{"as_of":"2026-08-13T06:30:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:94e6908cd501a5b0ba4292605a89cd4a2dc9d1098d98955e1b177d7eb6ae1c45","coverage":[{"denominator":25,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":25,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-10T20:27:22.002340Z","state":"measured"},{"denominator":28,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":28,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-12T06:34:41.77262+00:00","state":"measured"},{"denominator":3,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":3,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T14:25:45.658684Z","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":"2026-05-17T05:19:04.598689Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2501.08709","last_updated":"2025-03-14T09:29:19Z","snapshot_observed_at":"2026-08-13T02:50:54.334334Z","submitted_at":"2025-01-15T10:50:47Z","title":"Kernel EDMD for data-driven nonlinear Koopman MPC with stability guarantees","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2501.08709","snapshot_observed_at":"2026-08-07T14:25:45.658684Z","title":"Kernel EDMD for data-driven nonlinear Koopman MPC with stability guaran- tees","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2505.19131","last_updated":"2025-05-25T12:58:28Z","snapshot_observed_at":"2026-08-13T04:12:06.189656Z","submitted_at":"2025-05-25T12:58:28Z","title":"Two-component controller design to safeguard data-driven predictive control","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-07T14:25:45.658684Z"},"links":{"cited_paper":"/paper/2501.08709","citing_paper":"/paper/2505.19131"},"observation_digest":"sha256:f10b8c6e0b915edf318c85a30c1a9690c43ec2ae09a56240c3a72381446cd18e","observation_id":"8154cd62-2df5-462c-b6d0-79184ddc3ca9","resolution":{"observed_at":"2026-08-07T14:25:45.658684Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2501.08709","last_updated":"2025-03-14T09:29:19Z","snapshot_observed_at":"2026-08-13T02:50:54.334334Z","submitted_at":"2025-01-15T10:50:47Z","title":"Kernel EDMD for data-driven nonlinear Koopman MPC with stability guarantees","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2501.08709","snapshot_observed_at":"2026-08-06T20:31:41.244763Z","title":"Kernel EDMD for data-driven nonlinear Koopman MPC with stability guarantees,","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2507.02549","last_updated":"2025-07-03T11:47:45Z","snapshot_observed_at":"2026-08-12T11:41:34.579248Z","submitted_at":"2025-07-03T11:47:45Z","title":"A Data-Driven Prescribed-Time Control Framework via Koopman Operator and Adaptive Backstepping","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-06T20:31:41.244763Z"},"links":{"cited_paper":"/paper/2501.08709","citing_paper":"/paper/2507.02549"},"observation_digest":"sha256:458ebf51dbf84e318db37c98e18b8319fe13935ee6e4e478113cdff605fa02d7","observation_id":"4b168b0a-e254-4012-94b5-a304722b1586","resolution":{"observed_at":"2026-08-06T20:31:41.244763Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2501.08709","last_updated":"2025-03-14T09:29:19Z","snapshot_observed_at":"2026-08-13T02:50:54.334334Z","submitted_at":"2025-01-15T10:50:47Z","title":"Kernel EDMD for data-driven nonlinear Koopman MPC with stability guarantees","version":2},"cited_work":{"arxiv_id":"2501.08709","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2501.08709","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Kernel EDMD for data-driven nonlinear Koopman MPC with stability guar- antees","venue":null,"work_id":"c1cb04c4-9db4-44e9-aeef-70d98893cef4","year":2025},"citing_paper":{"arxiv_id":"2511.21248","last_updated":"2026-04-10T10:50:40Z","snapshot_observed_at":"2026-08-02T12:02:09.190094Z","submitted_at":"2025-11-26T10:25:54Z","title":"Stability of data-driven Koopman MPC with terminal conditions","version":2},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-05-17T05:18:03.966880Z"},"links":{"cited_paper":"/paper/2501.08709","citing_paper":"/paper/2511.21248"},"observation_digest":"sha256:829ceada831eeca1fe2a70f1a17c6331487cdeb7bc9a6a0179048366f1f37af8","observation_id":"11a0235d-0318-40f8-a094-19b6db5b27d3","resolution":{"observed_at":"2026-05-17T05:19:04.600894Z","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"}}],"links":{"evidence":"/evidence","html":"/paper/2501.08709/citation-record","integrity":"/paper/2501.08709/integrity","json":"/paper/2501.08709/citation-record.json","paper":"/paper/2501.08709"},"outbound":[{"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":"2026-08-13T02:50:54.334334Z","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":"sha256:31e506fc50d101d6430ca1aaa21748f212abc27757efe255344d14a1d8873656","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":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T20:27:22.710161Z","title":"Stability and feasibility of state constrained MPC without stabilizing terminal constraints","venue":null,"work_id":"df620331-acf5-487c-a42a-78e8fad64171","year":2014},"citing_paper":{"arxiv_id":"2501.08709","last_updated":"2025-03-14T09:29:19Z","snapshot_observed_at":"2026-08-13T02:50:54.334334Z","submitted_at":"2025-01-15T10:50:47Z","title":"Kernel EDMD for data-driven nonlinear Koopman MPC with stability guarantees","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-10T20:27:21.805553Z"},"links":{"citing_paper":"/paper/2501.08709"},"observation_digest":"sha256:ae8dc50465684aaffe4aab2a9c83ca08ca4ce3b8f265fc74207f51222344b4fb","observation_id":"d224b2ce-3e7e-47c5-9e31-a510cac6ea7a","resolution":{"observed_at":"2026-08-10T20:27:22.716427Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T20:27:22.692279Z","title":"Data-driven MPC with stability guarantees using extended dynamic mode decomposition","venue":null,"work_id":"404f59a6-4da6-4d0b-83cd-7982390d2a20","year":2025},"citing_paper":{"arxiv_id":"2501.08709","last_updated":"2025-03-14T09:29:19Z","snapshot_observed_at":"2026-08-13T02:50:54.334334Z","submitted_at":"2025-01-15T10:50:47Z","title":"Kernel EDMD for data-driven nonlinear Koopman MPC with stability guarantees","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-10T20:27:21.811208Z"},"links":{"citing_paper":"/paper/2501.08709"},"observation_digest":"sha256:042d040f3011d493bfb86f052bbef2b8098a27bf031019a40c47eac26314e2d5","observation_id":"0a954e23-39a8-4128-b4b7-bbe0834fb85e","resolution":{"observed_at":"2026-08-10T20:27:22.697946Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T20:27:21.820889Z","title":"Kernel-based Koopman approximants for control: Flexible sampling, error analysis, and stability","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2501.08709","last_updated":"2025-03-14T09:29:19Z","snapshot_observed_at":"2026-08-13T02:50:54.334334Z","submitted_at":"2025-01-15T10:50:47Z","title":"Kernel EDMD for data-driven nonlinear Koopman MPC with stability guarantees","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-10T20:27:21.820889Z"},"links":{"citing_paper":"/paper/2501.08709"},"observation_digest":"sha256:228af4a9169ab09e1b8cbfab4aee736c45018f588c2da24d3e14ea7009e8e188","observation_id":"9e9085d8-d7f5-444b-8dc8-5c686b65d984","resolution":{"observed_at":"2026-08-10T20:27:21.820889Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T20:27:22.658992Z","title":"Fasshauer and Q","venue":null,"work_id":"e2a696f5-1b3f-47c2-9fae-c1a4d8246f25","year":2011},"citing_paper":{"arxiv_id":"2501.08709","last_updated":"2025-03-14T09:29:19Z","snapshot_observed_at":"2026-08-13T02:50:54.334334Z","submitted_at":"2025-01-15T10:50:47Z","title":"Kernel EDMD for data-driven nonlinear Koopman MPC with stability guarantees","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-10T20:27:21.837664Z"},"links":{"citing_paper":"/paper/2501.08709"},"observation_digest":"sha256:ba4a78b0a846e66a3e6dca43858753aa162cb03f70a1388cdd5a78512d0db6d4","observation_id":"2849642a-9900-4091-8ae4-9de21509caeb","resolution":{"observed_at":"2026-08-10T20:27:22.663638Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T20:27:22.641002Z","title":"Behavioral theory for stochastic systems? A data-driven journey from Willems to Wiener and back again","venue":null,"work_id":"4bd3933f-a91c-4cd8-9d3c-7925b835d50a","year":2023},"citing_paper":{"arxiv_id":"2501.08709","last_updated":"2025-03-14T09:29:19Z","snapshot_observed_at":"2026-08-13T02:50:54.334334Z","submitted_at":"2025-01-15T10:50:47Z","title":"Kernel EDMD for data-driven nonlinear Koopman MPC with stability guarantees","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-10T20:27:21.847133Z"},"links":{"citing_paper":"/paper/2501.08709"},"observation_digest":"sha256:ca22cc1dde3bea08a0ebf7e76b24226d5c2f1889807a18e7e5d75460b1632431","observation_id":"5ba62bdb-2cd3-41ec-8c30-d57acf89862c","resolution":{"observed_at":"2026-08-10T20:27:22.647133Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T20:27:22.620927Z","title":"Bilinearization, reachability, and optimal control of control-affine nonlinear systems: A Koopman spectral approach","venue":null,"work_id":"baf7ab25-ce78-4ed4-be3a-1bd7b57c3696","year":2021},"citing_paper":{"arxiv_id":"2501.08709","last_updated":"2025-03-14T09:29:19Z","snapshot_observed_at":"2026-08-13T02:50:54.334334Z","submitted_at":"2025-01-15T10:50:47Z","title":"Kernel EDMD for data-driven nonlinear Koopman MPC with stability guarantees","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-10T20:27:21.853312Z"},"links":{"citing_paper":"/paper/2501.08709"},"observation_digest":"sha256:fc882e54d8a5fe77d0a36dbe24a4c55dedfc564d4290803b99945ac0d3ecd5e0","observation_id":"2b58b48e-fcb5-44ed-a143-cdb0cc1f6903","resolution":{"observed_at":"2026-08-10T20:27:22.627641Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T20:27:22.603371Z","title":"Nominally robust model predictive control with state constraints","venue":null,"work_id":"8291739a-9c58-4f82-8985-b63e62abe553","year":2007},"citing_paper":{"arxiv_id":"2501.08709","last_updated":"2025-03-14T09:29:19Z","snapshot_observed_at":"2026-08-13T02:50:54.334334Z","submitted_at":"2025-01-15T10:50:47Z","title":"Kernel EDMD for data-driven nonlinear Koopman MPC with stability guarantees","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-10T20:27:21.859550Z"},"links":{"citing_paper":"/paper/2501.08709"},"observation_digest":"sha256:9356374d06fce9c378d6de5293fe536d38a3876852e1cf1ce7bcd271a2020fc4","observation_id":"b67cf321-1cf0-4f48-bd35-2c8ff6de0864","resolution":{"observed_at":"2026-08-10T20:27:22.609083Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T20:27:22.586101Z","title":"Nonlinear model predictive control","venue":null,"work_id":"54338472-cce9-4bf4-82d7-3d9f2870b704","year":2017},"citing_paper":{"arxiv_id":"2501.08709","last_updated":"2025-03-14T09:29:19Z","snapshot_observed_at":"2026-08-13T02:50:54.334334Z","submitted_at":"2025-01-15T10:50:47Z","title":"Kernel EDMD for data-driven nonlinear Koopman MPC with stability guarantees","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-10T20:27:21.867167Z"},"links":{"citing_paper":"/paper/2501.08709"},"observation_digest":"sha256:6cd3886d6df5f01ec67a4cd8bac520653350b7d44188c60ab2e1e2731c59e30d","observation_id":"66c40df7-9708-452d-b037-a4d8745fe6b3","resolution":{"observed_at":"2026-08-10T20:27:22.591332Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T20:27:22.544288Z","title":"Analysis of unconstrained nonlinear MPC schemes with time varying control horizon","venue":null,"work_id":"d0a39796-81df-4181-bc14-62a0d608a14e","year":2010},"citing_paper":{"arxiv_id":"2501.08709","last_updated":"2025-03-14T09:29:19Z","snapshot_observed_at":"2026-08-13T02:50:54.334334Z","submitted_at":"2025-01-15T10:50:47Z","title":"Kernel EDMD for data-driven nonlinear Koopman MPC with stability guarantees","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-10T20:27:21.885883Z"},"links":{"citing_paper":"/paper/2501.08709"},"observation_digest":"sha256:5fe9d04f2ec8e1c8ce18998b9020f3677eb89c7aedb5070c9292f8aa1f74b56b","observation_id":"2527f639-df41-44d3-87a7-c87df5ab82ce","resolution":{"observed_at":"2026-08-10T20:27:22.559211Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T20:27:22.515513Z","title":"Koopman form of nonlinear systems with inputs","venue":null,"work_id":"9fc2620a-d2b2-41fe-8ac0-f76ecc9bd762","year":2024},"citing_paper":{"arxiv_id":"2501.08709","last_updated":"2025-03-14T09:29:19Z","snapshot_observed_at":"2026-08-13T02:50:54.334334Z","submitted_at":"2025-01-15T10:50:47Z","title":"Kernel EDMD for data-driven nonlinear Koopman MPC with stability guarantees","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-10T20:27:21.897221Z"},"links":{"citing_paper":"/paper/2501.08709"},"observation_digest":"sha256:004fb7da6c966ecd1166464017e396d525654b46db13a9b3b4adb5e103d653aa","observation_id":"b2b5f01b-e757-410d-a3f4-e6985492ff59","resolution":{"observed_at":"2026-08-10T20:27:22.531570Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":"2403.18809","last_updated":"2024-07-04T10:57:36Z","snapshot_observed_at":"2026-08-13T00:43:36.138510Z","submitted_at":"2024-03-27T17:55:32Z","title":"$L^\\infty$-error bounds for approximations of the Koopman operator by kernel extended dynamic mode decomposition","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2403.18809","snapshot_observed_at":"2026-08-10T20:27:21.903421Z","title":"L∞-error bounds for approximations of the Koopman operator by kernel extended dynamic mode decomposition.SIAM J","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2501.08709","last_updated":"2025-03-14T09:29:19Z","snapshot_observed_at":"2026-08-13T02:50:54.334334Z","submitted_at":"2025-01-15T10:50:47Z","title":"Kernel EDMD for data-driven nonlinear Koopman MPC with stability guarantees","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-10T20:27:21.903421Z"},"links":{"cited_paper":"/paper/2403.18809","citing_paper":"/paper/2501.08709"},"observation_digest":"sha256:cadcf6d33f4d20c039950498f66ae7eec39542a2afde309dc482a522cc27fd16","observation_id":"de1bd7cb-3964-4dda-90d4-c17545a89e3e","resolution":{"observed_at":"2026-08-10T20:27:21.903421Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T20:27:22.479764Z","title":"Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive control","venue":null,"work_id":"2e2fe9df-5e52-4644-a34b-2fa41a8126c9","year":2018},"citing_paper":{"arxiv_id":"2501.08709","last_updated":"2025-03-14T09:29:19Z","snapshot_observed_at":"2026-08-13T02:50:54.334334Z","submitted_at":"2025-01-15T10:50:47Z","title":"Kernel EDMD for data-driven nonlinear Koopman MPC with stability guarantees","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-10T20:27:21.911543Z"},"links":{"citing_paper":"/paper/2501.08709"},"observation_digest":"sha256:a69a9fd52e2feb805de370a18fa9104537c98c0c54e646883f3c58a6c570fb49","observation_id":"eb6b43a9-40b7-4340-a7e8-7ed082692a82","resolution":{"observed_at":"2026-08-10T20:27:22.490105Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T20:27:22.455015Z","title":"A stabilizing model-based predictive control algorithm for nonlinear systems","venue":null,"work_id":"a028ae26-8079-4436-9240-53e1ecb98193","year":2001},"citing_paper":{"arxiv_id":"2501.08709","last_updated":"2025-03-14T09:29:19Z","snapshot_observed_at":"2026-08-13T02:50:54.334334Z","submitted_at":"2025-01-15T10:50:47Z","title":"Kernel EDMD for data-driven nonlinear Koopman MPC with stability guarantees","version":2},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-10T20:27:21.917908Z"},"links":{"citing_paper":"/paper/2501.08709"},"observation_digest":"sha256:e690633ca6034df4ee001722aeba4d097963feb29ac9a041e66ab2b5ea616533","observation_id":"22d44e81-6dcd-41fe-8bb7-efd11e2ba41b","resolution":{"observed_at":"2026-08-10T20:27:22.461888Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T20:27:22.437859Z","title":"Introduction to the Koopman Operator in Dynamical Systems and Control Theory, pages 3–33","venue":null,"work_id":"0ccec411-b031-4f67-a94e-91dfdfd643b9","year":2020},"citing_paper":{"arxiv_id":"2501.08709","last_updated":"2025-03-14T09:29:19Z","snapshot_observed_at":"2026-08-13T02:50:54.334334Z","submitted_at":"2025-01-15T10:50:47Z","title":"Kernel EDMD for data-driven nonlinear Koopman MPC with stability guarantees","version":2},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-10T20:27:21.922814Z"},"links":{"citing_paper":"/paper/2501.08709"},"observation_digest":"sha256:7b03bd2664bdaa49f16893bc18fcbe22925324a681c5fed8081e3d2cc491e80e","observation_id":"3620a64b-07cd-479b-9a91-ab5b5afb2490","resolution":{"observed_at":"2026-08-10T20:27:22.443081Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T20:27:22.411952Z","title":"Finite-data error bounds for Koopman-based prediction and control","venue":null,"work_id":"11996aad-eeb2-48f0-bf27-f9bcb7e26879","year":2023},"citing_paper":{"arxiv_id":"2501.08709","last_updated":"2025-03-14T09:29:19Z","snapshot_observed_at":"2026-08-13T02:50:54.334334Z","submitted_at":"2025-01-15T10:50:47Z","title":"Kernel EDMD for data-driven nonlinear Koopman MPC with stability guarantees","version":2},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-10T20:27:21.928303Z"},"links":{"citing_paper":"/paper/2501.08709"},"observation_digest":"sha256:ddc88c978f80c6759fbd7db631faa0b14426ca221622a9ca80b3f751ca51bc6b","observation_id":"633386e8-5b5a-49ba-be2f-5cace270802b","resolution":{"observed_at":"2026-08-10T20:27:22.418340Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T20:27:22.391397Z","title":"Otto, and Clarence W","venue":null,"work_id":"d4985870-431a-4e8d-867f-9995036c65b4","year":2020},"citing_paper":{"arxiv_id":"2501.08709","last_updated":"2025-03-14T09:29:19Z","snapshot_observed_at":"2026-08-13T02:50:54.334334Z","submitted_at":"2025-01-15T10:50:47Z","title":"Kernel EDMD for data-driven nonlinear Koopman MPC with stability guarantees","version":2},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-10T20:27:21.941405Z"},"links":{"citing_paper":"/paper/2501.08709"},"observation_digest":"sha256:cc3994080e4ac6f0a0bbe0685658658010a05f39cd65f791b2cf087f116a3fe8","observation_id":"d79c8c91-1f60-4b4b-a83e-dc228f8c8fd6","resolution":{"observed_at":"2026-08-10T20:27:22.397848Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T20:27:21.946804Z","title":"Dynamic mode decomposition with control","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2501.08709","last_updated":"2025-03-14T09:29:19Z","snapshot_observed_at":"2026-08-13T02:50:54.334334Z","submitted_at":"2025-01-15T10:50:47Z","title":"Kernel EDMD for data-driven nonlinear Koopman MPC with stability guarantees","version":2},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-10T20:27:21.946804Z"},"links":{"citing_paper":"/paper/2501.08709"},"observation_digest":"sha256:fe2456593105e5d0affaaf659fd7702191dec0f8766c978302611ba114a37c73","observation_id":"a66a23f6-a5ec-44cb-867c-d28c219bae4e","resolution":{"observed_at":"2026-08-10T20:27:21.946804Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T20:27:22.359689Z","title":"Towards reliable data-based optimal and predictive control using extended DMD","venue":null,"work_id":"e92cbc3f-1095-4826-ba97-68e9080ead07","year":2023},"citing_paper":{"arxiv_id":"2501.08709","last_updated":"2025-03-14T09:29:19Z","snapshot_observed_at":"2026-08-13T02:50:54.334334Z","submitted_at":"2025-01-15T10:50:47Z","title":"Kernel EDMD for data-driven nonlinear Koopman MPC with stability guarantees","version":2},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-10T20:27:21.951954Z"},"links":{"citing_paper":"/paper/2501.08709"},"observation_digest":"sha256:bd3bdaa6232f132ee666f4c283cd3bcdc7ada50f475c1b79fc460737f1562dc0","observation_id":"78f2e98e-a7e6-407c-81d3-1d86beb4cddc","resolution":{"observed_at":"2026-08-10T20:27:22.365902Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T20:27:22.338193Z","title":"Scattered data approximation, volume 17","venue":null,"work_id":"9017d6e1-e75e-4607-944f-acd9a69ba790","year":2004},"citing_paper":{"arxiv_id":"2501.08709","last_updated":"2025-03-14T09:29:19Z","snapshot_observed_at":"2026-08-13T02:50:54.334334Z","submitted_at":"2025-01-15T10:50:47Z","title":"Kernel EDMD for data-driven nonlinear Koopman MPC with stability guarantees","version":2},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-10T20:27:21.958483Z"},"links":{"citing_paper":"/paper/2501.08709"},"observation_digest":"sha256:d08d1517abd8e2cd3deacdc3fe30db6d9931a1fdabc5dc96878662945ac90378","observation_id":"20e71524-dbae-4764-bcdd-71ea7a0a7e9e","resolution":{"observed_at":"2026-08-10T20:27:22.345228Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T20:27:21.967569Z","title":"A note on persistency of excitation","venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2501.08709","last_updated":"2025-03-14T09:29:19Z","snapshot_observed_at":"2026-08-13T02:50:54.334334Z","submitted_at":"2025-01-15T10:50:47Z","title":"Kernel EDMD for data-driven nonlinear Koopman MPC with stability guarantees","version":2},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-10T20:27:21.967569Z"},"links":{"citing_paper":"/paper/2501.08709"},"observation_digest":"sha256:83edcef8b7bd4cb5e53a1a4661675ffe90eeb8ce1fac60329b540ee34fd38839","observation_id":"f9ae8275-5bf2-4086-a2ed-cda23a8e0c2b","resolution":{"observed_at":"2026-08-10T20:27:21.967569Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T20:27:22.295708Z","title":"A data–driven approximation of the Koopman operator: Extending dynamic mode decomposition","venue":null,"work_id":"946e945b-f30c-4832-bb65-d7a5e929c5a7","year":2015},"citing_paper":{"arxiv_id":"2501.08709","last_updated":"2025-03-14T09:29:19Z","snapshot_observed_at":"2026-08-13T02:50:54.334334Z","submitted_at":"2025-01-15T10:50:47Z","title":"Kernel EDMD for data-driven nonlinear Koopman MPC with stability guarantees","version":2},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-10T20:27:21.978535Z"},"links":{"citing_paper":"/paper/2501.08709"},"observation_digest":"sha256:43a02612075e3bd457daf7004075210996223cc186f84496b68037f6f9e25fab","observation_id":"05f2a0de-c2a3-4fc2-b6ad-7bdf98d25576","resolution":{"observed_at":"2026-08-10T20:27:22.303799Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T20:27:22.269873Z","title":"Estimates on the prediction horizon length in MPC","venue":null,"work_id":"2fdb7cd0-4f5d-4932-b44e-67e44f0174d0","year":2012},"citing_paper":{"arxiv_id":"2501.08709","last_updated":"2025-03-14T09:29:19Z","snapshot_observed_at":"2026-08-13T02:50:54.334334Z","submitted_at":"2025-01-15T10:50:47Z","title":"Kernel EDMD for data-driven nonlinear Koopman MPC with stability guarantees","version":2},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-10T20:27:21.987895Z"},"links":{"citing_paper":"/paper/2501.08709"},"observation_digest":"sha256:649f2ff983db94595f95ceadf4ffeeb9afdc18226057cdaefa14bcaeea11d262","observation_id":"6798463d-3db9-4594-a4ff-4277b5cd74ca","resolution":{"observed_at":"2026-08-10T20:27:22.275689Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T20:27:22.244931Z","title":"Data-driven MPC with termi- nal conditions in the Koopman framework","venue":null,"work_id":"885e23e8-5a10-445e-b829-ba2d9b5a31d4","year":2024},"citing_paper":{"arxiv_id":"2501.08709","last_updated":"2025-03-14T09:29:19Z","snapshot_observed_at":"2026-08-13T02:50:54.334334Z","submitted_at":"2025-01-15T10:50:47Z","title":"Kernel EDMD for data-driven nonlinear Koopman MPC with stability guarantees","version":2},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-10T20:27:21.996249Z"},"links":{"citing_paper":"/paper/2501.08709"},"observation_digest":"sha256:3b64df9df70c19c13f12d55a7d3fd3a4a848b954f4237d643e9f60828051849d","observation_id":"9f5047c1-0cf1-4eeb-805e-3a982d5ee90c","resolution":{"observed_at":"2026-08-10T20:27:22.253719Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T20:27:22.198763Z","title":"Learning deep neural network representations for Koopman operators of nonlinear dynamical systems","venue":null,"work_id":"44c61e83-142e-4dc4-8e46-d0cb1ac74d91","year":2019},"citing_paper":{"arxiv_id":"2501.08709","last_updated":"2025-03-14T09:29:19Z","snapshot_observed_at":"2026-08-13T02:50:54.334334Z","submitted_at":"2025-01-15T10:50:47Z","title":"Kernel EDMD for data-driven nonlinear Koopman MPC with stability guarantees","version":2},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-10T20:27:22.002340Z"},"links":{"citing_paper":"/paper/2501.08709"},"observation_digest":"sha256:5e6769afa0eaf19d5c9ae92cbf30ca0d32b4357783fbe92d0ed96fcddc398e9e","observation_id":"8b690a5f-eb21-4848-89dd-b1006093ffcc","resolution":{"observed_at":"2026-08-10T20:27:22.213328Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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"}}],"paper":{"arxiv_id":"2501.08709","last_updated":"2025-03-14T09:29:19Z","latest_version":2,"primary_category":"math.OC","snapshot_observed_at":"2026-08-13T02:50:54.334334Z","submitted_at":"2025-01-15T10:50:47Z","title":"Kernel EDMD for data-driven nonlinear Koopman MPC with stability guarantees"},"reference_resolution":{"displayed":25,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":5,"verified_exact":0,"verified_fuzzy":20},"total_outbound_references":25},"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 25 of 25 outbound references and 3 inbound Pith citation observations for arXiv:2501.08709."}