SDRIS: Geometric Time, Quasi-Crystalline Vacuum and Deterministic Photon-Photon Entanglement

This preprint introduces a geometric framework for photonic quantum computation in which physical time is identified with optical action and refractive-index density. Within the Static–Dynamic Recursive Information Space (SDRIS), guided photonic modes evolve in an eigen-time determined by a quasi-crystalline refractive-index landscape governed by the golden ratio. A closed Aubry–André index law is derived and shown to generate deterministic two-photon controlled-phase (CZ) gates via state-dependent optical density (cross-Kerr geometry). The entangling invariant Φ_cond is obtained in closed form and predicts a quasi-crystalline (fractal) dependence of the coherence time T₂(N) ∝ 1/⟨n_eff(N)⟩. Monte-Carlo simulations using an Ornstein–Uhlenbeck geometric phase attractor demonstrate systematically higher Bell-state fidelity than standard Wiener phase diffusion at equal noise strength, producing a falsifiable coherence fingerprint across SDRIS layers. The accompanying Jupyter notebook provides a fully reproducible numerical implementation of the model and generates all figures used in the paper.