The Immirzi Parameter as a Cosmic Unifier: From High‑Energy Transparency to Dark Matter and MOND in Chrono‑Grid Dynamics

Chrono-Grid Dynamics (CGD) posits a fundamental temporal discreteness characterized by the Takt τ and the Immirzi parameter β via 8πGβ = τ^2. We show that the same β simultaneously explains three seemingly unrelated astrophysical anomalies: the transparency of the universe to ultra-high-energy photons (GRB 221009A), the emergence of the MOND acceleration scale a0 ~ cH0, and the existence of an effective dark matter component that reproduces the cosmic microwave background anisotropies and baryon acoustic oscillations. The effective dark matter emerges from a coherent phase of the quantum geometry, with an energy density ρ_CGD ~ ε H0^2 where ε ~ 10^{-2} is naturally explained by a phase transition in the spin-network. This unified framework suggests that dark matter and modified gravity are two facets of the same discrete spacetime structure.