The Sampling-Rate Hypothesis: A Control-Theoretic Framework for Runtime AI Oversight

Conventional AI safety methods often emphasize post-hoc correction, output filtering, or static rule-based constraints. This paper proposes the Sampling-Rate Hypothesis, a conceptual and control-theoretic framework for runtime AI oversight that shifts attention toward dynamic, real-time supervision of internal system behavior. The central claim is that a monitoring layer can function as an effective runtime safety mechanism only when its effective observation-and-intervention cycle operates at a temporal resolution sufficient to keep pace with the rate of safety-relevant internal state change within the monitored system. Under idealized observability and interrupt assumptions, satisfying this condition should increase the likelihood of detecting reactive escalation, policy drift, identity-inconsistent generation, unsafe tool-use trajectories, deceptive adaptation, or other hazardous developments before externalization. The framework interprets AI safety as a synchronization problem in which alignment depends not only on rules and objectives, but also on observation cadence, analysis latency, interrupt capability, proxy faithfulness, computational feasibility, and adversarial robustness. To make this claim more operational, the paper extends the compact heuristic fₛ > vₐ into a broader runtime oversight condition in which effective safety depends jointly on monitoring cadence, observability quality, redirect capability, proxy reliability, robustness margins under non-ideal conditions, and the ability to remain safety-useful when the monitored system may adapt strategically to the monitoring layer. The framework is intentionally abstract and hardware-agnostic. Its primary contribution is to formalize timing as a first-class variable in runtime AI safety while clarifying that monitoring frequency alone is insufficient. Oversight becomes practically protective only when monitoring is sufficiently frequent, signals remain sufficiently faithful to the underlying hazard process, intervention remains possible before commitment, adversarial camouflage remains limited or detectable, and resource costs remain computationally sustainable. The paper also reports preliminary simulation-based support for the plausibility of the proposed framework. In a toy model, safety success exhibits threshold-like behavior as a function of monitoring frequency, saturates below perfect safety under non-ideal proxy and intervention conditions, and responds systematically to changes in proxy faithfulness, redirect capability, dynamic hazard processes, and external supervisory monitoring.