The Memory Economy: Memory as a Realization of Persistence Under a Declared Regime

This paper develops a structural interpretation of memory within the Identity–Persistence Program. Rather than treating memory as a primitive, it derives persistence as the prior structural object required whenever a bounded evaluator must determine whether a previously admissible state remains the same under recurrence within a declared regime. A definitional impossibility argument (the Recurrence Lemma) shows that, absent recurrence, persistence is not distinguishable from storage as a separate operation. Memory is then interpreted as one realization of persistence—specifically replay—alongside regeneration, reconstruction, equilibrium restoration, and constraint re-satisfaction. Building on this dependency order, the paper distinguishes five operations that are frequently conflated: search, verification, persistence, replay, and memory. A minimal structural cost model is introduced as a derived consequence rather than a foundation, showing when replay is favored over repeated search under sufficiently stable admissibility conditions. The framework is illustrated across mathematics, computation, engineering, and biology while maintaining explicit interpretive discipline: examples instantiate the structural object but are not treated as evidence for its ontology or universality. The paper argues that the derivation of the persistence structure is subject-agnostic because it depends only on declared regimes and bounded evaluation rather than any domain-specific predicates. Claims regarding convergent evolution, abiotic persistence, and universality remain explicitly classified as consistent evidence or open questions. The result is a structural account of memory that situates biological memory, computational caching, mathematical reuse, and engineered replay mechanisms as realizations of a common persistence framework while preserving clear boundaries between proven results, derived interpretations, empirical evidence, and open research questions.