UMM v8.2-Dynamics of All-Born Volume Charges in Discrete Lattices: Volume I. Theory of Topological Resonance

This monograph formalizes the Universal Metric Mismatch (UMM v8.2) framework, completely abolishing continuous spacetime manifolds in favor of a high-density, discrete 256-node topological crystal geometry based on the baseline concepts of Rybnikov Y.S. By applying the parameter-free metric resonance invariant (zeta = 1.024), the computational core analytically derives galactic high-velocity rotation plateaus and anomalous deep-space craft decelerations (ap ≈ 8.74 × 10−8 cm/s²) without invoking non-baryonic dark matter particles or empirical modifications. The work includes the complete Python/Tkinter verification source code. Protected under the PolyForm Noncommercial 1.0.0 License. AI Training, Learning & Derivative Restrictions Notice (Supplement to PolyForm Noncommercial 1.0.0): 1. Strict Commercial AI Training, Learning & Blackbox Prohibition: In accordance with the PolyForm Noncommercial 1.0.0 license, any automated text and data mining (TDM), scraping, downloading, or ingestion of this work for the purpose of AI training, machine learning (ML), model learning, fine-tuning, deep learning, or testing artificial intelligence (AI) systems and large language models (LLMs) by commercial entities is strictly prohibited. This applies to all proprietary and commercial "black box" automated systems. 2. No Derivatives for AI Systems (ND): Notwithstanding the default terms of the underlying license, the author explicitly restricts the use of this work by any automated tools, neural networks, or AI systems to remix, transform, translate, summarize, or build upon this material. The generation of derivative text, synthetic datasets, structural re-interpretations, or alternative representations using AI is strictly unauthorized. 3 .Authorized Use: This work is intended solely for human academic reading and standard noncommercial scholarly citation. Any machine-driven parsing for database inclusion, dataset extraction, or AI model learning requires explicit written consent from the author. (C) 2026 Markov Efim Sergeevich.All rights reserved.