{"paper":{"title":"Partial Observation of Linear Systems with the Mori-Zwanzig Formalism","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Fan Wang, Jan Heiland, Peter Benner","submitted_at":"2026-06-22T13:46:03Z","abstract_excerpt":"The Mori-Zwanzig formalism provides a systematic framework for deriving reduced-order model of dynamical systems when only part of the state is observed, but its practical use is often limited by the complexity of the resulting computations. This paper develops an explicit formulation of the Mori-Zwanzig equation for linear time-invariant systems under partially observed observables. By expressing the dynamics in terms of observables, the Koopman generator, and projections onto resolved and unresolved components, we derive closed-form representations of the Markovian, noise, and memory contrib"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.23341","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.23341/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}