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| Format: | Recurso digital |
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Zenodo
2025
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| Online Access: | https://doi.org/10.5281/zenodo.16472257 |
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Table of Contents:
- <p>This paper presents a symbolic modular field theory (SMFT) in which interaction strengths are not fixed constants, but emergent quantities derived from ratios of modular resonance frequencies. We introduce a symbolic Lagrangian embedding the ratio <span><span>gab=ωa/ωbg_{ab} = \omega_a / \omega_b</span><span><span><span><span>g</span><span><span><span><span><span><span><span>ab</span></span></span></span><span></span></span></span></span></span><span>=</span></span><span><span><span>ω</span><span><span><span><span><span><span>a</span></span></span><span></span></span></span></span></span><span>/</span><span><span>ω</span><span><span><span><span><span><span>b</span></span></span><span></span></span></span></span></span></span></span></span>, simulate symbolic field evolution, and demonstrate how coupling drift, identity stabilization, and symbolic collapse emerge from the modular structure itself.</p> <p>The system is explored under multiple conditions:</p> <ul> <li> <p>Frequency drift (modular decoherence)</p> </li> <li> <p>Collapse triggers (symbolic breakdown)</p> </li> <li> <p>Resonance-locking potentials (e.g., [[K]], <span><span>ϕ\phi</span><span><span><span>ϕ</span></span></span></span>)</p> </li> </ul> <p>We also define a dual-layer model, linking symbolic dynamics to physical observables:</p> <ul> <li> <p>Entropy <span><span>S(t)\mathcal{S}(t)</span><span><span><span>S</span><span>(</span><span>t</span><span>)</span></span></span></span></p> </li> <li> <p>Resonance Coherence <span><span>F(t)\mathcal{F}(t)</span><span><span><span>F</span><span>(</span><span>t</span><span>)</span></span></span></span></p> </li> <li> <p>Modular Curvature <span><span>K(t)\mathcal{K}(t)</span><span><span><span>K</span><span>(</span><span>t</span><span>)</span></span></span></span></p> </li> </ul> <p>These simulations were generated using a symbolic modular engine, included in this upload. The Appendix formally defines the symbolic stabilizer constant [[K]] and provides full details on the symbolic update dynamics and observables.</p>