Global Regularity for 3D Navier–Stokes on the Periodic Torus via Dyadic Morrey–Envelope Closure

This upload provides a self-contained, referee-auditable proof package for global regularity of the 3D incompressible Navier–Stokes equations on the periodic torus 𝕋³. For smooth divergence-free initial data, we show that any Leray–Hopf weak solution obtained by a standard regularized construction and satisfying the local energy inequality cannot develop a space–time singularity, hence is smooth for all t≥0t 0t≥0. Main mechanism (one-line): a dyadic Morrey-envelope contraction M (ℓ) ≤ ρ M (2ℓ) + C0, with ρ = 2 Cᵢnt κ* + Cforc η < 1. closed by an explicit locking checklist and a dyadic dichotomy (bad step → forced CKN-large subcylinder, good step → diffusion-window absorption). How to verify (referee quick-start): Unconditional forcing/tail entry bound (Appendix AE). Two consecutive bad dyadic steps are excluded (Appendices D and AC). Morrey control implies KE smallness (Appendix AD). CKN ε-regularity yields smoothness; weak–strong uniqueness gives uniqueness in the admissible Leray–Hopf class. What is not claimed: No new ε-regularity theorem beyond standard Caffarelli–Kohn–Nirenberg, and no reliance on solution-dependent “hidden constants”; all constants and dependency arrows are explicitly tracked.