Dynamic Phase Resonances in Discrete Spacetime Topologies: Lattice Elasticity and 256-Node Rigidity as a Non-Baryonic Alternative to Dark Matter

This work formalizes the Universal Metric Mismatch (UMM) v8.2 framework, demonstrating that galactic kinematics emerge naturally from a discrete 256-node spacetime topology characterized by structural rigidity and lattice elasticity. By replacing continuous Riemannian spacetime manifolds with a discrete honeycomb substrate of indivisible volume quantum cells ("All-Born"), we derive the fundamental metric resonance invariant \zeta = 1.024 and the geometric clearance gap \mathcal{L}_e = 0.024 from first principles of network thermodynamics. The accumulation of metric mismatch induces an elastic shear tension within the lattice, functioning as a non-local geometric boost that completely eliminates the necessity for unobservable dark matter halos. The dynamic model is validated through a high-precision automated batch computation over the entire 175-galaxy Spitzer Photometry and Accurate Rotation Curves (SPARC) database, achieving a superior global statistical fit of \chi^2_{\text{red}} \approx 1.00 across all morphological types (from giant HSB spirals to gas-rich dwarfs). Furthermore, the model accounts for topological phase boundaries, explaining both the extended flat velocity plateaus and the sharp outer declines observed in modern high-precision astrometric surveys such as Gaia DR3.