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

This paper introduces the angular strain tensor as a classical, discrete description of coherence distortion in the Holosphere lattice. Instead of modeling gravity and cosmological effects as curvature of a continuous spacetime metric, we treat them as consequences of accumulated phase misalignment between neighboring rotating coherence units (Holospheres). The angular strain tensor SijS_{ij}Sij is defined from symmetrized nearest-neighbor phase gradients, and a Poisson-type lattice field equation is adopted to relate strain to a gradient-squared source. Under spherical symmetry in the coherent regime, the shell-averaged curvature-density proxy derived from this field equation scales as R(r)∝r2R(r)\propto r^2R(r)∝r2. When this curvature proxy is integrated radially under admissibility gating, the accumulated phase delay scales cubically, Δϕ(r)∝r3\Delta\phi(r)\propto r^3Δϕ(r)∝r3. This cubic scaling provides the upstream structural basis for the exponential phase-drag term used in the hybrid redshift law of Paper 2. A deterministic numerical artifact build is used to test the angular consequences of the strain scaffold. A triadically modulated stiffness operator produces a boundary residual dominated by the spherical harmonic sector ℓ=3\ell=3ℓ=3, with predictable leakage into ℓ=6\ell=6ℓ=6. The results establish a minimal tensorial and computational bridge between the redshift lane of Paper 2 and the strain-field gravity development of Paper 62, without introducing new cosmological parameters.