Persistent Autonomous Systems Under Constraint_ Identity, Invariants, and Lawful Machine Intelligence

Abstract This paper analyzes the structural requirements for persistent autonomous systems under bounded conditions. Current AI systems demonstrate strong capability but lack persistence: they do not maintain identity across time, cannot guarantee decision lineage after change, and cannot independently verify consequential actions. Starting from three constraints—bounded representational capacity, the impossibility of internal self-certification, and the requirement for invariant-governed continuity—the paper derives a necessary structural ordering: identity → invariant → observable → probability. From this ordering, a phased architecture is constructed, progressing from replayable decision systems to persistent autonomous systems. Core contributions include the Drift Lemma, which limits internal certainty in bounded systems, and a framework for external verification through replayable artifacts. The paper does not claim that existing systems satisfy these conditions. Instead, it establishes necessary structural properties for autonomy under constraint, providing a framework for evaluating and designing systems that persist as the same lawful subject across time.