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

Safe physical probing can establish that a robot meets a task demand, while a safety envelope can prevent it from ruling out feasibility. We formalize this asymmetry using a capability signature ${\theta }^{\star }$, the supremum level an embodiment reaches along a task's binding capability axis in a scene, compared with a demand computed from scene geometry alone. Probes are restricted to $[0,A_{\mathrm{safe}}]$, whereas ${\theta }^{\star }$ is defined over $[0,a_{\max }]$ with $A_{\mathrm{safe}}<a_{\max }$. Within the stated response class, feasibility can be certified with finitely many probes whenever the true response at some safe grid amplitude exceeds $c_{\mathrm{feas}}$, without a regularity constant. In the scalar-response observation model, for demands below the trivial upper bound, infeasibility has no uniformly valid test with non-trivial power: an infeasible response admits an indistinguishable extension beyond the envelope that changes the verdict. The upper identification endpoint remains at its trivial bound, even under smoothness or Lipschitzness with an unknown constant. SOMA-Probe combines a variance-adaptive, anytime-valid lower bound with four structural witnesses, each based on a stated, falsifiable, dimensionless order property. It selects probe amplitudes by risk-penalised information gain and returns Certified-Feasible, Certified-Infeasible, or Uncertified. A companion result bounds coverage for probing policies using the prescribed certification rules. The benchmark comprises four manipulation tasks and sixty embodiment perturbations, eighteen outside the parameter vector exposed to the identification baselines. On the $36$ blind perturbations, certification coverage is $0.61$, compared with $0.43$ for the strongest safe-exploration baseline. The reported mis-certification rate is $0.011$ at a nominal level of $0.05$, excluding $W_4^{\mathrm{cert}}$ on D5a and the optional regularity branch. In a tier analysis across all sixty perturbations, the end-to-end advantage over ASID is concentrated in the eighteen perturbations outside its fitted parameter vector.