C2 = C: Recoverable Continuity as the Structural Condition for Identity, Reference, and Attribution

This paper formalizes C² = C as a foundational structural condition beneath coherent identity, reference, attribution, and continuity. The central claim is that anything identified as itself across change requires recoverable continuity: the continuity relation by which a thing is tracked must itself remain continuous enough to be recovered. The paper distinguishes C² = C from ordinary idempotence, conservation laws, continuity equations, persistence theories, and domain-specific stability models. It introduces a minimal formal schema involving domains, states, transformations, recovery relations, continuity-classes, admissible transformations, and structural tests for traceability, composability, attributability, and reflexive stability. C² = C is presented not as a replacement for physics, biology, mathematics, consciousness studies, economics, language, or institutional theory, but as a prior condition those domains already require whenever they identify objects, track transformations, preserve reference, assign attribution, compare states, or explain persistence. The paper consolidates the broader recoverable-continuity research program by stating the underlying principle directly: continuity must remain continuous for anything to remain identifiable as itself across change.