Admissibility Decay: A Formal Model for the Rate at Which a Delegated Machine Authority Loses Its Governance Validity in Regulated Enterprises

Delegated machine authority does not remain valid indefinitely. A system authorised at T0 operates in a governance context — a set of operating parameters, organisational conditions, and regulatory circumstances — that may have changed materially by T1. As those conditions change, the governance basis for the delegation weakens. This paper names and formalises that process as admissibility decay: the rate at which a historically valid delegation of machine authority loses its current governance validity as conditions diverge from the authorisation baseline. The Continuous Admissibility Model (Hossain, 2026b) introduced admissibility decay as a conceptual framework and proposed four decay rate factors: operational volatility, governance sensitivity, authorisation specificity, and structural context stability, without specifying the formal relationship between these factors and the decay rate. This paper formalises that relationship. It introduces the Admissibility Decay Function (ADF), a governance model that produces a decay rate score for any in-scope AI system based on the four factors, and specifies how that score should govern the calibration of Continuous Admissibility Monitor threshold settings, reassessment cycle lengths, and authorisation specificity requirements at deployment. The paper argues that uniform threshold defaults, applied identically across all systems regardless of their decay rate profiles, are a governance design limitation that produces systematic under-governance of high-decay-rate systems and an excessive governance burden on low-decay-rate systems. The ADF provides the calibration framework that resolves this limitation. The paper demonstrates that the four decay rate factors are independently observable, that their combination yields a meaningful decay rate score across a range of deployment contexts, and that the ADF’s threshold calibration guidance is consistent with the governance design principles established in the Autonomy Budget and Continuous Admissibility frameworks. It analyses five major governance frameworks, ISO/IEC 42001:2023, the EU AI Act, APRA CPS 230, the NIST AI RMF, and the IMDA Model AI Governance Framework for Agentic AI, demonstrating that none specifies decay-rate-calibrated governance thresholds.