Two explicit error pitfalls

As a separate memory example, suppose an unreported classical memory bit $M$ is uniform. A device emits $M$ at two successive calls. Each one-call marginal is a uniform bit, just as for two independent fair coins. The two-call laws differ: the memory device returns only $00$ and $11$, while the independent device returns all four words. Their joint TV distance is $1/2$.

There is no zero-error second-stage comparison once the preceding record and the relevant memory are included. One-call marginal agreement cannot price the history channel.