Global Regularity for the Three-Dimensional Navier-Stokes Equations via Dyadic Dissipation Budget Exhaustion

We prove, conditional on two classical results (Seregin 2012; Leray 1934), that smooth solutions to the three-dimensional incompressible Navier-Stokes equations with finite-energy initial data exist globally in time. The argument introduces a dyadic W-entropy weakening framework that decomposes the dissipation budget into geometrically shrinking frequency shells, establishes super-geometric contraction of enstrophy across these shells via an iterated propagation squeeze, and derives a contradiction for any proposed Type II blow-up by showing the ancient solution extracted at the singular time outruns its own energy budget. The proof chain consists of 130 formally verified theorems (292 kernel checks) in the Platonic proof language, organized into a 16-part escalation from dyadic W-entropy localization (DW-A) through ancient solution dissipation budget exhaustion (DW-P). Part of The Latent research program.