Corollary: Fresh sequences after adaptive history

Before assessment block $k$, condition on the complete training, intervention, and calibration history. Choose the checkpoint, sample size, summary definitions, and confidence allocation before viewing the block. If its sequences are conditionally fresh and independent, the sequence-mean and ratio certificates hold conditionally.

Predictable allocations with total at most $\delta$ give simultaneous confidence at least $1-\delta$ across completed blocks.

Proof. Apply Theorem thm:sequencehoeffding conditional on the past. Average the conditional failure probabilities and sum them. This is the conditional-block argument recorded in Psy03-B CheungPsy03B.