Execution Exists Only If Admissible: A Formal Model for Deterministic Execution in AI Systems

This paper introduces a runtime admissibility model for AI systems, where execution is not controlled after the fact but conditionally permitted to exist. We formalize the principle: Execution exists if and only if admissibility (stateₜ, authorityₜ, conditionsₜ, invariants) = TRUE at time t. The paper defines: • Admissibility as a deterministic, side-effect-free runtime function• An execution boundary where invalid execution paths are structurally unreachable• A version-based time model eliminating TOCTOU inconsistencies• Concurrency-safe execution using single-writer guarantees• Dependency resolution without orchestration• Fail-closed system behavior with explicit ESCALATE semantics This work builds on the previously introduced deterministic execution layer: “The Deterministic Kernel: A New Execution Layer for AI Systems”DOI: https: //doi. org/10. 5281/zenodo. 19129720 While the Deterministic Kernel enforces correct execution, this paper extends the model by defining how admissibility is computed at runtime, ensuring that only valid execution paths can exist. Together, these works establish a foundation for AI systems that are: • deterministic• auditable• replayable• concurrency-safe• production-grade This paper is intended for system architects, AI engineers, and enterprises designing AI systems that must operate under strict correctness, auditability, and regulatory constraints. -JSR