Paper 100: Holosphere Resolution of the Navier–Stokes Regularity Problem A Physically Motivated Derivation of Global Regularity from Angular Coherence Constraints

Holosphere Theory asserts that physical fluids possess a finite coherence scale: local angular strain cannot grow without bound and relaxes on a finite healing time. Starting from an SU(2) angular-coherence lattice, we derive a continuum model—the Holosphere–Navier–Stokes (HNS) system—in which these constraints appear as a saturating nonlinear stress and a fourth-order hyperviscous smoothing term. We prove a strict energy dissipation law with a bi-Laplacian contribution, establish global existence and uniqueness of weak solutions on the torus via a monotone-operator/Galerkin framework, and show quantitative convergence to classical Navier–Stokes (NS): on any interval where NS remains smooth, HNS approaches NS with an O(ε) error as the regularization parameters vanish. We further obtain a coherence-conditional regularity statement that links classical Beale–Kato–Majda/Serrin criteria to a lattice-determined strain threshold S_sat, providing a falsifiable, physics-level condition under which NS must remain smooth. Pseudo-spectral simulations of a 2D shear layer and the 3D Taylor–Green vortex confirm the theory: maximum strain stays below S_sat, energy decays monotonically, the dropout fraction is essentially zero, and coherent flow structures are preserved while incipient blow-up is suppressed. The work does not solve the Clay Millennium Problem for the unmodified NS equations; instead, it reframes potential singularities as a breakdown of the continuum approximation and provides a physically grounded, testable route to regularity.