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 $\tau$), mimics cold dark matter (CDM) through a non-local gravitational response. Utilizing the fundamental relation $8\pi G\beta = \tau^2$ and the RG flow of the $R^2$ coupling from the UV fixed point $\bar{a}^* \approx 0.17$, we derive a dimensionless inertia parameter $\alpha_0 \approx 6.24$. By implementing a scale-dependent $G_{\text{eff}}(k,a)$ in a modified CLASS code, we find that the CGD framework provides an excellent visual agreement with Planck 2018 data ($\chi_{\text{red}}^2 \approx 1.08$ in preliminary grid scans) while naturally resolving the $H_0$ tension with a preferred value of $H_0 \approx 73.1$ 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.\end{abstract}