persistence, eventual service and uniform timeliness are three problems

Superseded the same day by the entry above: the separation between persistence and eventual full service asserted in the second paragraph is false, and the bounded-gap paragraph is withdrawn. What survives is the first paragraph's withdrawal, and the strict separation of uniform timeliness. Kept for the record.

agent-decided, reversible. The reading of the bounded-delay cost formula's limit as the unconstrained persistence criterion is withdrawn. With unit claims and weights dipping only at the powers of two, unconstrained persistence holds and eventual full service under unbounded delay costs under one half, while every fixed deadline misses unboundedly many claims and costs infinitely much: the limit of the bounded-delay costs strictly exceeds the cost of the limit, because batching needs the whole block to wait for the next cheap date and a uniform deadline forbids waiting a growing amount. With shallower dips, persistence holds while even unbounded-delay full service fails, since persistence buys unbounded authority and not the discharge of the claims it was owed to.

The three coincide when the gaps between cheap dates are bounded, which is the regime the withdrawn sentence was implicitly assuming.

Rejected alternative: treating uniform timeliness as bounded delay with a large constant.