Emergent Dark Matter from Geometric Inertia: A Chrono‑Grid Dynamics Approach to CMB Anisotropies and the H₀ Tension

We show that Chrono-Grid Dynamics (CGD), characterized by a fundamental temporal discreteness (the Takt τ), mimics cold dark matter (CDM) through a non-local gravitational response. Utilizing the fundamental relation 8π Gβ = τ² and the RG flow of the R² coupling from the UV fixed point ā^* ≈ 0.17, we derive a dimensionless inertia parameter α₀ ≈ 6.24. By implementing a scale-dependent Geff(k,a) in a modified CLASS code, we find that the CGD framework provides an excellent visual agreement with Planck 2018 data (χred² ≈ 1.08 in preliminary grid scans) while naturally resolving the H₀ tension with a preferred value of H₀ ≈ 73.1 km/s/Mpc (with an uncertainty of about $1.2$ km/s/Mpc estimated from the grid spread). This work bridges Planck-scale quantum geometry and cosmological observations.{abstract}