{"as_of":"2026-08-13T00:39:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:ab216c1af340b29dd94e9d3d2c323841a1f5e800028ee6208e24d9e90a42fd8d","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":8,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":8,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-12T06:34:41.77262+00:00","state":"measured"},{"denominator":8,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":8,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-12T19:47:53.950605Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"arxiv_reference","source_observed_at":"2026-07-03T06:17:42.548867Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2405.07312","last_updated":"2026-07-04T14:48:03Z","snapshot_observed_at":"2026-08-13T00:09:23.734900Z","submitted_at":"2024-05-12T15:46:52Z","title":"Nonparametric Control Koopman Operators","version":5},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2405.07312","snapshot_observed_at":"2026-08-12T19:47:53.950605Z","title":"Nonparametric control-Koopman operator learning: Flexible and scalable models for prediction and control.arXiv:2405.07312, 2024","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2411.10359","last_updated":"2025-08-08T07:26:24Z","snapshot_observed_at":"2026-08-12T19:40:01.092418Z","submitted_at":"2024-11-15T17:08:35Z","title":"Koopman-based control of nonlinear systems with closed-loop guarantees","version":4},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-12T19:47:53.950605Z"},"links":{"cited_paper":"/paper/2405.07312","citing_paper":"/paper/2411.10359"},"observation_digest":"sha256:3e7beb650f890f61611204e169efc87debc0050de4e025c301983675faeca091","observation_id":"f4b4adcd-b1f7-4ca1-a38e-04175c94e33c","resolution":{"observed_at":"2026-08-12T19:47:53.950605Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2405.07312","last_updated":"2026-07-04T14:48:03Z","snapshot_observed_at":"2026-08-13T00:09:23.734900Z","submitted_at":"2024-05-12T15:46:52Z","title":"Nonparametric Control Koopman Operators","version":5},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2405.07312","snapshot_observed_at":"2026-08-12T04:25:33.612930Z","title":"Nonparametric Control Koopman Operators","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2412.01591","last_updated":"2025-04-25T13:50:41Z","snapshot_observed_at":"2026-08-12T13:49:24.953884Z","submitted_at":"2024-12-02T15:08:55Z","title":"Kernel-Based Optimal Control: An Infinitesimal Generator Approach","version":3},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-08-12T04:25:33.612930Z"},"links":{"cited_paper":"/paper/2405.07312","citing_paper":"/paper/2412.01591"},"observation_digest":"sha256:60e384c0e2de9f11e4953323c7f1241400b8de1acfcc7a118901452d5af40a08","observation_id":"8cfa4685-6b16-4176-906d-498c96e9cc41","resolution":{"observed_at":"2026-08-12T04:25:33.612930Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2405.07312","last_updated":"2026-07-04T14:48:03Z","snapshot_observed_at":"2026-08-13T00:09:23.734900Z","submitted_at":"2024-05-12T15:46:52Z","title":"Nonparametric Control Koopman Operators","version":5},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2405.07312","snapshot_observed_at":"2026-08-10T20:27:21.798599Z","title":"Non- parametric control-Koopman operator learning: Flexible and scalable models for prediction and control","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2501.08709","last_updated":"2025-03-14T09:29:19Z","snapshot_observed_at":"2026-08-12T11:41:15.754236Z","submitted_at":"2025-01-15T10:50:47Z","title":"Kernel EDMD for data-driven nonlinear Koopman MPC with stability guarantees","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-10T20:27:21.798599Z"},"links":{"cited_paper":"/paper/2405.07312","citing_paper":"/paper/2501.08709"},"observation_digest":"sha256:db40dd03251e3197214f0be864a3a1d436acb95f215caad3b668302f3f5085c9","observation_id":"46533042-82dc-40bf-ba36-29820c5a2822","resolution":{"observed_at":"2026-08-10T20:27:21.798599Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2405.07312","last_updated":"2026-07-04T14:48:03Z","snapshot_observed_at":"2026-08-13T00:09:23.734900Z","submitted_at":"2024-05-12T15:46:52Z","title":"Nonparametric Control Koopman Operators","version":5},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2405.07312","snapshot_observed_at":"2026-08-06T15:53:08.801433Z","title":"Bevanda, B","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2507.15093","last_updated":"2025-07-20T19:18:17Z","snapshot_observed_at":"2026-08-07T13:24:58.342953Z","submitted_at":"2025-07-20T19:18:17Z","title":"Exact Finite Koopman Embedding of Block-Oriented Polynomial Systems","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-06T15:53:08.801433Z"},"links":{"cited_paper":"/paper/2405.07312","citing_paper":"/paper/2507.15093"},"observation_digest":"sha256:9e0c4130c1941d2a3b41c90804cfe635bf5c18d38c253305fc0a6f0945c920d6","observation_id":"de79a34e-7f20-4942-911f-769bbb7ceb04","resolution":{"observed_at":"2026-08-06T15:53:08.801433Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2405.07312","last_updated":"2026-07-04T14:48:03Z","snapshot_observed_at":"2026-08-13T00:09:23.734900Z","submitted_at":"2024-05-12T15:46:52Z","title":"Nonparametric Control Koopman Operators","version":5},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2405.07312","snapshot_observed_at":"2026-08-03T23:28:48.518131Z","title":"Nonparametric control Koopman operators.arXiv preprint arXiv:2405.07312,","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2511.06063","last_updated":"2026-07-27T12:20:31Z","snapshot_observed_at":"2026-08-07T02:47:20.798739Z","submitted_at":"2025-11-08T16:15:22Z","title":"Koopman Operator for Stability Analysis: Theory with a Linear--Radial Product Reproducing Kernel","version":2},"reference_index":2023,"source":"pdf_text","source_observed_at":"2026-08-03T23:28:48.518131Z"},"links":{"cited_paper":"/paper/2405.07312","citing_paper":"/paper/2511.06063"},"observation_digest":"sha256:201172f73797adc5702dd9346b47a56003a4ef65548f5b92eb920218265789f1","observation_id":"42c4da99-14bc-4416-8ec7-2574a6552dfe","resolution":{"observed_at":"2026-08-03T23:28:48.518131Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2405.07312","last_updated":"2026-07-04T14:48:03Z","snapshot_observed_at":"2026-08-13T00:09:23.734900Z","submitted_at":"2024-05-12T15:46:52Z","title":"Nonparametric Control Koopman Operators","version":5},"cited_work":{"arxiv_id":"2405.07312","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2405.07312","snapshot_observed_at":"2026-07-07T02:17:03.462656Z","title":"Nonparametric control Koopman operators","venue":null,"work_id":"74b3389e-7687-4971-b1d8-ed9dd559645c","year":2024},"citing_paper":{"arxiv_id":"2604.09267","last_updated":"2026-04-10T12:33:21Z","snapshot_observed_at":"2026-07-06T22:58:12.847181Z","submitted_at":"2026-04-10T12:33:21Z","title":"On the Existence of Quadratic Control Lyapunov Functions for Koopman-Operator based Bilinear Systems","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-05-10T18:14:59.681330Z"},"links":{"cited_paper":"/paper/2405.07312","citing_paper":"/paper/2604.09267"},"observation_digest":"sha256:8fbac9ae100882238c81865cfe744b43749ca735b92a2954d66fd9bd7ff07e00","observation_id":"72055baa-953c-46a4-833d-ed7d9fc2c37a","resolution":{"observed_at":"2026-07-07T02:17:03.462656Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2405.07312","last_updated":"2026-07-04T14:48:03Z","snapshot_observed_at":"2026-08-13T00:09:23.734900Z","submitted_at":"2024-05-12T15:46:52Z","title":"Nonparametric Control Koopman Operators","version":5},"cited_work":{"arxiv_id":"2405.07312","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2405.07312","snapshot_observed_at":"2026-07-07T02:17:03.462656Z","title":"Nonparametric control Koopman operators","venue":null,"work_id":"74b3389e-7687-4971-b1d8-ed9dd559645c","year":2024},"citing_paper":{"arxiv_id":"2606.10344","last_updated":"2026-06-09T02:53:47Z","snapshot_observed_at":"2026-08-09T16:23:36.477423Z","submitted_at":"2026-06-09T02:53:47Z","title":"Koopman Modeling and Stabilization of Discrete-Time Nonlinear Control Systems: Bilinearity on a Reproducing Kernel Hilbert Space","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-06-27T12:42:40.577718Z"},"links":{"cited_paper":"/paper/2405.07312","citing_paper":"/paper/2606.10344"},"observation_digest":"sha256:cf3ba94544630dd80f09308fdc2d8f09f362cd9845596d2b97166550322fde16","observation_id":"82441a28-afe9-4f8f-afd5-6e2eeb9c6e3f","resolution":{"observed_at":"2026-07-07T02:17:03.462656Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2405.07312","last_updated":"2026-07-04T14:48:03Z","snapshot_observed_at":"2026-08-13T00:09:23.734900Z","submitted_at":"2024-05-12T15:46:52Z","title":"Nonparametric Control Koopman Operators","version":5},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2405.07312","snapshot_observed_at":"2026-08-06T00:52:39.964512Z","title":"Nonparametric control Koopman operators,","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2608.01018","last_updated":"2026-08-09T05:36:34Z","snapshot_observed_at":"2026-08-13T00:12:34.836586Z","submitted_at":"2026-08-02T05:51:13Z","title":"Data-Driven Domain of Attraction Estimation via Convergent Koopman-Zubov Approximation","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-06T00:52:39.964512Z"},"links":{"cited_paper":"/paper/2405.07312","citing_paper":"/paper/2608.01018"},"observation_digest":"sha256:be3d8eab4f048f7f56a0727cdf2431abbe02fdced7a0281139cfa766a5beeb94","observation_id":"8dd921b3-8cd2-4b7d-b3f2-3ca4269d2737","resolution":{"observed_at":"2026-08-06T00:52:39.964512Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2405.07312/citation-record","integrity":"/paper/2405.07312/integrity","json":"/paper/2405.07312/citation-record.json","paper":"/paper/2405.07312"},"outbound":[],"paper":{"arxiv_id":"2405.07312","last_updated":"2026-07-04T14:48:03Z","latest_version":5,"primary_category":"eess.SY","snapshot_observed_at":"2026-08-13T00:09:23.734900Z","submitted_at":"2024-05-12T15:46:52Z","title":"Nonparametric Control Koopman Operators"},"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":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"thesis":"As of 13 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 8 inbound Pith citation observations for arXiv:2405.07312."}