Safe to Stop? Risk-Constrained Stopping for Sequential Clinical Diagnosis Agents

Clinical diagnosis agents must decide not only what test to request next, but also when to diagnose or defer. Existing agent benchmarks largely evaluate accuracy after fixed or unconstrained interaction, leaving autonomous stopping reliability implicit. We present Cros, a risk-constrained stopping layer combining state-wise error ranking, policy design on disjoint development splits, and LTT-style exact tests of selective diagnostic error and minimum autonomous coverage for complete sequential policies. Its finite-sample guarantee requires the candidate family, testing rule, and any randomization to be frozen before calibration labels are accessed. On a 1,834-episode MIMIC-derived abdominal-pain benchmark, the full ranker achieves exploratory state-error AUROC 0.853, compared with 0.715 for maximum class probability and 0.552 for the backbone's native stop score. On the previously viewed 367-episode evaluation split, analytically averaging over the frozen Crosmix weights yields 16.9\% selective error at 78.8% coverage, cost 5.57, and 0.68 tests, versus 30.8% error at 100% coverage, cost 8.14, and 1.53 tests under native stopping. Forced continuation is non-monotone: error is 28.3% with HPI alone and 34.3% after full workup. However, the uniform-weight mixture ablation is cheaper on this viewed split despite missing the locked development margins, and Crosmix nominally satisfies the joint criterion in only 6 of 20 development resplits. Because evaluation labels were inspected during earlier development, these findings provide exploratory feasibility and audit evidence, not a confirmatory safety certificate.