Universal Metric Mismatch: Topological Decomposition of Gravitational Potential and Resolution of the Hidden Mass Problem via Gibbs Oscillations.

Universal Metric Mismatch: Version 3.0 (Extended Edition) This paper provides a rigorous topological foundation for the "Universal Metric Mismatch" (UMM) framework, addressing key criticisms regarding the dynamical foundations and falsifiability of the theory. Key updates in Version 3.0: Mathematical Rigor: Introduction of the Banach-Steinhaus theorem as the formal basis for Gibbs oscillations in the discrete-to-continuous metric mapping. Field Dynamics: Derivation of the topological stress tensor and its integration into the Einstein Field Equations. Gravitational Lensing: Formal proof of photonic geodesic deflection within the UMM framework, providing a direct alternative to Dark Matter in galaxy clusters. Cosmological Context: Extension of the model to explain the Cosmic Microwave Background (CMB) anisotropy peaks via topological resonance of the 3-sphere. Empirical Validation: Detailed numerical calibration using the M31 (Andromeda) rotation curve, demonstrating superior statistical performance (chi-squared) compared to Lambda-CDM and MOND models. This version proves that "dark matter" effects can be fully accounted for by the geometry of a discrete spacetime manifold, satisfying Occam's Razor by eliminating non-baryonic entities.