Paper 101: Derivation of Coherence Constants in the Holosphere Lattice The Parameter Foundation of the Holosphere–Navier–Stokes System

This paper derives the coherence triad—(1) the maximum angular strain s_max, (2) the healing constant gamma, and (3) the coherence dropout threshold theta_break—that governs transport and regularity in the Holosphere lattice. From SU(2) compactness (SU(2) ≅ S^3) we obtain a geometry-fixed bound s_max = pi. We show how this hard angular limit becomes operational through threshold-constrained quantization and triadic closure, which together enforce categorical failure once the structural threshold is exceeded. The healing constant gamma is introduced at the lattice level as the exponential recovery rate of angular phase, with a continuum consistency relation nu = c_theta^2 / gamma linking lattice recovery to macroscopic viscosity. The dropout threshold is modeled as site percolation on the face-centered cubic (fcc) lattice, yielding a rigorous lower bound near 0.199; triadic compatibility and bootstrap effects raise the effective threshold into the 0.20–0.30 range. We validate this prediction with a jitterbug-enhanced SU(2) simulation on the fcc lattice: the dropout curve crosses theta = 0.21 at sigma* ≈ 0.122 ± 0.003 under a geodesic cutoff lambda_geo = sqrt(2 alpha), confirming that theta_break marks the frontier between healable and irreversible coherence loss. Together, the triad (s_max, gamma, theta_break) supplies angular, temporal, and spatial cutoffs that render the Holosphere–Navier–Stokes system geometry-fixed (once alpha is anchored) and falsifiable, with clear avenues for numerical and experimental tests.