Durable Reasoning Under Drift: Cost-Sensitive Reuse of Persistent Reasoning Artifacts over Continual Knowledge Streams

Large language models repeatedly recompute responses even when previously derived computation may remain reusable. This inefficiency becomes more consequential in continual knowledge environments, where persistent computation can become stale as the underlying information changes. We study persistent reasoning as a selective-refresh control problem: given a previously computed artifact and newly arriving information, when should the system reuse the artifact and when should it pay the additional inference cost required to refresh it? We introduce a drift-aware cost-sensitive persistence controller that scores observable signals of change and selects REUSE or REFRESH. We evaluate a frozen controller on an untouched 636-transition test set derived from the OAKS continual knowledge-stream benchmark. At a validation-locked threshold of 0.50, the controller achieved 55.75% recall and an F1 score of 0.4145 for changed transitions, while selecting reuse on 69.97% of test transitions. Relative to always recomputing, the evaluated policy reduced model-query tokens by 69.97% and query latency by approximately 70%. Bootstrap analysis and offline ablations quantify uncertainty and sensitivity.