Emergent Architectural Entities in Information Systems: A Formal Theory of Entity Emergence, Escalation, and Lifecycle

This work presents a formal theory of emergent architectural entities — a class of architectural objects that are not designed in advance but emerge as stabilized computations over attributes of first-order objects. Emergence is understood as a transition from quantity (repeated queries and accumulating relations) to quality (a new ontological status of the entity). The central result is a formal theory of architectural escalation: an irreversible phase transition in which a computed entity becomes an autonomous second-order object — a stable carrier of relations with its own state. The transition is formalized through a state function Φ(E, t): the critical point occurs when the dynamics of Φ cease to be describable through the dynamics of the entity's extension. Key contributions:1. Formal definition of an information system as a triple (D, P, A).2. Architectural addressability as a criterion for the transition from computation to entity.3. The class of emergent architectural entities — objects arising from queries.4. State function Φ(E, t) and formalization of the phase transition.5. Pre-Escalation Reduction Theorem and Structural Irreducibility Theorem.6. Criterion of intrinsic identity: E is a second-order object if there exist times t₁, t₂ such that its extension is identical, yet its state differs.7. Empirical predictions testable against historical platform data. The theory bridges database theory (materialized views), software architecture (DDD, CQRS, Data Mesh), and complexity science (emergence, phase transitions). It provides a formal language for describing how architectural entities can not only be designed but also arise spontaneously from computational processes and structural relations.