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

This record provides a single, self-contained manuscript presenting an auditable proof program for global regularity of the 3D incompressible Navier–Stokes equations on the periodic domain 𝕋³. The text is written with referee-style navigation: explicit dependency structure, parameter locking, and internal proof-closure checkpoints designed to make a technical audit feasible within one document. This journal-ready revision is derived from the earlier Zenodo record (DOI: 10.5281/zenodo.18254516) and refines terminology and claim boundaries for peer review; the core proof structure is unchanged. Reader contract: One manuscript, one proof chain, with all assumptions stated explicitly. Main result: A quantile–interface regularity criterion yielding global smoothness on 𝕋³ under explicitly stated geometric/interface hypotheses, with a closed internal proof chain and parameter locking. How to verify (audit map): Key closure checkpoints are explicitly signposted (Appendix AE, parameter locking, and the kinetic decay estimate), enabling a local technical audit within one document. What this record does NOT claim: No claims are made beyond what is proved internally; remainder terms are explicitly tracked and absorbed within the stated mechanism, with fixed parameters. Supporting archival volumes and diagnostic materials may be released separately for transparency, but they are not required to follow the argument in this record.