Gardado en:
| Autor Principal: | |
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| Formato: | Recurso digital |
| Idioma: | inglés |
| Publicado: |
Zenodo
2026
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| Subjects: | |
| Acceso en liña: | https://doi.org/10.5281/zenodo.20263283 |
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Table of Contents:
- <p>We establish an absolute geometric lower bound on the local dissipation rate within open, discrete relational networks whose coupling coefficients undergo Fibonacci-modulated scaling. Representing the network states as a transfer-matrix track over a unimodular lattice, we demonstrate that the system's global phase balance maps identically onto a non-linear trace recurrence. By applying Hurwitz's theorem on Diophantine approximations, we prove that the golden ratio φ = (1+\sqrt{5})/2 acts as an absolute, irremovable boundary barrier against external stochastic dephasing. </p> <p>Because φ possesses the slowest converging continued fraction expansion among all real numbers, a network parameterized precisely to this fixed point maximizes its topological distance from environmental rational resonances. This result provides a simple, self-contained number-theoretic mechanism explaining the universal emergence of golden-ratio scaling in stable, non-equilibrium physical and biological architectures, independent of empirical tuning parameters.</p> <p>Pipeline Disclosure: The core conceptual formulation—structuring the trace-map recurrence matrix parameters into the formalisms of adelic product formulas, non-equilibrium steady states, and Hurwitz continued-fraction minima—was fully authorized and directed by the author. Initial layout organized via Grok (xAI); rigorous mathematical validation, domain confinement tracking, and production-ready LaTeX typesetting finalized via Gemini (Google).</p>