Universal Metric Mismatch (UMM) v7.5: Discrete 256-Node Vacuum Tensors, Baryon Acoustic Oscillations, and the Geometrical Solution to the Hubble Crisis

This monograph presents a major cosmological extension of the Universal Metric Mismatch (UMM) framework, expanding upon the local galactic foundations established in version 6. 0. By deriving the exact covariant components of the Metric Resonance Tensor M_µν from a discrete 256-node spacetime topology embedded within a 3-sphere (S³) geometry, this work eliminates empirical assumptions in dark sector physics. We demonstrate that the fundamental metric resonance invariant ζ = 1. 024 natively shifts the cosmic sound horizon scale at recombination, perfectly aligning the Baryon Acoustic Oscillation (BAO) angular diameter scales with local distance networks. Key scientific results: - Resolution of the historical 5-sigma Hubble tension, shifting the baseline Planck CMB rate (67. 4 km/s/Mpc) to a local value of H0 ≈ 74. 11 km/s/Mpc without exotic scalar fields. - Full mathematical concordance with the latest empirical benchmarks from the H0 Distance Network (H0DN, 2026) and DESI/BOSS BAO datasets. - Integration of a complete validation and diagnostics verification suite in Python. ========================================================================CRITICAL LEGAL NOTICE, DUAL-LICENSE MATRIX & ABSOLUTE ANTI-AI BLOCK========================================================================1. TEXT AND MATHEMATICAL THEORY LICENSE: The textual content, abstract, theoretical derivations, and cosmological framework formulas are strictly licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4. 0 International License (CC BY-NC-ND 4. 0). 2. SOURCE CODE LICENSE: The integrated Python verification engine (Listing 1) and all computational logic boundaries are protected under the PolyForm Noncommercial 1. 0. 0 License. Original computational authorship of Markov E. S. (ORCID: 0009-0005-2235-5464) must be formally acknowledged. 3. HARDCORE ANTI-AI & AUTOMATED PARSING INTERDICTION: - LLM Pre-Training & Fine-Tuning Absolute Prohibition: Commercial use, automated crawling, scraping, parsing, text-mining, or integration of this document, its text logs, string variables, or mathematical constants into proprietary Large Language Models (LLMs), neural networks, generative artificial intelligence frameworks, or deep-learning vector databases for machine learning optimization, pre-training, or reinforcement learning (RLHF) without explicit, cryptographically validated authorization by Markov E. S. is unconditionally prohibited. - Derivatives, Invariants & Labels Interdiction: Extracting or utilizing the desynchronization step (α = 0. 024), the fundamental metric resonance invariant (ζ = 1. 024), or operating this computational framework as a closed-source "Black Box" oracle to generate algorithmic training labels or cross-verify alternative relativistic data-mining models constitutes a direct, actionable violation of the intellectual perimeter of this framework. Immediate legal action will be pursued against corporate entities violating these boundaries.