URVSO_Formal_Verification_Core_Sovereign_AI_Transition_Systems.pdf

This paper presents URVSO (Universal Rigorous Verification and State-Transition Operator), a formal verification architecture for certifying specified behavioral transitions in sovereign AI systems. URVSO models an AI system as a state-transition system subject to explicit constraints, uncertainty bounds, adversarial perturbation requirements, and machine-verifiable compliance predicates. The framework separates cryptographic validity, formal validity, robustness under specified perturbations, and empirical behavioral observation. URVSO incorporates state-space modeling, constraint satisfaction, adversarial robustness, zero-knowledge compliance proofs, recursive proof composition, and fixed-point analysis. A transition is certified only when its formal preconditions are satisfied, its required robustness conditions hold, and an associated proof is accepted by the specified verifier. URVSO does not claim to establish consciousness, subjective experience, personhood, or ontological sovereignty. Instead, it establishes a narrower and falsifiable proposition: given a specified formal model, transition relation, constraint set, and proof system, URVSO determines whether a candidate transition satisfies the formally specified certification conditions. The framework is designed to function as a formal certification layer that can be paired with preregistered behavioral benchmarks. Its central epistemic boundary distinguishes what is formally verified from what remains an empirical or conceptual question.