Proposition: Full and delayed rule cues

Supplying $R_t$ alongside $X_t$ gives Bayes accuracy one.

If a rule is fixed within a segment and its ID is supplied only at the first segment trial, an ideal predictor with memory of that cue also has accuracy one throughout the segment. The later trials then test retention and execution of an observed rule, rather than discovery of an unobserved rule.

Proof. Evaluate $f_{R_t}(X_t)$. In the delayed-cue case, retain the supplied ID until the next segment cue.