When Should an AI Scientist Stop? Verifiable Experiment Steering and Refusal for Autonomous Discovery

We present CARTOGRAPH, a verification layer for AI scientists that couples unresolved-subspace experiment steering (select), explicit ambiguity closure (resolve), and residual-based library inadequacy detection (refuse). Under a local linear-Gaussian bridge, raw unresolved projection is the isotropic unresolved Fisher-information trace, while CARTOGRAPH-A is the exact unresolved A-optimal rule; closed-form EIG and Box–Hill arise as local comparators rather than global equivalents. Across five testbeds, CARTOGRAPH-A beats raw projection 129W/0T/15L at d = 8 (p < 10−21) in a replicated structured cascade. More distinctively, the framework tentatively identifies three out- of-library pharmacokinetic mechanisms and then revokes those identifications as residuals expose structural misfit, while one perturbed in-library control stays identified throughout. In low-dimensional pharmacokinetic and filtered EPA settings, near-ties against disagreement are predicted by theory and observed. Finally, in a retrospective audit of 40 positive claims from the published A-Lab autonomous materials system, the refuse guard flags all 4 claims later marked inconclusive under manual reanalysis while passing 32/36 confirmed claims. Codes can be found at the anonymous repository https://github.com/ai4science-boed/cartograph.git