Human-on-the-Loop: A Theory of Oversight Capacity, Its Failure Modes, and the Non-Delegable Residual in the Age of AI Agents

Title: Human-on-the-Loop: A Theory of Oversight Capacity, Its Failure Modes, and the Non-Delegable Residual in the Age of AI Agents Abstract / Description:As enterprises rapidly deploy autonomous AI agents, "Human-on-the-Loop" (HOTL) has emerged as the dominant governance posture—promising an arrangement where AI executes by default while humans maintain oversight, exercise governance, and intervene at exceptions. This paper subjects that proposition to rigorous theoretical, mathematical, and empirical scrutiny, demonstrating that HOTL cannot be adopted as conventionally stated. Building on an extensive refutation set—from human factors and HCI to signal detection psychophysics, multi-agent evaluations, and primary legal records—this paper establishes four core contributions: 1. Loop Position as a Feasibility Bound: Loop position is not a policy stance management chooses, but a physical property determined by the ratio of system consequence latency to human response latency. Throughput, not governance statements, determines loop position.2. Oversight as a Consumable Resource: Oversight capacity is bounded by uncommitted attention, interaction time, context re-acquisition cost, and neglect time. When arrival rates exceed capacity, oversight becomes "insolvent"—failing not by refusing exceptions, but by ratifying them (rubber-stamping).3. The Low-Prevalence Effect & Verification Independence: As AI accuracy improves, human failure detection probability decays due to criterion shifts under low prevalence ("The Oversight Scissors"). Because supervisor AI agents running on identical base models share correlated blind spots, the human's irreplaceable contribution is not superior judgement, but statistical Verification Independence.4. The Scaling Dichotomy: Control oversight (contemporaneous monitoring) scales at Ω(T) in attention cost for a fixed detection guarantee, whereas Constitutive Oversight (setting objectives, values, and hard constraints ex-ante) costs O(1). High-throughput deployment inevitably exhausts control oversight, rendering Constitutive Oversight the only sustainable governance model at scale. Finally, the paper identifies the "Non-Delegable Residual"—the structural, logical, and fiduciary human duties that survive arbitrary AI capability growth—and introduces an 11-item audit protocol (Appendix B) to make corporate human oversight claims empirically falsifiable. JEL Classification: D23, M12, M14, M54, L23, K22, O33, D83Keywords: Human-on-the-Loop, Supervisory Control, Oversight Capacity, Automation Bias, Low-Prevalence Effect, AI Agents, Real Authority, Verification Independence, Duty of Oversight, Constitutive Oversight, Corporate Governance