{"as_of":"2026-08-16T21:08:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:820090504f2e0fd6185473f5271cb2feb4a278316039a703c6eee9b268521340","coverage":[{"denominator":0,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":18,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":18,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-16T06:30:59.297886+00:00","state":"measured"},{"denominator":18,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":18,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-04T23:15:50.534885Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":1,"source":"doi_reference","source_observed_at":"2026-07-09T21:16:33.953460Z","state":"measured"}],"external_citation_measurements":[{"count":1732,"observed_at":"2026-07-09T21:16:33.953460Z","source":"doi_reference"}],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"1408.4408","last_updated":"2014-08-19T17:41:20Z","snapshot_observed_at":"2026-08-16T04:01:54.125514Z","submitted_at":"2014-08-19T17:41:20Z","title":"A Data-Driven Approximation of the Koopman Operator: Extending Dynamic Mode Decomposition","version":1},"cited_work":{"arxiv_id":"1408.4408","doi":"10.1007/s00332-015-9258-5","metadata_source":"doi_reference","pith_arxiv_id":"1408.4408","snapshot_observed_at":"2026-07-11T11:50:26.030339Z","title":"and Kevrekidis, Ioannis G","venue":"Journal of Nonlinear Science","work_id":"646860c2-8baf-4ff3-aed5-77f931d8f7e5","year":2015},"citing_paper":{"arxiv_id":"2407.11107","last_updated":"2026-04-21T14:49:07Z","snapshot_observed_at":"2026-07-06T18:46:43.829115Z","submitted_at":"2024-07-15T15:22:52Z","title":"Latent Linear Quadratic Regulator for Robotic Control Tasks","version":3},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-05-23T22:46:28.280885Z"},"links":{"cited_paper":"/paper/1408.4408","citing_paper":"/paper/2407.11107"},"observation_digest":"sha256:dc7173987fb8bd58ad553b1b62d67370ea24cecf89b022eb6637cb171d4612f6","observation_id":"5d86969d-75a5-4f17-932e-0dbb5d97aa27","resolution":{"observed_at":"2026-07-04T20:29:39.197368Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-03T18:38:35.750465+00:00","source":"crossref_status_cache"},{"observed_at":"2026-08-03T18:38:35.750465+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1408.4408","last_updated":"2014-08-19T17:41:20Z","snapshot_observed_at":"2026-08-16T04:01:54.125514Z","submitted_at":"2014-08-19T17:41:20Z","title":"A Data-Driven Approximation of the Koopman Operator: Extending Dynamic Mode Decomposition","version":1},"cited_work":{"arxiv_id":"1408.4408","doi":"10.1007/s00332-015-9258-5","metadata_source":"doi_reference","pith_arxiv_id":"1408.4408","snapshot_observed_at":"2026-07-11T11:50:26.030339Z","title":"and Kevrekidis, Ioannis G","venue":"Journal of Nonlinear Science","work_id":"646860c2-8baf-4ff3-aed5-77f931d8f7e5","year":2015},"citing_paper":{"arxiv_id":"2507.12474","last_updated":"2026-05-11T00:56:11Z","snapshot_observed_at":"2026-08-14T10:54:15.820009Z","submitted_at":"2025-07-03T09:23:55Z","title":"Spatio-Temporal Prediction via Operator-Valued RKHS and Koopman Approximation","version":2},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-05-19T07:04:08.231838Z"},"links":{"cited_paper":"/paper/1408.4408","citing_paper":"/paper/2507.12474"},"observation_digest":"sha256:1012574c183d5b7ad9c1a229cc853dd178cdd5127d3b1ce1c6c2f35ffd729215","observation_id":"13e181f7-711f-4093-910c-641457a59180","resolution":{"observed_at":"2026-07-04T20:29:39.197368Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-03T18:38:35.750465+00:00","source":"crossref_status_cache"},{"observed_at":"2026-08-03T18:38:35.750465+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1408.4408","last_updated":"2014-08-19T17:41:20Z","snapshot_observed_at":"2026-08-16T04:01:54.125514Z","submitted_at":"2014-08-19T17:41:20Z","title":"A Data-Driven Approximation of the Koopman Operator: Extending Dynamic Mode Decomposition","version":1},"cited_work":{"arxiv_id":"1408.4408","doi":"10.1007/s00332-015-9258-5","metadata_source":"doi_reference","pith_arxiv_id":"1408.4408","snapshot_observed_at":"2026-07-11T11:50:26.030339Z","title":"and Kevrekidis, Ioannis G","venue":"Journal of Nonlinear Science","work_id":"646860c2-8baf-4ff3-aed5-77f931d8f7e5","year":2015},"citing_paper":{"arxiv_id":"2507.18147","last_updated":"2026-04-08T12:01:23Z","snapshot_observed_at":"2026-08-15T08:57:32.889315Z","submitted_at":"2025-07-24T07:29:03Z","title":"Learning graphons from data: Random walks, transfer operators, and spectral clustering","version":2},"reference_index":54,"source":"pdf_text","source_observed_at":"2026-05-19T03:11:28.081455Z"},"links":{"cited_paper":"/paper/1408.4408","citing_paper":"/paper/2507.18147"},"observation_digest":"sha256:b3052dadc29c87a37aaad860eaa5a7b9443faacaa5ebfdddb7bfac0597f106d9","observation_id":"9fd9d579-711f-4107-82a6-b72c4ab5a1f3","resolution":{"observed_at":"2026-07-04T20:29:39.197368Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-03T18:38:35.750465+00:00","source":"crossref_status_cache"},{"observed_at":"2026-08-03T18:38:35.750465+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1408.4408","last_updated":"2014-08-19T17:41:20Z","snapshot_observed_at":"2026-08-16T04:01:54.125514Z","submitted_at":"2014-08-19T17:41:20Z","title":"A Data-Driven Approximation of the Koopman Operator: Extending Dynamic Mode Decomposition","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1408.4408","snapshot_observed_at":"2026-08-04T23:15:50.534885Z","title":null,"venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2509.06735","last_updated":"2026-07-02T13:50:00Z","snapshot_observed_at":"2026-08-16T13:33:14.054263Z","submitted_at":"2025-09-08T14:28:23Z","title":"Data-driven discovery of dynamical models in biology","version":2},"reference_index":116,"source":"pdf_text","source_observed_at":"2026-08-04T23:15:50.534885Z"},"links":{"cited_paper":"/paper/1408.4408","citing_paper":"/paper/2509.06735"},"observation_digest":"sha256:a0a34e96f4939f8ae481ce90c3f4f680476ba946334ca94c6b9fd80f2a2a9574","observation_id":"ad85b240-cb09-4b29-a351-54e8b21c391c","resolution":{"observed_at":"2026-08-04T23:15:50.534885Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1408.4408","last_updated":"2014-08-19T17:41:20Z","snapshot_observed_at":"2026-08-16T04:01:54.125514Z","submitted_at":"2014-08-19T17:41:20Z","title":"A Data-Driven Approximation of the Koopman Operator: Extending Dynamic Mode Decomposition","version":1},"cited_work":{"arxiv_id":"1408.4408","doi":"10.1007/s00332-015-9258-5","metadata_source":"doi_reference","pith_arxiv_id":"1408.4408","snapshot_observed_at":"2026-07-11T11:50:26.030339Z","title":"and Kevrekidis, Ioannis G","venue":"Journal of Nonlinear Science","work_id":"646860c2-8baf-4ff3-aed5-77f931d8f7e5","year":2015},"citing_paper":{"arxiv_id":"2604.08414","last_updated":"2026-04-09T16:12:34Z","snapshot_observed_at":"2026-08-16T05:38:51.934951Z","submitted_at":"2026-04-09T16:12:34Z","title":"Numerical approximation of the Koopman-von Neumann equation: Operator learning and quantum computing","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-05-10T17:23:46.750399Z"},"links":{"cited_paper":"/paper/1408.4408","citing_paper":"/paper/2604.08414"},"observation_digest":"sha256:ed6f9c775c98b0ab66d5019c856ee0b010150fc3518d7d643ed509027303e1d4","observation_id":"fe67a738-a9ac-4cc9-8c97-dff321410fda","resolution":{"observed_at":"2026-07-04T20:29:39.197368Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-03T18:38:35.750465+00:00","source":"crossref_status_cache"},{"observed_at":"2026-08-03T18:38:35.750465+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1408.4408","last_updated":"2014-08-19T17:41:20Z","snapshot_observed_at":"2026-08-16T04:01:54.125514Z","submitted_at":"2014-08-19T17:41:20Z","title":"A Data-Driven Approximation of the Koopman Operator: Extending Dynamic Mode Decomposition","version":1},"cited_work":{"arxiv_id":"1408.4408","doi":"10.1007/s00332-015-9258-5","metadata_source":"doi_reference","pith_arxiv_id":"1408.4408","snapshot_observed_at":"2026-07-11T11:50:26.030339Z","title":"and Kevrekidis, Ioannis G","venue":"Journal of Nonlinear Science","work_id":"646860c2-8baf-4ff3-aed5-77f931d8f7e5","year":2015},"citing_paper":{"arxiv_id":"2604.23952","last_updated":"2026-04-27T01:58:16Z","snapshot_observed_at":"2026-08-03T10:50:28.048168Z","submitted_at":"2026-04-27T01:58:16Z","title":"Conditional Score-Based Modeling of Effective Langevin Dynamics","version":1},"reference_index":64,"source":"pdf_text","source_observed_at":"2026-05-08T01:20:34.912358Z"},"links":{"cited_paper":"/paper/1408.4408","citing_paper":"/paper/2604.23952"},"observation_digest":"sha256:628e6c7a6d43dae2043b96d833d909fa74f08bb4bc7bda01c71040339367d8fd","observation_id":"4ed1a1f5-3363-4a95-9af8-5ca893aea383","resolution":{"observed_at":"2026-07-04T20:29:39.197368Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-03T18:38:35.750465+00:00","source":"crossref_status_cache"},{"observed_at":"2026-08-03T18:38:35.750465+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1408.4408","last_updated":"2014-08-19T17:41:20Z","snapshot_observed_at":"2026-08-16T04:01:54.125514Z","submitted_at":"2014-08-19T17:41:20Z","title":"A Data-Driven Approximation of the Koopman Operator: Extending Dynamic Mode Decomposition","version":1},"cited_work":{"arxiv_id":"1408.4408","doi":"10.1007/s00332-015-9258-5","metadata_source":"doi_reference","pith_arxiv_id":"1408.4408","snapshot_observed_at":"2026-07-11T11:50:26.030339Z","title":"and Kevrekidis, Ioannis G","venue":"Journal of Nonlinear Science","work_id":"646860c2-8baf-4ff3-aed5-77f931d8f7e5","year":2015},"citing_paper":{"arxiv_id":"2604.26933","last_updated":"2026-04-29T17:47:19Z","snapshot_observed_at":"2026-08-11T17:01:06.677630Z","submitted_at":"2026-04-29T17:47:19Z","title":"Data-driven discovery of polynomial ODEs with provably bounded solutions","version":1},"reference_index":62,"source":"pdf_text","source_observed_at":"2026-05-07T09:26:56.733873Z"},"links":{"cited_paper":"/paper/1408.4408","citing_paper":"/paper/2604.26933"},"observation_digest":"sha256:f9b0f8316279b58a96cdf57f7c6b5c2bba03a7d3b927b222e476219f0c3cae53","observation_id":"a06fe4d1-842a-4600-ae75-41f4e5d8dcd9","resolution":{"observed_at":"2026-07-04T20:29:39.197368Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-03T18:38:35.750465+00:00","source":"crossref_status_cache"},{"observed_at":"2026-08-03T18:38:35.750465+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1408.4408","last_updated":"2014-08-19T17:41:20Z","snapshot_observed_at":"2026-08-16T04:01:54.125514Z","submitted_at":"2014-08-19T17:41:20Z","title":"A Data-Driven Approximation of the Koopman Operator: Extending Dynamic Mode Decomposition","version":1},"cited_work":{"arxiv_id":"1408.4408","doi":"10.1007/s00332-015-9258-5","metadata_source":"doi_reference","pith_arxiv_id":"1408.4408","snapshot_observed_at":"2026-07-11T11:50:26.030339Z","title":"and Kevrekidis, Ioannis G","venue":"Journal of Nonlinear Science","work_id":"646860c2-8baf-4ff3-aed5-77f931d8f7e5","year":2015},"citing_paper":{"arxiv_id":"2605.01803","last_updated":"2026-05-03T09:58:20Z","snapshot_observed_at":"2026-08-14T10:54:16.264017Z","submitted_at":"2026-05-03T09:58:20Z","title":"Koopman Representations for Early Outbreak Warning and Minimal Counterfactual Intervention in Multi-Agent Epidemic Simulations","version":1},"reference_index":31,"source":"arxiv_source","source_observed_at":"2026-05-09T16:31:35.560051Z"},"links":{"cited_paper":"/paper/1408.4408","citing_paper":"/paper/2605.01803"},"observation_digest":"sha256:2090a06e843d0ab4e16934cce6efbedcb17f3c167895c3c567876b219bd1f44f","observation_id":"1b6c8421-7e26-4f6f-9843-1b8b661b6299","resolution":{"observed_at":"2026-07-04T20:29:39.197368Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-03T18:38:35.750465+00:00","source":"crossref_status_cache"},{"observed_at":"2026-08-03T18:38:35.750465+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1408.4408","last_updated":"2014-08-19T17:41:20Z","snapshot_observed_at":"2026-08-16T04:01:54.125514Z","submitted_at":"2014-08-19T17:41:20Z","title":"A Data-Driven Approximation of the Koopman Operator: Extending Dynamic Mode Decomposition","version":1},"cited_work":{"arxiv_id":"1408.4408","doi":"10.1007/s00332-015-9258-5","metadata_source":"doi_reference","pith_arxiv_id":"1408.4408","snapshot_observed_at":"2026-07-11T11:50:26.030339Z","title":"and Kevrekidis, Ioannis G","venue":"Journal of Nonlinear Science","work_id":"646860c2-8baf-4ff3-aed5-77f931d8f7e5","year":2015},"citing_paper":{"arxiv_id":"2605.06000","last_updated":"2026-05-07T10:51:47Z","snapshot_observed_at":"2026-08-11T05:55:30.896711Z","submitted_at":"2026-05-07T10:51:47Z","title":"Deep-Koopman-KANDy: Dictionary Discovery for Deep-Koopman Operators with Kolmogorov-Arnold Networks for Dynamics","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-05-08T04:33:37.095528Z"},"links":{"cited_paper":"/paper/1408.4408","citing_paper":"/paper/2605.06000"},"observation_digest":"sha256:7bcb071a8a6404a2563d040a1956da251b11efd555db5c12d3b189a9a535137b","observation_id":"1615cd4d-cfd4-4d00-a80b-086eee66cb33","resolution":{"observed_at":"2026-07-04T20:29:39.197368Z","resolver_source":"doi","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-03T18:38:35.750465+00:00","source":"crossref_status_cache"},{"observed_at":"2026-08-03T18:38:35.750465+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1408.4408","last_updated":"2014-08-19T17:41:20Z","snapshot_observed_at":"2026-08-16T04:01:54.125514Z","submitted_at":"2014-08-19T17:41:20Z","title":"A Data-Driven Approximation of the Koopman Operator: Extending Dynamic Mode Decomposition","version":1},"cited_work":{"arxiv_id":"1408.4408","doi":"10.1007/s00332-015-9258-5","metadata_source":"doi_reference","pith_arxiv_id":"1408.4408","snapshot_observed_at":"2026-07-11T11:50:26.030339Z","title":"and Kevrekidis, Ioannis G","venue":"Journal of Nonlinear Science","work_id":"646860c2-8baf-4ff3-aed5-77f931d8f7e5","year":2015},"citing_paper":{"arxiv_id":"2605.08856","last_updated":"2026-05-15T09:57:10Z","snapshot_observed_at":"2026-08-14T11:05:19.842879Z","submitted_at":"2026-05-09T10:10:30Z","title":"Controlling Transient Amplification Improves Long-horizon Rollouts","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-05-12T01:34:35.242342Z"},"links":{"cited_paper":"/paper/1408.4408","citing_paper":"/paper/2605.08856"},"observation_digest":"sha256:569e1e86ab0c96bdccf4a9f224099142cfe1af7b2e01d500cf93f818650ff651","observation_id":"03c764ba-7ac6-4afb-be72-e8974179c0c8","resolution":{"observed_at":"2026-07-04T20:29:39.197368Z","resolver_source":"doi","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-03T18:38:35.750465+00:00","source":"crossref_status_cache"},{"observed_at":"2026-08-03T18:38:35.750465+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1408.4408","last_updated":"2014-08-19T17:41:20Z","snapshot_observed_at":"2026-08-16T04:01:54.125514Z","submitted_at":"2014-08-19T17:41:20Z","title":"A Data-Driven Approximation of the Koopman Operator: Extending Dynamic Mode Decomposition","version":1},"cited_work":{"arxiv_id":"1408.4408","doi":"10.1007/s00332-015-9258-5","metadata_source":"doi_reference","pith_arxiv_id":"1408.4408","snapshot_observed_at":"2026-07-11T11:50:26.030339Z","title":"and Kevrekidis, Ioannis G","venue":"Journal of Nonlinear Science","work_id":"646860c2-8baf-4ff3-aed5-77f931d8f7e5","year":2015},"citing_paper":{"arxiv_id":"2605.08856","last_updated":"2026-05-15T09:57:10Z","snapshot_observed_at":"2026-08-14T11:05:19.842879Z","submitted_at":"2026-05-09T10:10:30Z","title":"Controlling Transient Amplification Improves Long-horizon Rollouts","version":2},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-05-19T17:43:58.827806Z"},"links":{"cited_paper":"/paper/1408.4408","citing_paper":"/paper/2605.08856"},"observation_digest":"sha256:91e7565bdd5fb07180d954fb826373aa3a99a5fc1c6d2d62d545657d7b6d3a5a","observation_id":"186a8ade-b01b-4e8a-afc1-4e0b5ce33a56","resolution":{"observed_at":"2026-07-04T20:29:39.197368Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-03T18:38:35.750465+00:00","source":"crossref_status_cache"},{"observed_at":"2026-08-03T18:38:35.750465+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1408.4408","last_updated":"2014-08-19T17:41:20Z","snapshot_observed_at":"2026-08-16T04:01:54.125514Z","submitted_at":"2014-08-19T17:41:20Z","title":"A Data-Driven Approximation of the Koopman Operator: Extending Dynamic Mode Decomposition","version":1},"cited_work":{"arxiv_id":"1408.4408","doi":"10.1007/s00332-015-9258-5","metadata_source":"doi_reference","pith_arxiv_id":"1408.4408","snapshot_observed_at":"2026-07-11T11:50:26.030339Z","title":"and Kevrekidis, Ioannis G","venue":"Journal of Nonlinear Science","work_id":"646860c2-8baf-4ff3-aed5-77f931d8f7e5","year":2015},"citing_paper":{"arxiv_id":"2605.09545","last_updated":"2026-05-10T14:01:05Z","snapshot_observed_at":"2026-07-06T23:21:39.966502Z","submitted_at":"2026-05-10T14:01:05Z","title":"Diagnostic Certificates of Data Quality and Regression Identifiability for Koopman Identification","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-05-12T04:16:06.658166Z"},"links":{"cited_paper":"/paper/1408.4408","citing_paper":"/paper/2605.09545"},"observation_digest":"sha256:ffaa110bd4df3e0b2c5997b672cea9d2453b0685d4142de852cc54b3e89b04ae","observation_id":"ac3aabfd-2adf-4935-84c5-e6619d12cfb8","resolution":{"observed_at":"2026-07-04T20:29:39.197368Z","resolver_source":"doi","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-03T18:38:35.750465+00:00","source":"crossref_status_cache"},{"observed_at":"2026-08-03T18:38:35.750465+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1408.4408","last_updated":"2014-08-19T17:41:20Z","snapshot_observed_at":"2026-08-16T04:01:54.125514Z","submitted_at":"2014-08-19T17:41:20Z","title":"A Data-Driven Approximation of the Koopman Operator: Extending Dynamic Mode Decomposition","version":1},"cited_work":{"arxiv_id":"1408.4408","doi":"10.1007/s00332-015-9258-5","metadata_source":"doi_reference","pith_arxiv_id":"1408.4408","snapshot_observed_at":"2026-07-11T11:50:26.030339Z","title":"and Kevrekidis, Ioannis G","venue":"Journal of Nonlinear Science","work_id":"646860c2-8baf-4ff3-aed5-77f931d8f7e5","year":2015},"citing_paper":{"arxiv_id":"2605.16574","last_updated":"2026-07-15T23:32:59Z","snapshot_observed_at":"2026-08-16T09:18:07.378245Z","submitted_at":"2026-05-15T19:25:01Z","title":"Data-driven analysis of metastability in a stochastic bistable system","version":1},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-05-19T20:54:37.190512Z"},"links":{"cited_paper":"/paper/1408.4408","citing_paper":"/paper/2605.16574"},"observation_digest":"sha256:7d46b77c07cdd0b6cd6a7d63c22723a61f5fc62ca1881799f1e7f9e6213d4e99","observation_id":"8e1a6773-6279-44b7-b84d-617f60fb106b","resolution":{"observed_at":"2026-07-04T20:29:39.197368Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-03T18:38:35.750465+00:00","source":"crossref_status_cache"},{"observed_at":"2026-08-03T18:38:35.750465+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1408.4408","last_updated":"2014-08-19T17:41:20Z","snapshot_observed_at":"2026-08-16T04:01:54.125514Z","submitted_at":"2014-08-19T17:41:20Z","title":"A Data-Driven Approximation of the Koopman Operator: Extending Dynamic Mode Decomposition","version":1},"cited_work":{"arxiv_id":"1408.4408","doi":"10.1007/s00332-015-9258-5","metadata_source":"doi_reference","pith_arxiv_id":"1408.4408","snapshot_observed_at":"2026-07-11T11:50:26.030339Z","title":"and Kevrekidis, Ioannis G","venue":"Journal of Nonlinear Science","work_id":"646860c2-8baf-4ff3-aed5-77f931d8f7e5","year":2015},"citing_paper":{"arxiv_id":"2605.23689","last_updated":"2026-05-22T14:47:17Z","snapshot_observed_at":"2026-08-16T04:01:37.690096Z","submitted_at":"2026-05-22T14:47:17Z","title":"Optimization of randomized neural networks for transfer operator approximation","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-05-25T05:09:03.516584Z"},"links":{"cited_paper":"/paper/1408.4408","citing_paper":"/paper/2605.23689"},"observation_digest":"sha256:a4278e646d8016526399bf6ce9ab58322607719ae0aaa5c751687177498a8def","observation_id":"fcf083da-89ea-410c-84b2-72c0f634f274","resolution":{"observed_at":"2026-07-04T20:29:39.197368Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-03T18:38:35.750465+00:00","source":"crossref_status_cache"},{"observed_at":"2026-08-03T18:38:35.750465+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1408.4408","last_updated":"2014-08-19T17:41:20Z","snapshot_observed_at":"2026-08-16T04:01:54.125514Z","submitted_at":"2014-08-19T17:41:20Z","title":"A Data-Driven Approximation of the Koopman Operator: Extending Dynamic Mode Decomposition","version":1},"cited_work":{"arxiv_id":"1408.4408","doi":"10.1007/s00332-015-9258-5","metadata_source":"doi_reference","pith_arxiv_id":"1408.4408","snapshot_observed_at":"2026-07-11T11:50:26.030339Z","title":"and Kevrekidis, Ioannis G","venue":"Journal of Nonlinear Science","work_id":"646860c2-8baf-4ff3-aed5-77f931d8f7e5","year":2015},"citing_paper":{"arxiv_id":"2606.06728","last_updated":"2026-06-17T03:10:16Z","snapshot_observed_at":"2026-08-13T02:29:53.272629Z","submitted_at":"2026-06-04T21:25:28Z","title":"Data-driven methods for computation of optimal linear response in high-dimensional dynamical systems","version":2},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-06-27T23:03:28.524079Z"},"links":{"cited_paper":"/paper/1408.4408","citing_paper":"/paper/2606.06728"},"observation_digest":"sha256:aa75d0f130429a8739de701849bddd8b0c9a6f15cff2b8a56b18320816788b0e","observation_id":"9cc77056-4f4d-4618-94f2-6582b2a34e3e","resolution":{"observed_at":"2026-07-04T20:29:39.197368Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-03T18:38:35.750465+00:00","source":"crossref_status_cache"},{"observed_at":"2026-08-03T18:38:35.750465+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1408.4408","last_updated":"2014-08-19T17:41:20Z","snapshot_observed_at":"2026-08-16T04:01:54.125514Z","submitted_at":"2014-08-19T17:41:20Z","title":"A Data-Driven Approximation of the Koopman Operator: Extending Dynamic Mode Decomposition","version":1},"cited_work":{"arxiv_id":"1408.4408","doi":"10.1007/s00332-015-9258-5","metadata_source":"doi_reference","pith_arxiv_id":"1408.4408","snapshot_observed_at":"2026-07-11T11:50:26.030339Z","title":"and Kevrekidis, Ioannis G","venue":"Journal of Nonlinear Science","work_id":"646860c2-8baf-4ff3-aed5-77f931d8f7e5","year":2015},"citing_paper":{"arxiv_id":"2607.01746","last_updated":"2026-07-02T06:00:32Z","snapshot_observed_at":"2026-08-16T19:10:31.413029Z","submitted_at":"2026-07-02T06:00:32Z","title":"Finite-Lag Operator Geometry of Recurrent Representations","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-07-03T17:41:17.917727Z"},"links":{"cited_paper":"/paper/1408.4408","citing_paper":"/paper/2607.01746"},"observation_digest":"sha256:6332ad0f7e9f48c0e340817e88aa83bad0ffb6246e903267a4534f672cd5d97b","observation_id":"3b175745-8c1a-4382-9609-dc65e7646c28","resolution":{"observed_at":"2026-07-04T20:29:39.197368Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-03T18:38:35.750465+00:00","source":"crossref_status_cache"},{"observed_at":"2026-08-03T18:38:35.750465+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1408.4408","last_updated":"2014-08-19T17:41:20Z","snapshot_observed_at":"2026-08-16T04:01:54.125514Z","submitted_at":"2014-08-19T17:41:20Z","title":"A Data-Driven Approximation of the Koopman Operator: Extending Dynamic Mode Decomposition","version":1},"cited_work":{"arxiv_id":"1408.4408","doi":"10.1007/s00332-015-9258-5","metadata_source":"doi_reference","pith_arxiv_id":"1408.4408","snapshot_observed_at":"2026-07-11T11:50:26.030339Z","title":"and Kevrekidis, Ioannis G","venue":"Journal of Nonlinear Science","work_id":"646860c2-8baf-4ff3-aed5-77f931d8f7e5","year":2015},"citing_paper":{"arxiv_id":"2607.06459","last_updated":"2026-07-07T16:21:49Z","snapshot_observed_at":"2026-08-15T16:54:48.542151Z","submitted_at":"2026-07-07T16:21:49Z","title":"Input-to-State Stability Certification via Projection Residuals for Koopman Learning Control of Nonlinear Repetitive Systems","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-07-08T05:28:52.448484Z"},"links":{"cited_paper":"/paper/1408.4408","citing_paper":"/paper/2607.06459"},"observation_digest":"sha256:3707cdd670eaccf78dbf93d7002fdb116be520d2cee57379273932c3c98c193f","observation_id":"dadcd189-a608-46fc-a4c0-eb6328e7b644","resolution":{"observed_at":"2026-07-08T05:34:32.265434Z","resolver_source":"doi","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-03T18:38:35.750465+00:00","source":"crossref_status_cache"},{"observed_at":"2026-08-03T18:38:35.750465+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1408.4408","last_updated":"2014-08-19T17:41:20Z","snapshot_observed_at":"2026-08-16T04:01:54.125514Z","submitted_at":"2014-08-19T17:41:20Z","title":"A Data-Driven Approximation of the Koopman Operator: Extending Dynamic Mode Decomposition","version":1},"cited_work":{"arxiv_id":"1408.4408","doi":"10.1007/s00332-015-9258-5","metadata_source":"doi_reference","pith_arxiv_id":"1408.4408","snapshot_observed_at":"2026-07-11T11:50:26.030339Z","title":"and Kevrekidis, Ioannis G","venue":"Journal of Nonlinear Science","work_id":"646860c2-8baf-4ff3-aed5-77f931d8f7e5","year":2015},"citing_paper":{"arxiv_id":"2607.07043","last_updated":"2026-07-08T06:20:44Z","snapshot_observed_at":"2026-08-15T09:31:34.387689Z","submitted_at":"2026-07-08T06:20:44Z","title":"Probe-Conditioned Memory for Actuator-Deadband-Aware Koopman MPC in Industrial Sealing","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-07-09T21:14:28.636408Z"},"links":{"cited_paper":"/paper/1408.4408","citing_paper":"/paper/2607.07043"},"observation_digest":"sha256:cc08b94d5a1bf1c6dc30688ace5b417a43331a20584fb943a6384c24d42c6828","observation_id":"436fc08d-085c-431d-93b1-2fabfcbee7bf","resolution":{"observed_at":"2026-07-09T21:16:33.955244Z","resolver_source":"doi","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-03T18:38:35.750465+00:00","source":"crossref_status_cache"},{"observed_at":"2026-08-03T18:38:35.750465+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/1408.4408/citation-record","integrity":"/paper/1408.4408/integrity","json":"/paper/1408.4408/citation-record.json","paper":"/paper/1408.4408"},"outbound":[],"paper":{"arxiv_id":"1408.4408","last_updated":"2014-08-19T17:41:20Z","latest_version":1,"primary_category":"math.DS","snapshot_observed_at":"2026-08-16T04:01:54.125514Z","submitted_at":"2014-08-19T17:41:20Z","title":"A Data-Driven Approximation of the Koopman Operator: Extending Dynamic Mode Decomposition"},"reference_resolution":{"displayed":0,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":0,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":0},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"thesis":"As of 16 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 18 inbound Pith citation observations for arXiv:1408.4408."}