Paper T14: A Classical Derivation of the Born Rule from Angular Coherence Filtering Probability as Real-Valued Path Volume in a Rotational Lattice

We present a classical, geometric derivation of the Born rule based on angular coherence filtering in a triadic lattice of rotating units (holospheres). Instead of postulating probabilities, outcomes arise from counting and normalizing the set of angular paths that preserve local coherence below a fixed strain threshold. The resulting probability map in angle space matches the squared coherence amplitude predicted by the SU(2) overlap on S3, so the familiar squaring law appears as a geometric intensity, not as an axiom. We validate this with large scale simulations. With N = 2^22 samples on a 50 by 100 grid, the conditional empirical maps (after applying the same coherence corridor and renormalizing) agree with the predicted probability map at the following error levels: MSE = 6.69 x 10^-9, 1.09 x 10^-8, and 3.63 x 10^-8 for epsilon_crit = 0.0, 0.5, 0.9, respectively; L1 errors are 5.53 x 10^-5, 6.97 x 10^-5, and 8.42 x 10^-5. Bootstrap 95 percent confidence intervals for the MSE are [8.65 x 10^-8, 9.31 x 10^-8], [7.65 x 10^-8, 8.27 x 10^-8], and [1.53 x 10^-7, 1.62 x 10^-7], respectively. An independent S3 test reproduces the exact Beta(1/2, 3/2) distribution for P = |C|^2 (Kolmogorov Smirnov p approximately 0.55), confirming the SU(2) overlap geometry. Together these results support the claim that angular coherence filtering yields the Born rule as a classical volume law, with clear, falsifiable structure tied to SU(2) holonomy.