ERRAND: Budgeted Maintenance of Agent Memory

Deployed agents run on handed-over knowledge: a frozen policy consults a briefing of consolidated items written before the stream begins. The world then moves while the store stands still: paths close, flags change, price bands move; every item was true at handover, and the failure is staleness, not ignorance. We introduce ERRAND, which treats revalidation as a priced errand: a recheck competes with the task it protects for the same scarce actions, funded only when the value per action of resolving a doubt clears a running wage. The errand index is single-peaked, vanishing at both ends of belief, so certainty in either direction costs nothing; free en-route receipts maintain on-path knowledge, and repair writes a version, never a deletion. Under equal action budgets in two drifting tool-use worlds, ERRAND clears every non-oracle policy on the preregistered calibers, primary in every setting and conditional at every binding budget, leading eager revalidation by 10.0pp at the base cap. Restraint wins: given no cap, ERRAND stops on its own, spending 11.0% of steps, while uncapped eager revalidation spends 70.7% and still finishes 4.5pp behind capped ERRAND. The margin sits where the briefing's coverage is thinnest, the shadow price of long-tail knowledge: a small budget, well priced, beats a bigger store that never rechecks.