Execution Sufficiency and State Sufficiency: Record Sufficiency in Reflexive Research Systems

AI-mediated research records often preserve enough information to replay a process without preserving enough information to resume it. This article formalizes that distinction through execution sufficiency and state sufficiency. A record is execution-sufficient when it determines a replayable continuation class; it is state-sufficient when it determines the operative state required for continuation. Using a compact model of operative state, record projection, replay, and restoration, the article proves that replayability and resumability separate whenever the record projection collapses distinct operative states into the same externalized trace. It then shows constructively that augmenting the artifact family can remove the relevant collapse on a targeted state class. The architectural consequence is direct: future AI-mediated research systems require state-bearing records, not merely replayable logs.