When Is a Temporal Statement Store a Statement Graph? Export Boundaries for Occurrence Records with Two Clocks

A temporal statement store keeps every occurrence of a statement as a record. Each record has its own identifier, a triple, a transaction-time lifetime and a valid-time interval, and other records can refer to it. This paper asks which part of such a store can be exported as a Statement Graph without inventing or renaming any occurrence. Statement Graphs are the DAG model behind OneGraph, which lets RDF-star and property graphs interoperate. A record set can be exported this way exactly when it is closed under references and acyclic. Every set contains a largest exportable subset, the export kernel. A linear-time topological peel computes it, and it can be kept up to date with one bit per record. If records are immutable and never deleted, the full history is closed. Exporting it then loses only the cycles that atomic corrections create, and a batch-local check at correction time prevents those as well. Exporting a single snapshot also drops supersession lineage. A dual reference closure keeps that lineage by adding the retracted records it points to. Every omitted record is reported with a reason. The exported history can be written into RDF-star with both clocks stored as reserved statements, and read back without loss. Conjunctive queries over the asserted part return the same answers, up to a quoting bijection. Two alternatives mark the boundary from either side:- RDF 1.2 reifiers export any store, cycles included, but assert per triple rather than per occurrence.- The property-graph branch admits only edges and properties that nothing references. The proofs in the paper are by hand. The validation archive adds:- a Lean 4 development that re-proves the main results;- an executable validator covering exhaustive small stores, random stores and random protocol histories;- traces of both counterexamples through the tiramemsu engine.