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

This paper presents a classical derivation of the Born Rule from angular coherence filtering in a discrete rotational lattice. In Holosphere Theory, particles such as electrons are modeled not as quantum wavefunctions, but as real angular distortions propagating through a network of spinning units called Holospheres. Each Holosphere maintains a triadic spin structure, and only trajectories that preserve angular phase continuity across the lattice are physically viable. We show that the probability of a measurement outcome arises from the real-valued volume of coherence-preserving paths in angular phase space. The coherence amplitude is derived from first principles using a classical Lagrangian for angular strain propagation. The resulting amplitude, ψcoh(θ,ϕ)=sin⁡θcos⁡ϕ\psi_{\text{coh}}(\theta, \phi) = \sin\theta \cos\phiψcoh(θ,ϕ)=sinθcosϕ, leads to a coherence density ρ=ψcoh2\rho = \psi_{\text{coh}}^2ρ=ψcoh2, whose normalized integral over angular regions yields probabilities that match the Born Rule. This framework eliminates the need for complex amplitudes, stochastic collapse, or quantum axioms. Instead, quantum probability emerges from classical strain filtering and the discrete geometry of the triadic spin lattice. The derivation includes both a geometric trigonometric explanation and a full field-theoretic Lagrangian treatment. We conclude that the Born Rule is not a fundamental postulate but a classical statistical consequence of structural filtering in angular phase space.