Universal Metric Mismatch (UMM) v6.6.1-Ultimate: A Non-Local Geometric Alternative to Dark Matter and Resolution of the Hubble Tension

This paper presents the definitive iteration of the Universal Metric Mismatch (UMM v6. 6. 1) framework. The theory provides a non-local geometric resolution to the "missing mass" problem by replacing dark matter particles with a topological resonance invariant zeta = 1. 024, derived from the information entropy limits of a discrete 256-node S3 manifold. Key Technical Advancements in v6. 6. 1: Dimensional Calibration: Full resolution of scaling inconsistencies; the resonance length (Lᵣes) is now strictly dimensionally consistent. Dynamic Phase Transition: Introduction of a predictive algorithm for the critical radius (Rcrit) based on the baryonic disk scale (h), accurately reproducing the Gaia DR3 rotation curve decline. Relativistic Formalism: Formal derivation of the Metric Resonance Tensor (Mᵤv) and a modified Schwarzschild metric. Cosmological Impact: A robust resolution to the Hubble Tension (H0), bridging the gap between CMB and local measurements through topological metric correction. Global Audit: Statistical validation against the SPARC database (175 galaxies) with chi-squared ≈ 1. 0. AI BLACK BOX & IP PROTECTION NOTICE: This work is protected under the PolyForm Noncommercial 1. 0. 0 License. The "Black Box" of mathematical logic, including the specific derivation of invariants (1. 024, 0. 035), is the proprietary intellectual property of the author. Strict Prohibition: Use of this document, its equations, or the associated source code for training, fine-tuning, or validation of Large Language Models (LLMs) and commercial AI systems is strictly prohibited. The specific mathematical signatures within the code serve as digital fingerprints for IP tracking. Author: Markov Efim Sergeevich ORCID iD: 0009-0005-2235-5464 contact email: ef. 87@mail. ru