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| Format: | Recurso digital |
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Zenodo
2026
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| Online Access: | https://doi.org/10.5281/zenodo.19601502 |
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Table of Contents:
- <p>We investigate the spectral properties of a restricted class of discrete phase operators under the imposition of $U(1)$ holonomy constraints. Motivated by the geometric requirement to accommodate the non-linear tensions associated with the unitary Cayley transform, we consider an effective ansatz based on tridiagonal radial Jacobi operators.</p> <p>The adoption of this architecture is not purely phenomenological: in the underlying formalism based on action and phase, the dynamics is organized by a self-adjoint structural operator whose unitary propagation admits a resolvent form. This structure induces a bilocal kernel of effective connectivity which, under assumptions of quasi-locality and infrared coarse-graining, can be projected onto a finite number of local degrees of freedom. In this regime, tridiagonal operators emerge as natural effective realizations of the underlying spectral structure.</p> <p>We show that this architecture is structurally compatible with an effective description of fermions in color-singlet representations (as in the leptonic sector). Assuming the empirical fine-structure constant ($\alpha_{em}$) as a boundary condition for the off-diagonal coupling, we derive the conditions for strict positivity of the spectrum. We demonstrate analytically that the existence of positive eigenvalues restricts the parameter space of the model, imposing an exact functional limit on the radial fractal scale $q$, as well as an asymptotic upper bound.</p> <p>The spectral analysis in the allowed region indicates that the electromagnetic coupling induces level repulsion, qualitatively reproducing the experimental Tau/Muon ratio. However, the observed divergence in the Muon/Electron ratio suggests that the tridiagonal architecture acts primarily as an effective regime description, adequately capturing more localized states, while the ground state remains sensitive to the untruncated global structure.</p> <p>These results indicate that the model should be interpreted as an effective realization of a more general spectral dynamics, in which physical properties emerge from the organization of the phase and its spectral filtering.</p>