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We investigate the origin of fermion mass hierarchies within the framework of Universal Modular Dynamics (UMD), where the density operator ρ is taken as the fundamental object encoding physical structure. In this approach, geometry, correlations, and dynamics emerge from properties of ρ and its associated modular generator. We systematically analyze a sequence of candidate mechanisms for generating Yukawa structures, including geometric overlap models, phase-dependent constructions, external flavor matrices, and interaction-based operators. While each of these approaches reproduces partial features of the observed mass spectrum, none simultaneously achieves hierarchical scaling, stability, and predictive consistency. We identify the missing structural ingredient as a sector decomposition induced by a pointer algebra Z, which defines dynamically stable subspaces of the Hilbert space. By projecting the density operator onto these sectors, ρZ = Pμ PμρPμ, we obtain a reduced operator encoding superselection structure. Yukawa couplings constructed from ρZ naturally reproduce exponential mass hierarchies with high numerical stability and predictive power across independent realizations. This leads to a new interpretation of flavor: fermion generations do not arise from fundamental symmetries or external structures, but from superselection sectors of the underlying quantum state. In this picture, fermion masses are determined by the sector-resolved spectrum of ρ, while geometric contributions control the overall scale. Our results provide a minimal and self-consistent mechanism for the emergence of fermion mass hierarchies, derived entirely from intrinsic properties of the quantum state and its sectoral organization, without invoking ad hoc flavor symmetries or fine-tuned parameters.
Nesen O. I. 2026. Sector-Resolved Origin of Fermion Mass Hierarchies in Universal Modular Dynamics. PREPRINTS.RU. https://doi.org/10.24108/preprints-3115676