Dynamic Phase Resonances in Hexagonal Close-Packed Media: Donor-Acceptor Desynchronization, Helical Winding, and Non-Singular Topological Collapse

This paper proposes a rigorous dynamic extension to discrete space-medium mechanics and the "electro-atom" classification paradigm originally formulated by Y. S. Rybnikov (p. 2). By replacing continuous spacetime manifolds and distance-dependent gravitational potentials with a discrete, perfectly elastic hexagonal close-packed (honeycomb) matrix of fundamental spatial units ("All-Born"), this framework resolves the historical limitation of structural static immobility in classical ether theories (pp. 2-4). The study mathematically demonstrates how an inherent geometric packing clearance of 0.024 induces localized phase desynchronization between hyper-compressed donor nodes and volume-deficit acceptor nodes (pp. 2, 11-12). This asymmetry converts linear displacement pulses into localized angular vortices ("helical winding") (pp. 2, 8, 12). First-principles computational modeling successfully accounts for the flat rotation curves of spiral galaxies (e.g., Andromeda M31) without dark matter halos (pp. 2, 18-19) and models black hole horizons as non-singular topological collapses (\(256 \equiv 0\)) governed by modular register capacities (pp. 2, 10, 23). Open-source multiscale HTML5 Canvas/JavaScript simulation engines are provided in the appendix for verification (p. 34). The monograph includes fully functional, open-source HTML5/Canvas/JavaScript simulation scripts (Appendix A) to ensure full computational reproducibility and empirical verification by independent research groups worldwide. Author:Markov Efim Sergeevich contact email:[email protected] Doi:10.5281/zenodo.20209670 --- LEGAL NOTICE & COPYRIGHT PROTECTION: 1. Textual & Mathematical Content: © 2026 Efim S. Markov. The theoretical framework, mathematical derivations of Rus' Volumetric Calculus, physical models, and textual content of this monograph are strictly protected and licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0). Any commercial or academic utilization, translation, or modification of these materials requires mandatory, explicit attribution to the author (Efim S. Markov) and this original Zenodo publication via its assigned DOI. 2. Software & Simulation Code: The fully functional HTML5/Canvas/JavaScript source code and core algorithmic engines of the V256 core detailed in Appendix A are licensed under the Apache License, Version 2.0 (the "License"). You may not use this code except in compliance with the License. The License strictly enforces copyright retention and includes a reciprocal patent grant, legally preventing third parties from patenting or secretly commercializing these proprietary algorithms without attributing original authorship to Efim S. Markov. © 2026 Efim S. Markov. Licensed under CC BY 4.0