The Earned Stride When Verification Becomes Suboptimal: A Threshold Theorem for Accumulated Model Trust

We prove that there exists a threshold N ∗(d) in confirmed non-trivial predictions within a domain d, after which requiring verification before action is throughput-suboptimal. An agent whose internal model has been validated by N ∗ consecutive non-trivial confirmations maximizes long-run throughput by acting on model predictions directly—striding—until failures accumulate sufficiently to push the posterior back below threshold. The stride threshold R∗ = 1−Cv /Cmistake converges to the throughput knee p∗ = 0.8 (Elliott 2025, CBS Risk Corridor) when the verification-to-mistake cost ratio equals the rate-to-quality elasticity ratio δ/γ. The number of confirmations required to earn stride is small: N ∗ ≈ 7–8 under a uniform prior with all predictions confirmed, because non-trivial predictions carry high information per confirmation. We prove that stride transfers across domain neighborhoods connected by shared evidential bases or causal relation- ships, that stride is revocable upon failure accumulation with hysteresis preventing oscillation, and that the Archivist regime (permanent verification, p > p∗) is throughput-suboptimal by exactly the amount predicted by the throughput curve J (p) = pγ (1− p)δ . The result formalizes a phenomenon familiar to every competent practitioner: the transition from “check everything” to “trust the model, correct on failure” that occurs after sufficient domain experience. The transition is not overconfidence. It is the mathematically optimal operating point for throughput-maximizing agents with validated models. Keywords: earned stride, verification threshold, throughput knee, confidence-based stopping, domain trust, model validation, non-trivial prediction, stride transfer, hysteresis, Archivist pathology