A Quantile–Interface Regularity Criterion for 3D Incompressible Navier–Stokes on T³: Dyadic Closure with Explicit Locking Verification (v1.3)

This upload provides the journal-ready, single-manuscript closure (v1.3.13) of the Quantile–Interface Law (qIL) regularity program for the 3D incompressible Navier–Stokes equations on T³, written in a fully auditable form. Problem: Can smooth solutions develop finite-time singularities in 3D Navier–Stokes on T³? Main result: Under explicit quantile–interface geometric hypotheses on vorticity sparseness across dyadic scales, we prove a closed dyadic Morrey-envelope contractionM(ℓ) ≤ ρ M(2ℓ) + C_initwith a single explicit contraction factorρ = 2 C_int κ* + C_forc η < 1,yielding regularity up to any prescribed final time T via the classical Caffarelli–Kohn–Nirenberg ε-regularity criterion. How to verify (referee checklist):(i) R_r forcing control is unconditional (Appendix AE).(ii) Two consecutive bad dyadic scales are excluded (Appendix AD/AC).(iii) KE smallness follows from Morrey input (Appendix AD).(iv) Locking is explicit with ρ = 2 C_int κ* + C_forc η < 1 (Appendix J + Appendix AC). What is NOT claimed.This manuscript does not introduce a new ε-regularity theorem beyond standard CKN, and does not propose a new notion of weak solution. All logical dependencies are explicitly acyclic (Appendix J) and all auxiliary estimates are stated with explicit constant/quantifier dependencies. c materials may be released separately for transparency, but they are not required to follow the argument in this record.