-compatible assembly step from the NS-IV critical norm closure theorem to global smooth periodic solutions. The central implication assembled in NS-V is\[0≤ t≤ T\|A1/4u_N(t)\|L^2^2+ν∫_0^T\|A3/4u_N(t)\|L^2^2\,dt≤ C(T,ν,u_0)\]uniformly in the Galerkin cutoff \(N\), followed by the Galerkin compactness passage, synchronization with the local classical branch, weak--strong uniqueness, continuation beyond any finite maximal time, and smoothness bootstrap. The module proves that, relative to the upstream NS-I--NS-IV exports, the cutoff-uniform critical estimate excludes finite-time blow-up and yields a unique global smooth solution for smooth divergence-free mean-zero initial data on \( T^3\). The pressure is reconstructed by the periodic Poisson equation\[-Δ p=∂_i∂_j(u_i u_j),∫T^3p(x,t)\,dx=0.\] Status statement: NS-V is a final assembly module in the TEBAC Navier--Stokes candidate proof chain. It closes the Clay-compatible global regularity assembly relative to the upstream module exports. It should not be read as an independently refereed or officially certified solution of the Clay Millennium problem; the full external status depends on referee-level verification of the entire NS-I--NS-V chain, especially the critical NS-IIIa/NS-IV interface.