Universal Metric Mismatch (UMM) v4.0: A Rigorous Computational Framework and Cross-Scale Validation without Dark Matter

Version 4. 0 Update: This version introduces a major advancement in the Universal Metric Mismatch (UMM) theory by providing a standardized computational framework (Python) and empirical verification across multiple cosmic scales. Key updates in v4. 0: Formal Mathematical Proof: Application of the Banach-Steinhaus theorem to the discrete spacetime metric mapping. Universal Constants: Identification of invariant parameters (\ (ₔ₌₌ = 0. 854\) kpc and \ (= 1. 418\) ) that function consistently from individual galaxies (M31, M33) to the Coma Cluster. Computational Implementation: Inclusion of a verifiable Python-based algorithm that replaces the Dark Matter requirement with a geometric metric mismatch kernel. Numerical Validation: Direct comparison with SPARC and virial dispersion data, demonstrating high statistical accuracy without individualized halo tuning. The provided source code enables independent verification of the UMM effect on any baryonic mass distribution. This is the most complete and computationally verified version of the theory to date. 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 (Non-Commercial use only)