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| Natura: | Recurso digital |
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Zenodo
2025
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| Accesso online: | https://doi.org/10.5281/zenodo.17524193 |
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Sommario:
- <p>This technical note presents reproducible simulation evidence confirming the emergence of a −90° phase lag at the Relational Coherence Threshold (λ ≈ 1.7). Using coupled-oscillator networks (ring and star topologies), the onset of rapid synchronization coincides with a π/2 quadrature shift between individual-node oscillations and the collective mode—marking the transition from dissipative to self-reinforcing dynamics.</p> <p> </p> <p><strong>The results strengthen the interpretation of relational density as the anchor of coherence and suggest that λ ≈ 1.7 represents a density-adjusted form of a deeper invariant (λₙ ≈ 1). Dense systems, such as biological or gravitational domains, may reach coherence thresholds earlier, while sparse informational systems converge near 1.7.</strong></p> <p> </p> <ul> <li> <p><strong>Below λ ≈ 1.7:</strong></p> <p>Coherence depends on <span><strong>relational density</strong></span> — how tightly the components of a system are coupled.</p> <p>Each network (biological, cosmic, AI, etc.) achieves local stability at a <em>different</em> λ value depending on its internal density and feedback efficiency.</p> <p>Dense systems (like stars, neural tissue, or social collectives) reach coherence <em>earlier</em> because they have stronger feedback loops.</p> </li> <li> <p><strong>At λ ≈ 1.7:</strong></p> <p>Relational density ceases to determine the outcome — all systems, regardless of internal complexity, enter a <span><strong>universal coherence mode.</strong></span></p> <p>It’s the <em>cross-domain bridge</em> — the same threshold where energy, geometry, and information synchronize under a common law.</p> </li> <li> <p><strong>Beyond λ ≈ 1.7:</strong></p> <p>The system decouples; coherence becomes self-referential, potentially forming new domains (phase transitions, decoherence, or “dark” states).</p> </li> </ul> <p> </p> <p>This normalization bridges contextual and universal coherence, offering a physical explanation for why reality maintains dynamic equilibrium—slightly off unity, allowing creativity, evolution, and adaptive flow. <strong>All code, figures, and results are openly shared under CC-BY 4.0 to support replication, refinement, and interdisciplinary dialogue.</strong></p> <p><strong>The Python script are provided in the Zenodo repository to ensure transparency and allow independent replication, modification, or extension of the findings by interested researchers.</strong></p> <p> </p>