Atomic Decision Boundaries: A Structural Requirement for Guaranteeing Execution-Time Admissibility in Autonomous Systems

Autonomous systems increasingly execute actions that directly modify shared state, creating an urgent need for precise control over which transitions are permitted to occur. Existing governance mechanisms evaluate policies prior to execution or reconstruct behavior post hoc, but do not enforce admissibility at the exact moment a state transition is committed. We introduce the atomic decision boundary, a structural property of admission control systems in which the decision and the resulting state transition are jointly determined as a single indivisible step in the labeled transition system (LTS) model of execution. We distinguish two classes: atomic systems, where evaluation and transition are coupled within a single LTS step, and split evaluation systems, where they are separate transitions interleaved by environmental actions. The separation introduces an architectural gap -- the decision is evaluated in one system state; the transition fires in a potentially different one -- that no policy, regardless of sophistication, can close from within a split architecture. Under realistic concurrent environments, we prove via a constructive counterexample trace that no construction can make a split system equivalent to an atomic system with respect to admissibility. Three corollaries follow: impossibility of execution-time guarantees in split systems, insufficiency of external state enrichment, and admissibility as an execution-time rather than evaluation-time property. We further formalize the Escalate outcome -- absent from classical TOCTOU analyses -- proving that it transfers rather than eliminates the atomicity requirement: resolution is safe if and only if it is itself atomic. We classify RBAC, ABAC, OPA, Cedar, and AWS IAM as split systems and ACP as atomic, providing a structural taxonomy of existing governance mechanisms. Admissibility is a property of execution, not evaluation.