Independent-run sampling

This certificate is for the specified inputs and complete protocols. It is not a universal all-input verification of $T^{\ast }(E_w)={\Pi }_w$, and not a mechanism-identification theorem. A finite input bank can be certified by an additional union bound; coverage of all states requires a separate argument. Identical complete laws remain indistinguishable, as in ip:process and the supplied sampling comparison CheungPsy02B.