Paper 61: The Angular Strain Tensor and Coherence Curvature in the Holosphere Lattice

This paper defines the angular strain tensor Sij for the discrete Holosphere lattice and establishes its role as the geometric origin of gravitational phenomena in a coherence-based spacetime. Unlike classical field theories that treat gravity as curvature of a continuous metric, Holosphere Theory describes spacetime as a rotationally phase-locked lattice of nested Holospheres, where coherence strain, not curvature, gives rise to observable dynamics. We derive the strain tensor from local angular phase differences between adjacent Holospheres and show how its divergence produces effective force-like behavior. From this foundation, we construct a curvature analog, Rij, that describes second-order coherence deformation across lattice regions. These quantities allow us to express gravitational influence, geodesic deviation, and redshift as emergent effects of strain gradients within the angular coherence field. [4] This formulation sets the stage for Paper 62, which will use the derived tensors to reproduce and reinterpret Einsteinian gravity within a fully discrete, deterministic framework. Here, we establish the missing mathematical link between coherence geometry and field-like behavior, placing Holosphere Theory on equal footing with conventional differential geometry and general relativity.