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, geometry-based derivation of the Born rule in which measured probabilities arise from deterministic filtering of angular coherence in a triadic rotational lattice (“Holosphere” framework). Instead of postulating complex amplitudes and collapse, we model particles as real angular modes that propagate only along strain-compatible directions; the density of viable directions in angle space is the observed probability. We show that this classical “coherence density” is exactly the squared overlap on SU(2)/S³ (the spinor overlap), so the standard Born rule emerges as the visible shadow of rotational holonomy rather than an axiom. We then provide a concrete, testable micro-mechanism for spin-½ systems: the two-defect ring (TDR), a great-circle ring with two antipodal vacancy cuts that enforces the 2π sign flip (4π return) and maps chirality to a single scaffold rail. Impedance-matched (Robin) defects reduce leakage and yield strong circumferential localization in small graph models of the cuboctahedral scaffold. The Born rule remains universal: photon polarization lives on the Poincaré sphere and obeys Malus’ law without requiring a TDR, while spin-½ matter benefits from a TDR-like spinor boundary to realize and preserve low-leakage coherence corridors. Numerical checks confirm the analytic forms, reproduce the spinor vs polarization angle laws, and quantify the TDR’s leakage reduction and folding regime. The framework yields falsifiable signatures, including periodic suppression at S³ “dark nodes” (Δ = π, 3π) and an impedance optimum that outperforms Dirichlet-like clamps.