Experimental Confirmation of the –90° Phase Lag at the Relational Coherence Threshold
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2025
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| _version_ | 1866901654071148544 |
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| author | De Jesus, Elias |
| author_facet | De Jesus, Elias |
| contents | <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> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_17524193 |
| institution | Zenodo |
| language | |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Experimental Confirmation of the –90° Phase Lag at the Relational Coherence Threshold De Jesus, Elias Relational Physics, Coherence Threshold, Phase Lag, Quadrature, Synchronization, Relational Density, Information Dynamics, Adaptive Systems, Critical Coupling, Universal Invariant, Complex Networks, Emergent Stability, Open Science <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> |
| title | Experimental Confirmation of the –90° Phase Lag at the Relational Coherence Threshold |
| topic | Relational Physics, Coherence Threshold, Phase Lag, Quadrature, Synchronization, Relational Density, Information Dynamics, Adaptive Systems, Critical Coupling, Universal Invariant, Complex Networks, Emergent Stability, Open Science |
| url | https://doi.org/10.5281/zenodo.17524193 |