Paper 4: Thermalization and Measurement from Triplet Coherence Collapse in the Holosphere Lattice

This paper presents a classical, deterministic model of quantum measurement, decoherence, and thermalization based on the Holosphere lattice framework. In this model, electrons are composed of three angular phase structures—called dark bosons—orbiting coherence defects within a discrete, rotating lattice of Holospheres. Each Holosphere maintains a triadic spin structure that constrains angular propagation via phase continuity. Measurement is modeled as the deterministic collapse of two dark bosons into aligned pointer basins, while the third preserves long-range coherence, enabling entanglement without superluminal signaling. Decoherence arises from angular misalignment beyond a geometric threshold, and thermalization results from statistical realignment into incoherent strain configurations. The Born Rule is not postulated, but derived from the classical volume of coherence-compatible angular paths, as developed in Paper T14. The coherence amplitude ψcoh(θ,ϕ)=sin⁡θcos⁡ϕ\psi_{\text{coh}}(\theta, \phi) = \sin\theta \cos\phiψcoh(θ,ϕ)=sinθcosϕ emerges from the lowest-order eigenmode of a discrete angular Lagrangian. This model predicts measurable deviations from standard quantum theory in high-strain or orientation-sensitive environments, such as anisotropic decoherence, pointer bias, and Bell test deviations at the δ∼10−3\delta \sim 10^{-3}δ∼10−3 level. The coherence structure also scales to cosmological domains, connecting angular filtering to large-scale structure formation. This work reframes quantum behavior as the observable outcome of geometric selection in a discrete, angularly constrained medium.