Structural Time and the Architecture of Persistent Physical Systems

Physical theories describe dynamical evolution but typically treat time as a fundamental parameter. This work develops a structural account in which temporal direction and persistence arise from the topology of admissible transformations in persistent systems. Persistent systems are represented as (S,G,I), where S is a state space, G⊆End(S) the admissible transformations, and I an identity relation invariant under admissible transformations. From these minimal assumptions it follows that persistent differentiation cannot be maintained in fully symmetric transformation structures. Asymmetric reachability relations necessarily generate irreversible transitions between transformation domains. These domains form strongly connected components whose condensation graph induces a partial order that defines structural temporal direction. Irreversible transitions progressively reduce the set of reachable future domains, generating a structural entropy gradient. Together with energy-driven transformation dynamics this leads to a universal persistence boundary that constrains the stability of physical systems. The theory introduces a multidimensional concept of structural time consisting of ordering time, structural load time, and integration time. These quantities determine the conditions under which physical systems can maintain identity while undergoing transformation.