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

This paper introduces the atomic decision boundary as a structural requirement for admission control systems that must enforce admissibility at execution time. Existing governance mechanisms — including RBAC, policy engines such as Open Policy Agent (OPA), and pre-execution policy evaluation — share a common architecture: they evaluate policies separately from the state transition they authorize. This separation creates a structural gap that no policy enrichment, external state, or re-evaluation can close. We formalize agent execution as a labeled transition system (LTS) and define two classes of admission systems: atomic systems, where evaluation and state transition occur as a single indivisible LTS step, and split evaluation systems, where they are separate transitions that may be interleaved by environmental actions. Under realistic concurrent environment assumptions, we prove that no construction can make a split system equivalent to an atomic system with respect to admissibility across all execution traces. This is a structural impossibility — independent of policy expressiveness, state availability, or implementation sophistication. We extend the analysis to the Escalate outcome, absent from classical time-of-check/time-of-use (TOCTOU) analyses, and prove that escalation transfers rather than removes the atomicity obligation: any system that resolves an escalated request must itself be atomic at the point of resolution. Key results: - Theorem (Structural Impossibility): No split evaluation system can guarantee execution-time admissibility under all traces in a concurrent environment. - Corollary (Enrichment Futility): Adding policies, external state, or re-evaluation steps to a split architecture cannot close the structural gap. - Theorem (Escalation Atomicity): The resolution of an Escalate outcome is itself subject to the atomic boundary requirement. - Mapping: RBAC and OPA are classified as split systems; the Agent Control Protocol (ACP, Paper 1) is shown to instantiate the atomic boundary via its evaluate-then-mutate pipeline with serializable ledger and atomic commit. This paper is the formal foundation of a six-paper series on agent governance. Paper 1 (ACP) instantiates the atomic boundary as a concrete protocol. Paper 2 (IML) detects behavioral drift above the enforcement layer. Paper 3 (Fair Atomic Governance) addresses fair allocation of access to the boundary. Paper 4 proves the four-layer architecture is irreducible under finite observability. Paper 5 (RAM) operationalizes execution validity under partial observability, providing the runtime closure of the series. Series repository: https://github.com/chelof100/decision-boundary-model Full series (Agent Governance Series, Papers 0–5): P0 — Atomic Decision Boundaries (this paper): https://doi.org/10.5281/zenodo.19642166 P1 — Agent Control Protocol (ACP): https://arxiv.org/abs/2603.18829 | https://doi.org/10.5281/zenodo.19642405 P2 — From Admission to Invariants (IML): https://doi.org/10.5281/zenodo.19643761 P3 — Fair Atomic Governance: https://doi.org/10.5281/zenodo.19643928 P4 — Irreducible Multi-Scale Governance: https://doi.org/10.5281/zenodo.19643950 P5 — Reconstructive Authority Model (RAM): https://doi.org/10.5281/zenodo.19669430