Paper 26: Coherence Fields and Angular Strain Tensors in the Holosphere Lattice

This paper builds the mathematical foundation for Holosphere Theory by introducing new field variables that describe how space and matter emerge from a lattice of spinning spheres. The main variable, called the coherence field φ(x,t)\varphi(x, t)φ(x,t), tracks how well the spins of nearby spheres stay aligned. When this alignment breaks down, it creates strain—similar to tension in a stretched fabric. We define a new quantity called the angular strain tensor σij\sigma_{ij}σij, which measures this misalignment in different directions. These strain patterns explain how mass, inertia, and gravity can arise from the geometry of the lattice itself, without needing spacetime curvature. We also define how angular momentum and energy move through the lattice. These tools allow us to describe particles and forces using simple geometric rules. Finally, we connect this framework to a recent result (Paper T14) that explains quantum probabilities using the same kind of angular coherence filtering. This work lays the groundwork for a fully discrete, coherence-based theory of physics.