Paper T4: Entanglement and Decoherence via Triadic Spin

This paper presents a structural explanation of entanglement and decoherence within Holosphere Theory. Instead of treating quantum collapse as a fundamental random event, the model describes it as a geometric threshold failure in a discrete lattice of angular coherence. A key structure in the theory, the Two-Defect Ring (TDR), selects one long-range “rail” mode that preserves phase alignment across the lattice and two more fragile “sideband” modes that are sensitive to local disturbance. Entanglement persists as long as the rail mode maintains alignment between systems. When angular misalignment grows beyond a critical threshold, coherence fails and the system undergoes a redistribution of strain that ends the entanglement channel. The paper connects this local threshold rule to a global geometric description using the three-sphere S3S^3S3 representation of SU(2)SU(2)SU(2). In this geometry, the overlap law cos⁡(Δ/2)\cos(\Delta/2)cos(Δ/2) predicts complete suppression of entanglement intensity at specific angles, called dark nodes, at Δ=π\Delta = \piΔ=π and Δ=3π\Delta = 3\piΔ=3π, with a characteristic 4π4\pi4π revival pattern. The same structure appears locally as a threshold condition on angular misalignment. In addition, the coherence profile that determines where entanglement is strongest is derived from classical lattice symmetry, producing a directional pattern proportional to sin⁡2θcos⁡2ϕ\sin^2\theta \cos^2\phisin2θcos2ϕ. This connects the geometry of the lattice with the statistical patterns typically associated with the Born rule. The framework separates calibration predictions that agree with standard quantum mechanics from new, model-specific tests. Calibration tests include the dark-node minima and 4π4\pi4π revival pattern, angular coherence mapping, and operational no-signalling checks. Holosphere-specific predictions include orientation-dependent robustness of entanglement, step-like decoherence plateaus, partial recoherence after realignment, and small path-dependent visibility shifts for gate sequences that have the same net rotation but different trajectories in S3S^3S3. Each prediction is paired with a proposed experimental protocol and statistical acceptance criteria. By describing entanglement as shared lattice coherence rather than nonlocal influence, the model aims to replace several traditional quantum paradoxes with structural mechanisms. Collapse becomes a threshold failure followed by strain redistribution, and correlations arise from shared geometry rather than instantaneous action at a distance. The paper therefore proposes a geometry-based foundation for quantum behavior and outlines experimental tests that could confirm or falsify the mechanism.