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

The incompressible Navier–Stokes equations admit finite-time singularities under classical continuum assumptions — yet no physical fluid exhibits infinite strain. This paper derives a globally regularized fluid system (Holosphere–Navier–Stokes, HNS) from first principles, based on SU(2) angular strain propagation across a discrete coherence lattice. The model enforces nonlinear stress saturation and fourth-order hyperviscous smoothing derived directly from geometric strain limits and healing dynamics. We prove global well-posedness via energy methods and compactness, derive a coherence-conditional regularity theorem paralleling Beale–Kato–Majda, and validate the framework with simulations of 2D shear and 3D Taylor–Green vortex flows. The HNS system reframes the Millennium Prize Problem within a physically constrained, falsifiable geometry where singularities are prohibited not by assumption, but by lattice structure.