The Invisible Constitution of AI: Operational Identity and Constitutional Equivalence in Composed AI Systems

Artificial-intelligence applications increasingly operate as compositions of language models, memory services, retrieval systems, authorization mechanisms, tools, agent runtimes, and consequential external services. Their apparent unity can survive extensive architectural change, while the conditions that make their behavior admissible do not necessarily survive with it. Equivalent answers can be produced under different evidence permissions, authority chains, policy versions, and effect-verification states. This paper investigates the invisible constitution of AI as a candidate mission-relative relational representation of the obligations that make composed operation legitimate and accountable. It formalizes operational constitution, conformance, constitutional equivalence, and authorized constitutional succession, distinguishing the preservation of an existing contract from the legitimate evolution of that contract. A three-valued witness model accounts for incomplete observability; typed obligations connect authority, evidence, state transitions, and verified consequences. Bounded propositions establish why output equality alone cannot imply constitutional equivalence, why legitimate succession need not preserve an unchanged permission set, and why no representational vocabulary enjoys an information advantage over equally informed conventional engineering. A preregisterable comparative protocol evaluates the candidate against output-only assessment and a strong composite baseline built from established access-control, provenance, software-contract, distributed-tracing, and transactional mechanisms. Intervention families include carrier substitution, memory migration, retrieval-policy drift, temporal revocation, delegated actions, failed commits, legitimate policy revision, and missing evidence. Outcomes include diagnostic accuracy, selective risk, explanation adequacy, human effort, instrumentation burden, and misclassification of authorized change. The paper is conceptual and methodological: no new experiment or implementation is reported, and no independent scientific Field or superior efficacy is assumed. Its contribution is an explicit and refutable investigation of when relational descriptions improve operational-continuity assessments, when they are merely useful syntheses, and when established engineering is sufficient.