A Diophantine Lower Bound on Spectral Dissipation in Fibonacci-Scaled Open Graphs
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| Format: | Recurso digital |
| Langue: | anglais |
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2026
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| _version_ | 1866901691569274880 |
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| author | Garrido, Daphne |
| author_facet | Garrido, Daphne |
| 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> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_20263283 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | A Diophantine Lower Bound on Spectral Dissipation in Fibonacci-Scaled Open Graphs Garrido, Daphne Hurwitz Theorem Diophantine Approximation Open Graph Spectral Gap Trace-Map Recurrence Non-Equilibrium Steady States Fibonacci Scaling <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> |
| title | A Diophantine Lower Bound on Spectral Dissipation in Fibonacci-Scaled Open Graphs |
| topic | Hurwitz Theorem Diophantine Approximation Open Graph Spectral Gap Trace-Map Recurrence Non-Equilibrium Steady States Fibonacci Scaling |
| url | https://doi.org/10.5281/zenodo.20263283 |