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) + Cᵢnitwith a single explicit contraction factorρ = 2 Cᵢnt κ* + Cforc 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) Rᵣ 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 Cᵢnt κ* + Cforc 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.
Branimir Sabljić (Fri,) studied this question.