{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:KQLRX72XFDPVUMWMKV7CHMKW3T","short_pith_number":"pith:KQLRX72X","schema_version":"1.0","canonical_sha256":"54171bff5728df5a32cc557e23b156dccf1327c15b8e25a9cc0e4c3167717fe2","source":{"kind":"arxiv","id":"1707.01146","version":4},"attestation_state":"computed","paper":{"title":"Data-driven discovery of Koopman eigenfunctions for control","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.OC","authors_text":"Eurika Kaiser, J. Nathan Kutz, Steven L. Brunton","submitted_at":"2017-07-04T20:33:14Z","abstract_excerpt":"Data-driven transformations that reformulate nonlinear systems in a linear framework have the potential to enable the prediction, estimation, and control of strongly nonlinear dynamics using linear systems theory. The Koopman operator has emerged as a principled linear embedding of nonlinear dynamics, and its eigenfunctions establish intrinsic coordinates along which the dynamics behave linearly. Previous studies have used finite-dimensional approximations of the Koopman operator for model-predictive control approaches. In this work, we illustrate a fundamental closure issue of this approach a"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1707.01146","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-07-04T20:33:14Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"b2d2d6037db9e8df11b761c558d4e3e33b5924e61b9b213bed1bfc4999da87d5","abstract_canon_sha256":"3e95acf609286402a3e3ca3cedab9a821a03702aaef18815f69ad5f4bd3f9007"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:14:07.619541Z","signature_b64":"xGZp76Cm+ExlnVl1H7WiUtzinM+wKg1QF5TwHLoNOWqAo60cWsraCup+31HlmmvWiJop+Ce6j0upTYpmErIiCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"54171bff5728df5a32cc557e23b156dccf1327c15b8e25a9cc0e4c3167717fe2","last_reissued_at":"2026-07-05T02:14:07.618926Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:14:07.618926Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Data-driven discovery of Koopman eigenfunctions for control","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.OC","authors_text":"Eurika Kaiser, J. Nathan Kutz, Steven L. Brunton","submitted_at":"2017-07-04T20:33:14Z","abstract_excerpt":"Data-driven transformations that reformulate nonlinear systems in a linear framework have the potential to enable the prediction, estimation, and control of strongly nonlinear dynamics using linear systems theory. The Koopman operator has emerged as a principled linear embedding of nonlinear dynamics, and its eigenfunctions establish intrinsic coordinates along which the dynamics behave linearly. Previous studies have used finite-dimensional approximations of the Koopman operator for model-predictive control approaches. In this work, we illustrate a fundamental closure issue of this approach a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.01146","kind":"arxiv","version":4},"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/1707.01146/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1707.01146","created_at":"2026-07-05T02:14:07.618991+00:00"},{"alias_kind":"arxiv_version","alias_value":"1707.01146v4","created_at":"2026-07-05T02:14:07.618991+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.01146","created_at":"2026-07-05T02:14:07.618991+00:00"},{"alias_kind":"pith_short_12","alias_value":"KQLRX72XFDPV","created_at":"2026-07-05T02:14:07.618991+00:00"},{"alias_kind":"pith_short_16","alias_value":"KQLRX72XFDPVUMWM","created_at":"2026-07-05T02:14:07.618991+00:00"},{"alias_kind":"pith_short_8","alias_value":"KQLRX72X","created_at":"2026-07-05T02:14:07.618991+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2605.18720","citing_title":"Data-Driven Dynamic Modeling of a Tendon-Actuated Continuum Robot","ref_index":22,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/KQLRX72XFDPVUMWMKV7CHMKW3T","json":"https://pith.science/pith/KQLRX72XFDPVUMWMKV7CHMKW3T.json","graph_json":"https://pith.science/api/pith-number/KQLRX72XFDPVUMWMKV7CHMKW3T/graph.json","events_json":"https://pith.science/api/pith-number/KQLRX72XFDPVUMWMKV7CHMKW3T/events.json","paper":"https://pith.science/paper/KQLRX72X"},"agent_actions":{"view_html":"https://pith.science/pith/KQLRX72XFDPVUMWMKV7CHMKW3T","download_json":"https://pith.science/pith/KQLRX72XFDPVUMWMKV7CHMKW3T.json","view_paper":"https://pith.science/paper/KQLRX72X","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1707.01146&json=true","fetch_graph":"https://pith.science/api/pith-number/KQLRX72XFDPVUMWMKV7CHMKW3T/graph.json","fetch_events":"https://pith.science/api/pith-number/KQLRX72XFDPVUMWMKV7CHMKW3T/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KQLRX72XFDPVUMWMKV7CHMKW3T/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KQLRX72XFDPVUMWMKV7CHMKW3T/action/storage_attestation","attest_author":"https://pith.science/pith/KQLRX72XFDPVUMWMKV7CHMKW3T/action/author_attestation","sign_citation":"https://pith.science/pith/KQLRX72XFDPVUMWMKV7CHMKW3T/action/citation_signature","submit_replication":"https://pith.science/pith/KQLRX72XFDPVUMWMKV7CHMKW3T/action/replication_record"}},"created_at":"2026-07-05T02:14:07.618991+00:00","updated_at":"2026-07-05T02:14:07.618991+00:00"}