Authority, Admissibility, and Replayability: Why Executable Governance Requires Structural Preconditions, Not Oversight

Contemporary approaches to artificial intelligence governance rely predominantly on post-hoc oversight mechanisms such as logging, audits, explainability, and human review. While these mechanisms provide narrative accountability, they consistently fail to constrain behavior at the moment where risk becomes irreversible: execution. This paper argues that governance cannot be achieved through supervision alone and must instead be embedded as a set of structural preconditions that determine whether a system is permitted to enter an executable state at all. Building on prior work establishing structural impossibility as a safety mechanism (Paper I) and admissibility before autonomy as a governance invariant (Paper II), this paper formalizes three system properties as first-class governance requirements: authority, admissibility, and replayability. Authority is treated not as a command or permission but as an executable condition that must be satisfied prior to action. Admissibility is defined as the set of structurally reachable states within a system, rendering prohibited behaviors non-existent rather than forbidden. Replayability is introduced as the minimal substrate for accountability, enabling deterministic reconstruction of decision paths rather than retrospective interpretation. The paper demonstrates why apparent compliance with regulatory frameworks frequently fails to deliver enforceable governance, particularly in financial, healthcare, defense, and enterprise AI systems. It further maps these structural requirements to existing regulatory regimes, including the EU AI Act, FDA GxP expectations, financial model risk management, and data protection law, without optimizing for any single jurisdiction. This work does not propose an implementation or architecture. Instead, it establishes a foundational theory for executable governance, positioning authority, admissibility, and replayability as conserved system properties necessary for defensible, scalable, and legally coherent AI deployment.