Layered Bitemporal Graphs: Statement Identity, Two Clocks, and Metagraphs as Tags

Agent memory needs durable statement identity, provenance, and a distinction between when a claim held and when the system recorded it. We study layered bitemporal graphs, in which statement occurrences can reference other occurrences and carry both transaction-time lifetimes and valid-time intervals. On a referentially complete history, reference-closed sets form an Alexandrov topology. Its interior operator, the ground core, characterises minimal retraction cascades, grounded snapshots, and effective valid-time intervals. We give a correction contract that preserves structural closure under explicit patch and lineage conditions. A typed anchor-and-role encoding of metagraphs commutes with well-formed bitemporal snapshots. The calculus is realised in Tiramemsu, an embedded SQLite graph database. Retained checks identified four implementation gaps, and endpoint validation, closed retention and transaction-date guards now prevent those counterexamples. These checks support selected contracts rather than certifying the entire implementation. Our contribution is an operational account of recursive temporal reference integrity, not a new theory of temporal databases or finite topologies. Revision 4, 3 October 2026. Code: https://github.com/Volland/tiramemsu Keywords: agent memory, bitemporal data, temporal graphs, metagraphs, knowledge graphs, provenance, truth maintenance, Alexandrov topology, RDF-star, SQLite