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On the Emergence of Boundaries in Universal Modular Dynamics
2026-06-21

We investigate the origin of boundaries within the framework of Universal Modular Dynamics (UMD), where physical structure is defined in terms of the density operator ρ, its modular generator K = −log ρ, and the associated spectral distribution p(k). While all observable systems exhibit finite extent and well-defined limits, it remains unclear whether such boundaries are fundamental properties of the underlying structure or emergent features of its organization. We show that within UMD, boundaries need not be imposed a priori. Even in the absence of intrinsic spectral bounds, effective finiteness arises naturally through three mechanisms: localization of the spectral distribution, suppression of contributions outside its dominant region, and limited accessibility of structure. In this framework, observable systems correspond to localized regions of p(k), giving rise to effective boundaries without requiring fundamental cutoffs. We further demonstrate that the appearance of boundaries is inherently linked to the role of the observer, understood as a localized structural configuration with restricted access to the full organization. These results provide a unified structural interpretation of finiteness, scale, and stability, and suggest that boundaries are emergent features arising from the interplay of structure, dynamics, and observation. This work extends the structural program developed in previous studies and motivates further investigation of observation, measurement, and accessibility as fundamental components of physical reality.

Ссылка для цитирования:

Nesen O. I. 2026. On the Emergence of Boundaries in Universal Modular Dynamics. PREPRINTS.RU. https://doi.org/10.24108/preprints-3115621

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