Input precision and robust positive margins

A supplied-value approximation $|d-\tilde{d}|\le {ϵ}_d$ contributes at most $|\nu |{ϵ}_d/(2\sigma )$ to the preparation distance by Lemma lem:lipschitz. A channel error does not validate a false enclosure.

These are complete-interface comparison statements Watrous,XIST. They do not assert a finite-sample confidence level without an additional sampling model.