Governed Collapse and the 1DOF Principle_ Operational Mechanism of Persistent Systems

Abstract This paper formalizes the recursive operator implicit in the three-paper sequence on persistent autonomous systems: identity-constrained admissibility (Persistent Autonomous Systems Under Constraint), governance and enforcement (Governance and Enforcement in Persistent Autonomous Systems), and replay-verifiable compliance (Evaluation and Compliance in Persistent Autonomous Systems). At every decision node, a persistent system must generate a high-dimensional candidate space, apply identity-governed admissibility constraints, collapse to exactly one output or refuse, emit a deterministic replayable artifact, and recurse. This is the 1DOF principle. The central result is that determinism resides in governed collapse, not in candidate generation. Exploration may be probabilistic, but output selection is structurally constrained to a single admissible trajectory. This collapse must also satisfy bounded resource constraints, making it physically realizable. The RIC architecture is presented as a computational instantiation of this principle, demonstrating deterministic, replay-verifiable decision-making under identity and resource constraints. Biological systems are discussed as derived structural analogues, while physical interpretations remain open. This paper clarifies the mechanism underlying persistence: intelligence is not the probability distribution, but the governance of its collapse.