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

This paper derives three core control quantities for the Holosphere–Navier–Stokes (HNS) framework: a geometric strain cap, a healing rate, and a connectivity cutoff. First, we show that the maximum possible angular mismatch between neighboring lattice sites is fixed by geometry at π, because the underlying spin structure is compact. This bound is purely geometric and does not depend on dynamics or material parameters. Second, we derive a healing constant that governs how quickly small mismatches relax back toward coherence. At the lattice level, this appears as an exponential recovery rate; under coarse-graining, it produces a diffusion-like relation consistent with a viscosity term in HNS. We carefully separate the microscopic spinor-memory hypothesis from the macroscopic recovery rate to avoid circular definitions. Third, we determine the lattice-wide dropout fraction at which incoherent sites form a spanning cluster on the face-centered cubic (fcc) neighbor graph. Using finite-size scaling under declared boundary and spanning conventions, we obtain consistent estimates of the connectivity threshold near 0.192, in line with the known fcc site-percolation baseline (~0.199 lower bound). No additional uplift mechanism is adopted as a model-level constant. Together, these three quantities—the maximum angular strain, the healing constant, and the percolation-controlled dropout fraction—supply angular, temporal, and spatial controls within the HNS formulation. The paper enforces strict lane discipline between geometric definitions, mechanism-level dynamics, connectivity modeling, and reporting-layer diagnostics. All numerical artifacts are generated by a single turnkey script with a run manifest to ensure auditability and reproducibility.