Universal Metric Mismatch (UMM) v5.0: A Non-local Geometric Alternative to Dark Matter

This preprint (v5.0) presents a formal geometric derivation of the Universal Metric Mismatch (UMM) theory. We demonstrate that galactic rotation curves emerge from the topological resonance between discrete spacetime nodes and continuous manifolds, characterized by the 1.024 invariant.Key updates in v5.0:Formalization of the Metric Resonance Tensor within the Einstein field equations.Resolution of Bianchi identity consistency in non-local manifolds.Comparative statistical analysis against the SPARC database (175 galaxies), showing superior fit quality over empirical MOND models.Successful validation against anomalous objects such as NGC 1052-DF2. The source code for this project is available in version 4.0 and is licensed under Creative Commons Attribution Non Commercial Share Alike 4.0 International