Navier–Stokes Regularity Program (Vol. XV): Interface Law, Viscous Barrier, and Dynamic Closure of Interface Hypotheses

This record contains Vol. XV of the Navier–Stokes Regularity Program, which formulates a compact conditional regularity mechanism for 3D Navier–Stokes on the periodic torus T³, based on an interface law and a viscous barrier inequality, and then specifies a minimal dynamic lemma chain that targets an unconditional closure. Main result: a conditional regularity theorem showing that three interface hypotheses (interface law, Morrey calibration, and dissipation gap) imply global regularity, together with an explicit reduction of unconditional closure to a single geometric target estimate (near-field defect bound). What is included Main paper (Vol. XV): analytical framework, conditional theorem, and dynamic-closure target lemma chain. SabljicNSVol15InterfaceLawViscousBarrierDynamicClosure Companion Supplementary Material: Taylor–Green DNS diagnostics (N = 256, 260), robustness across quantiles q ∈ 0. 95, 0. 97, 0. 99, and grid-limited coherence-decay measurements; includes technical proofs for the two invoked truncation/limit steps. SabljicNSVol15SupplementTaylorGreenDiagnostics What this record does NOT claimThe supplementary measurements provide empirical plausibility checks only and are not used as logical input to any theorem or lemma in the analytical argument. No numerical result is claimed as a proof of the near-field defect estimate. Files Main PDF (SabljicNSVol15InterfaceLawViscousBarrierDynamicClosure) Supplementary Material PDF (SabljicNSVol15SupplementTaylorGreenDiagnostics) Tables/artifacts ZIP containing the CSV outputs used for the supplement. (SabljicNSVol15EpsilonDecayCSVFiguresAudit. zip)