Safe Probing Certifies What a Robot Can Do, Not What It Cannot

摘要

A robot handed an instruction should be able to say whether the body it currently has can carry it out. We pose that as certifying a capability signature θ*, the supremum level an embodiment reaches along a task's binding capability axis in a scene, against a demand computed from scene geometry alone. Safety confines probing to [0, A_safe] while θ* is a supremum over [0, a_max], and the two sides of the question do not survive that truncation equally. Feasibility does: if some safe amplitude already carries the body past the demand, finitely many probes certify it, through a bound invoking no regularity constant. Infeasibility does not, at any sample size. Every admissible response curve is matched by another agreeing with it throughout the envelope and disagreeing about the verdict, so the upper endpoint of the identification interval sits at its trivial value however much data arrives, and neither smoothness nor an unknown Lipschitz constant moves it. We therefore treat Uncertified as a verdict rather than a failure, and recover the infeasible side only where the shape of the curve inside the envelope rules the alternatives out, through four structural witnesses that each spend one falsifiable, dimensionless order property. SOMA-Probe holds an anytime-valid lower bound under a variance-adaptive confidence sequence, picks amplitudes by risk-penalised information gain, and returns one of three verdicts; a companion result caps what any safe prober can certify at all. On four manipulation tasks and sixty embodiment perturbations, eighteen of them outside the parameter vector the simulator exposes and the baselines identify, it certifies 0.61 of instances against 0.43 for the strongest safe-exploration baseline, at a mis-certification rate of 0.011 against a nominal 0.05; nearly the whole margin sits on those eighteen.