TGMS is a bi-temporal property graph management system that exposes thirteen verified temporal operators as agent tools that can answer belief-state questions such as ``as of transaction time $T$, what did the system believe?''
Abstract
Temporal graph questions require reliable handling of time, identifiers, and arithmetic. Large language model (LLM) agents often fail on these tasks, especially when a graph records both ordinary evolution and later corrections. We present TGMS, a bi-temporal property graph management system that exposes thirteen verified temporal operators as agent tools. Each operator is typed, deterministic, bounded, cost-guarded, and bi-temporal by default. The LLM plans operator calls and writes the final response, while the system performs all graph computation. Numeric, entity, ordering, and pattern claims are checked against the content-addressed execution trace. TGMS separates valid time from transaction time. It can therefore answer belief-state questions such as ``as of transaction time $T$, what did the system believe?''Standard latest-state snapshots and retrieval pipelines do not preserve enough information to answer such questions. On a development benchmark built from a real communication network, TGMS with a 14B open-source model reaches 0.409 exact match. Vector-RAG, static-graph RAG, and text-to-Cypher reach 0.045--0.182 under the same serving setup. TGMS reaches 0.67 exact match on correction probes, while the three 14B baselines score zero. The claim verifier detects all 500 injected count and entity errors with no false positives on the clean answers. Two implementation findings were especially important. First, operator output contracts prevent plans from referring to fields that do not exist. Second, verification must track whether the cited evidence is complete, because correct arithmetic over a truncated result is still misleading. The code, benchmark, and trace viewer are open source under Apache-2.0.
Knowledge graph engineering often distributes accepted state, observations, constraints, processes, and hypothetical scenarios across artifacts whose combined execution contract remains external. We present PULSE, an Object-Process-Methodology-inspired language that localizes four operational roles and their write effects in one typed runtime. Here, modes denote operational roles rather than modal or deontic logic. The implemented contract fixes evidence non-overwrite, branch isolation, grounded multi-subject timers, guarded state change, and declaration-ranked event ordering over time and space; an external runner still decides whether evidence becomes an authoritative move. GeoSPARQL, SOSA, and SHACL remain generated views. A core calculus gives an effect-confinement lemma and six safety properties. Lean 4 checks kernel analogues for positions, evidence, clocks, monitors, atomicity, and branch source retention; 88 tests, 3,534 bounded checks, and 32 Lean/Python runtime-kernel cases bound the implementation claim to the checked cases. First-author implementations of a standards composition and a separate Sismic statechart reproduce the tested cold-chain trace. Across 37,440 generated temporal traces, PULSE matches a separate workflow and distinguishes ten single-field mutants. On the complete NOAA IBTrACS since1980 subset it agrees with GEOS and an event sweep on 1,476,290 transition-zone pairs, including 4,800 sampled and 12,831 duration-qualified events. Project-specific GeoSPARQL probes measure interface coverage. Overall, the results support contract localization, safety arguments, and trace parity for the tested fragment; language superiority and usability remain outside the evaluation.
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