Coherent Coupling and Emergent Geometry: A Variational Closure of Modal Dynamics
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2025
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| _version_ | 1866901742869807104 |
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| author | Fedotov, Anton SynqraTech |
| author_facet | Fedotov, Anton SynqraTech |
| contents | <p>In previous formulations of structural modal dynamics, the evolution of mode states <span><span><span><span><span>R</span><span><span><span><span><span><span>i</span></span></span><span></span></span></span></span></span></span></span></span> relied on a fixed coupling matrix <span><span><span><span><span>K</span><span><span><span><span><span><span><span>ij</span></span></span></span><span></span></span></span></span></span></span></span></span>, leaving open the fundamental origin of geometry, gauge structure, and physical observables. In this work, we resolve this incompleteness by introducing a variational principle that dynamically determines <span><span><span><span><span>K</span><span><span><span><span><span><span><span>ij</span></span></span></span><span></span></span></span></span></span></span></span></span> from the current configuration of <span><span><span><span><span>R</span><span><span><span><span><span><span>i</span></span></span><span></span></span></span></span></span></span></span></span>. The resulting coupled system defines a self-consistent evolution in which metric structure, gauge potentials, and curvature naturally emerge from coherence-based relations. Numerical simulations demonstrate quantum-like phenomena such as interference, tunneling, Zeno suppression, and decoherence. The theory supports stable coherent clusters, reproduces Dirac-like spectra via spinor kernels, and admits a continuous field limit. This variationally closed framework thus elevates the structural modal approach into a predictive, internally coherent physical theory.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_15646463 |
| institution | Zenodo |
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| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Coherent Coupling and Emergent Geometry: A Variational Closure of Modal Dynamics Fedotov, Anton SynqraTech <p>In previous formulations of structural modal dynamics, the evolution of mode states <span><span><span><span><span>R</span><span><span><span><span><span><span>i</span></span></span><span></span></span></span></span></span></span></span></span> relied on a fixed coupling matrix <span><span><span><span><span>K</span><span><span><span><span><span><span><span>ij</span></span></span></span><span></span></span></span></span></span></span></span></span>, leaving open the fundamental origin of geometry, gauge structure, and physical observables. In this work, we resolve this incompleteness by introducing a variational principle that dynamically determines <span><span><span><span><span>K</span><span><span><span><span><span><span><span>ij</span></span></span></span><span></span></span></span></span></span></span></span></span> from the current configuration of <span><span><span><span><span>R</span><span><span><span><span><span><span>i</span></span></span><span></span></span></span></span></span></span></span></span>. The resulting coupled system defines a self-consistent evolution in which metric structure, gauge potentials, and curvature naturally emerge from coherence-based relations. Numerical simulations demonstrate quantum-like phenomena such as interference, tunneling, Zeno suppression, and decoherence. The theory supports stable coherent clusters, reproduces Dirac-like spectra via spinor kernels, and admits a continuous field limit. This variationally closed framework thus elevates the structural modal approach into a predictive, internally coherent physical theory.</p> |
| title | Coherent Coupling and Emergent Geometry: A Variational Closure of Modal Dynamics |
| url | https://doi.org/10.5281/zenodo.15646463 |