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. Formalizing execution as a labeled transition system (LTS), 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 that may be interleaved by environmental actions. Under realistic concurrent environments, we prove that no construction can make a split system equivalent to an atomic system with respect to admissibility under all execution traces. This limitation is structural, not a matter of policy expressiveness or state availability. We further formalize the Escalate outcome -- absent from classical TOCTOU analyses -- and show its resolution is itself subject to the atomic boundary requirement. We map RBAC and OPA to the split model and contrast them with atomic systems. Admissibility is a property of execution, not evaluation. This paper is the formal foundation of a 4-paper Agent Governance Series: ACP/Paper 1 (arXiv:2603.18829), IML/Paper 2 (10.5281/zenodo.19643761), Fair Allocation/Paper 3 (10.5281/zenodo.19643928), Irreducibility/Paper 4 (10.5281/zenodo.19643950).