Navier–Stokes Regularity Program (Vol. XVI): Deriving the Near-Field Defect Bound (Assumption 4)

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. Sabljic_NS_Vol16_NearFieldDefectBound.pdf • Companion Supplementary Notes: full technical proofs (kernel bounds, truncation estimates, covering/selection steps, and all auxiliary lemmas). Sabljic_NS_Vol16_NearFieldDefectBound_Supplement.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.