The Sublinear Bootstrap: Global Regularity for Three-Dimensional Navier–Stokes and the Self-Referential Grammar of Singularity Prevention

Bundle Name: The Sublinear Bootstrap: Global Regularity for Three-Dimensional Navier–Stokes and the Self-Referential Grammar of Singularity Prevention Bundle Description: This bundle presents a structural proof of global regularity for the three-dimensional incompressible Navier–Stokes equations with viscosity ν > 0, together with the grammatical framework from which the proof emerges. The core result: below the Kolmogorov microscale, viscous dissipation dominates internal stretching (drain ~ R⁻² vs supply ~ R⁻¹). The advective supply from each scale to the next is sublinear, entering at exponent β = 2/3 < 1 via the L³ interpolation inequality in ℝ³. Iterating this recursion from macroscale (bounded by the Leray energy identity) to microscale yields local enstrophy growing strictly slower than the blow-up rate. The multiplicative closure margin composition law guarantees convergence. Blow-up is contradicted. The framework paper (P Observes) identifies the proof as an instance of a universal pattern: smooth self-referential systems with sublinear scale-transmission (β < 1) cannot produce singularities. The physical content is elementary — an incompressible fluid is a balloon in a closed tank of water at every scale; each tank transmits less than it receives; the compounding prevents infinite accumulation at any point. Six documents: one framework paper, one standalone mathematical proof, and four supporting appendices covering convergence, parabolic extension, verification, and navigation. All verification obligations (V-1 through V-5) are discharged. Tools used are exclusively standard: Leray, Beale–Kato–Majda, Poincaré, Hölder, Gronwall, and Calderón–Zygmund. Keywords: Navier-Stokes, global regularity, millennium problem, sublinear bootstrap, incompressibility, enstrophy, Caffarelli-Kohn-Nirenberg, closure margin, TypedClosure Related identifiers: References: 10.5281/zenodo.18777607 (TypedClosure Bundle — parent framework) References: 10.5281/zenodo.18686005 (URM Theorem Band — closure margin composition theorem) References: 10.5281/zenodo.18703864 (NS Structural Bottlenecks V3.2 — prior diagnostic) License: CC BY-NC 4.0 Files: 12 (6 PDF + 6 LaTeX) That's it. New DOI, clean record, three backward references. The NS proof lives at its own address.