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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.17693290 |
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Sommario:
- <p>This third installment in the SMFT Born-rule series completes the derivation of quantum probabilities by incorporating three additional structural components of symbolic modular field dynamics:</p> <p> </p> <ol> <li>External symbolic attractors, exemplified by the Leema resonance event—the first naturally occurring, empirically documented symbolic attractor with a stable cycle of length \ell = 11.</li> <li>The Modular Coupling Lagrangian, which provides the first explicit dynamical construction of the operator M responsible for Born-rule deviations in high-dissonance regimes.</li> <li>Moonshine-based stabilizers, particularly the universal constant [[K]] \approx 0.77, which govern symbolic curvature, collapse behavior, and resonance-locked probability flow.</li> </ol> <p> </p> <p> </p> <p>In the low-dissonance limit, the KN-isometry structure derived in Born I is recovered, yielding the standard Born probability distribution P_i = |c_i|^2.</p> <p>In the high-dissonance regime, the modular coupling operator produces a controlled, falsifiable deviation term</p> <p>P_i = |c_i|^2 + \Delta_i(D, \lambda, M),</p> <p>where \Delta_i is computed from symbolic curvature, resonance length, and coupling strength.</p> <p> </p> <p>The paper integrates these structures into a single unified probability framework grounded in SMFT, modular resonance geometry, and empirical symbolic phenomena. Moonshine resonance windows \ell \in \{11,13,17,24,29,37,41\} define regions where Born behavior is enforced, while modular coupling dynamics describe how deviations arise outside those windows.</p> <p> </p> <p>Three TikZ diagrams visualize the Moonshine energy plateau, the modular-coupling chain, and the Leema attractor cycle.</p> <p> </p> <p>This work extends the foundations established in Born I and Born II and completes the SMFT program of deriving the Born rule from symmetry, thermodynamics, and symbolic modular geometry.</p>