Axioms of Research Continuation: A State-Restoration Theory for Transcript-Sufficient Research Systems

This paper develops a formal state-restoration account of research continuation for transcript-sufficient research systems. It distinguishes replayable records from resumable research states by modeling an operative research state, externalized record, record projection, replay operator, restore operator, and continuation-equivalence relation based on admissible next operations. The central claim is modest: a record can support replay while failing to support resumption when projection collapses states that are not continuation-equivalent. The paper then specifies research-specific state distinctions required for accountable continuation, including evidence-mediated working state, re-entry and non-erasure, artifact identity, proposal/admissibility/update separation, enacted authority, and validation-gated advancement. Existing infrastructures such as provenance standards, research-object packages, process mining, checkpoint/restore mechanisms, and software configuration management are treated as analogues or implementation substrates. The Reflexive Laboratory is used as a worked transcript-sufficient case, not as the only possible implementation. Keywords: research continuation; state restoration; transcript sufficiency; record projection; replayability; resumability; artifact authority; validation; canonicality; Reflexive Laboratory; AI-assisted research; research objects; provenance