Realization Multiplicity and Persistence Selection in Structure-First Systems

This paper introduces realization space as an explicit layer within structure-first descriptions of physical systems. Motivated by mathematical demonstrations of realization multiplicity in topology, the work distinguishes between structure, realization, accessibility, persistence, occupancy, and observability.

The paper argues that structure determines admissibility but does not necessarily uniquely determine realization. A single underlying structure may support multiple admissible realizations, forming a realization space from which persistence-stable configurations are selected. Persistence is proposed as a realization-selection mechanism acting upon accessible realizations, while occupancy and observability emerge as subsequent observer-level constraints.

The framework hierarchy developed is:

Ψ → ℛ → A → P → Ω → O

where structure determines admissibility, realization defines possible configurations, accessibility determines reachability, persistence selects stable configurations, occupancy determines active realization, and observability determines observer-resolved registration.

The paper provides a conceptual foundation for understanding realization multiplicity, persistence selection, conjugate realizations, occupancy switching, phase transitions, and observer-resolved occupancy within a unified structure-first framework.