Memory as Operational Re-Identifiability in Unified Information Phases

This version substantially revises the conceptual foundation of the paper and updates the title to Memory as Operational Re-Identifiability in Unified Information Phases. The central formulation is shifted from a general unification of memory and storage regimes to a structural theory in which memory is defined as the stable re-identifiability of an operational identity within an admissible information phase. In this formulation, information is not identified with the preservation of a microscopic configuration, but with the continued recoverability of an equivalence class under admissible evolution, access, switching, and readout. The revised paper develops this viewpoint systematically. Operational identity, operational equivalence, finite-temperature admissibility, retention, accessibility, switching, multi-state encoding, and relational readout are all reformulated as coordinated admissibility conditions on one structure. Retention becomes stable re-identifiability under uncontrolled stochastic evolution; accessibility and switching become controlled re-identification between admissible identities; multi-state encoding becomes simultaneous re-identifiability of several distinguishable identities; and readout is treated as relational re-identification without requiring externally imposed precision. The main conclusion is that memory, storage, volatility, persistence, density, access, and readout are not independent foundational categories. They are parameter regimes selected by admissibility inequalities. Volatility hierarchies therefore do not arise from the concept of information itself, but from non-uniform regimes of operational re-identifiability. This revision clarifies the foundational role of the paper and prepares the ground for subsequent architectural, performance, and semantic analyses.