This record contains Vol. XVI of the Navier–Stokes Regularity Program. The purpose of this volume is to close the single remaining analytic gap needed by Vol. XV: a quantitative near-field defect bound on the interface layer, formulated as Assumption 4 in Vol. XV. Main result: we derive a localized singular-integral estimate for the truncated Biot–Savart gradient, combining (i) a cancellation identity for the near-field truncation, (ii) a derivative-gain estimate in differential form, and (iii) a Morrey-calibrated extraction principle via a covering argument. The resulting theorem converts Assumption 4 from Vol. XV into a derived lemma within the Navier–Stokes framework, requiring only a dynamically chosen scale r (t) and an appropriate Morrey control input. What is included• Main paper (Vol. XVI): problem formulation, main statements, and the logical structure of the argument. SabljicNSVol16NearFieldDefectBound. pdf • Companion Supplementary Notes: full technical proofs (kernel bounds, truncation estimates, covering/selection steps, and all auxiliary lemmas). SabljicNSVol16NearFieldDefectBoundSupplement. pdf What this record does NOT claimThis volume does not claim unconditional global regularity by itself. It provides a technical derivation of the near-field defect bound (Assumption 4) used by Vol. XV. In particular, it does not establish Morrey calibration as a standalone fact and does not introduce numerical diagnostics as logical input to any theorem.
Branimir Sabljić (Fri,) studied this question.