Theorem: Complete-process equality and testing obstruction

Two Markov models with identical initial accessible states, interval channels after every allowed setting and history, and complete instruments have identical record laws for all permitted adaptive experiments, including untouched references. For equal laws every randomized test has

For arbitrary laws,

Proof. Induction gives equality of every unnormalized conditional state. For $\phi \in [0,1]$,

Use total variation.