{"as_of":"2026-08-10T20:14:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:883b40699329af97cf16f907dc0f44a8297647400dbaacb8b2ab9f2ec21ece39","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":7,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":7,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-10T06:31:04.303077+00:00","state":"measured"},{"denominator":7,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":7,"source":"paper_references, paper_reference_links","source_observed_at":"2026-07-13T14:24:40.195364Z","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":"2026-07-03T08:07:44.939518Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2311.13033","last_updated":"2025-01-14T00:19:38Z","snapshot_observed_at":"2026-07-06T16:50:50.547528Z","submitted_at":"2023-11-21T22:45:07Z","title":"Invariance Proximity: Closed-Form Error Bounds for Finite-Dimensional Koopman-Based Models","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2311.13033","snapshot_observed_at":"2026-07-13T14:24:40.195364Z","title":"Invariance proximity: closed-form error bounds for finite-dimensional Koopman-based models,","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2604.01459","last_updated":"2026-06-07T03:12:18Z","snapshot_observed_at":"2026-08-10T07:06:01.296377Z","submitted_at":"2026-04-01T23:13:13Z","title":"Koopman Subspace Pruning in Reproducing Kernel Hilbert Spaces via Principal Vectors","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-07-13T14:24:40.195364Z"},"links":{"cited_paper":"/paper/2311.13033","citing_paper":"/paper/2604.01459"},"observation_digest":"sha256:3b349b4d5eec31745115da2199c6e4f0b4f6f2ad0d928d753de044a92543af88","observation_id":"173e93bb-6cb3-4c59-9bc7-474296368bca","resolution":{"observed_at":"2026-07-13T14:24:40.195364Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2311.13033","last_updated":"2025-01-14T00:19:38Z","snapshot_observed_at":"2026-07-06T16:50:50.547528Z","submitted_at":"2023-11-21T22:45:07Z","title":"Invariance Proximity: Closed-Form Error Bounds for Finite-Dimensional Koopman-Based Models","version":4},"cited_work":{"arxiv_id":"2311.13033","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2311.13033","snapshot_observed_at":"2026-07-03T08:07:44.939518Z","title":"Invariance proximity: Closed-form error bounds for finite-dimensional","venue":null,"work_id":"02a45e90-0643-426b-94be-f3ddd99a2668","year":2024},"citing_paper":{"arxiv_id":"2605.13135","last_updated":"2026-06-07T03:17:50Z","snapshot_observed_at":"2026-08-08T08:45:24.938052Z","submitted_at":"2026-05-13T08:04:38Z","title":"Subspace Pruning via Principal Vectors for Accurate Koopman-Based Approximations","version":1},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-05-14T18:52:51.984903Z"},"links":{"cited_paper":"/paper/2311.13033","citing_paper":"/paper/2605.13135"},"observation_digest":"sha256:e9bbe973c71e88433c2e8a8efe9bee498e8238ea1ebdff252f97c340e5044ff3","observation_id":"b02bd6d8-e50b-4fc8-9ad0-c59e2e8ceeac","resolution":{"observed_at":"2026-05-14T18:57:50.348771Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2311.13033","last_updated":"2025-01-14T00:19:38Z","snapshot_observed_at":"2026-07-06T16:50:50.547528Z","submitted_at":"2023-11-21T22:45:07Z","title":"Invariance Proximity: Closed-Form Error Bounds for Finite-Dimensional Koopman-Based Models","version":4},"cited_work":{"arxiv_id":"2311.13033","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2311.13033","snapshot_observed_at":"2026-07-03T08:07:44.939518Z","title":"Invariance proximity: Closed-form error bounds for finite-dimensional","venue":null,"work_id":"02a45e90-0643-426b-94be-f3ddd99a2668","year":2024},"citing_paper":{"arxiv_id":"2605.13135","last_updated":"2026-06-07T03:17:50Z","snapshot_observed_at":"2026-08-08T08:45:24.938052Z","submitted_at":"2026-05-13T08:04:38Z","title":"Subspace Pruning via Principal Vectors for Accurate Koopman-Based Approximations","version":2},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-06-30T21:46:33.868361Z"},"links":{"cited_paper":"/paper/2311.13033","citing_paper":"/paper/2605.13135"},"observation_digest":"sha256:76580d8d34b580c2ac3b5e3f68e5ca8edb1a79d8d3a127d00ac38ba94c67429a","observation_id":"10a23ade-ba11-407b-a8a9-d53126059e08","resolution":{"observed_at":"2026-07-01T14:15:47.699301Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2311.13033","last_updated":"2025-01-14T00:19:38Z","snapshot_observed_at":"2026-07-06T16:50:50.547528Z","submitted_at":"2023-11-21T22:45:07Z","title":"Invariance Proximity: Closed-Form Error Bounds for Finite-Dimensional Koopman-Based Models","version":4},"cited_work":{"arxiv_id":"2311.13033","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2311.13033","snapshot_observed_at":"2026-07-03T08:07:44.939518Z","title":"Invariance proximity: Closed-form error bounds for finite-dimensional","venue":null,"work_id":"02a45e90-0643-426b-94be-f3ddd99a2668","year":2024},"citing_paper":{"arxiv_id":"2605.16660","last_updated":"2026-05-15T21:55:32Z","snapshot_observed_at":"2026-08-01T15:28:44.909997Z","submitted_at":"2026-05-15T21:55:32Z","title":"Trajectory-based Safety of Monotone Systems: Verification and Control Synthesis","version":1},"reference_index":26,"source":"arxiv_source","source_observed_at":"2026-05-20T15:31:08.637769Z"},"links":{"cited_paper":"/paper/2311.13033","citing_paper":"/paper/2605.16660"},"observation_digest":"sha256:531b6c05056745a7e39f9d04fbf405dc19c8d7d02cd427d307dc75971219a3f0","observation_id":"cc3dec2a-2d85-43fa-945a-a79861e48b01","resolution":{"observed_at":"2026-05-20T15:33:25.557286Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2311.13033","last_updated":"2025-01-14T00:19:38Z","snapshot_observed_at":"2026-07-06T16:50:50.547528Z","submitted_at":"2023-11-21T22:45:07Z","title":"Invariance Proximity: Closed-Form Error Bounds for Finite-Dimensional Koopman-Based Models","version":4},"cited_work":{"arxiv_id":"2311.13033","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2311.13033","snapshot_observed_at":"2026-07-03T08:07:44.939518Z","title":"Invariance proximity: Closed-form error bounds for finite-dimensional","venue":null,"work_id":"02a45e90-0643-426b-94be-f3ddd99a2668","year":2024},"citing_paper":{"arxiv_id":"2605.31438","last_updated":"2026-05-29T15:35:21Z","snapshot_observed_at":"2026-08-08T00:17:34.190170Z","submitted_at":"2026-05-29T15:35:21Z","title":"Flow map learning in nonlinear vector autoregressive models: influence of the feature-library structure on the training error","version":1},"reference_index":94,"source":"pdf_text","source_observed_at":"2026-06-28T23:19:08.971339Z"},"links":{"cited_paper":"/paper/2311.13033","citing_paper":"/paper/2605.31438"},"observation_digest":"sha256:04c4e807995c3a9c10ace20a1c5c08dc35d3da7c2c7c77e704de9494306e7f00","observation_id":"302ce9b1-1fab-4997-81e3-6244051478fb","resolution":{"observed_at":"2026-06-28T23:22:46.978411Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2311.13033","last_updated":"2025-01-14T00:19:38Z","snapshot_observed_at":"2026-07-06T16:50:50.547528Z","submitted_at":"2023-11-21T22:45:07Z","title":"Invariance Proximity: Closed-Form Error Bounds for Finite-Dimensional Koopman-Based Models","version":4},"cited_work":{"arxiv_id":"2311.13033","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2311.13033","snapshot_observed_at":"2026-07-03T08:07:44.939518Z","title":"Invariance proximity: Closed-form error bounds for finite-dimensional","venue":null,"work_id":"02a45e90-0643-426b-94be-f3ddd99a2668","year":2024},"citing_paper":{"arxiv_id":"2606.07758","last_updated":"2026-06-05T18:13:50Z","snapshot_observed_at":"2026-08-08T17:43:58.268827Z","submitted_at":"2026-06-05T18:13:50Z","title":"Koopman meets input-output data: Data-driven output-feedback control of nonlinear systems with closed-loop guarantees","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-06-27T20:51:24.309148Z"},"links":{"cited_paper":"/paper/2311.13033","citing_paper":"/paper/2606.07758"},"observation_digest":"sha256:eccdb58623580ce5b6292051d9888def45920843a45076dec21e1cfc90ce1433","observation_id":"c86f0ef2-cd2a-4f0a-9dd0-c14aa006c836","resolution":{"observed_at":"2026-07-02T20:07:22.543308Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2311.13033","last_updated":"2025-01-14T00:19:38Z","snapshot_observed_at":"2026-07-06T16:50:50.547528Z","submitted_at":"2023-11-21T22:45:07Z","title":"Invariance Proximity: Closed-Form Error Bounds for Finite-Dimensional Koopman-Based Models","version":4},"cited_work":{"arxiv_id":"2311.13033","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2311.13033","snapshot_observed_at":"2026-07-03T08:07:44.939518Z","title":"Invariance proximity: Closed-form error bounds for finite-dimensional","venue":null,"work_id":"02a45e90-0643-426b-94be-f3ddd99a2668","year":2024},"citing_paper":{"arxiv_id":"2607.01819","last_updated":"2026-07-02T07:31:47Z","snapshot_observed_at":"2026-08-04T21:14:25.257579Z","submitted_at":"2026-07-02T07:31:47Z","title":"Koopman operator theory: fundamentals, control, and applications","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-07-03T08:05:16.851267Z"},"links":{"cited_paper":"/paper/2311.13033","citing_paper":"/paper/2607.01819"},"observation_digest":"sha256:013dc6b9ab58c3a78aa06f48948c47e4ac0faa5a1e1adc8dca33df5932ff4003","observation_id":"bcaefcbf-530b-4b79-9f6b-7d1e78638509","resolution":{"observed_at":"2026-07-03T08:07:44.941065Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2311.13033/citation-record","integrity":"/paper/2311.13033/integrity","json":"/paper/2311.13033/citation-record.json","paper":"/paper/2311.13033"},"outbound":[],"paper":{"arxiv_id":"2311.13033","last_updated":"2025-01-14T00:19:38Z","latest_version":4,"primary_category":"math.OC","snapshot_observed_at":"2026-07-06T16:50:50.547528Z","submitted_at":"2023-11-21T22:45:07Z","title":"Invariance Proximity: Closed-Form Error Bounds for Finite-Dimensional Koopman-Based Models"},"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":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"thesis":"As of 10 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 7 inbound Pith citation observations for arXiv:2311.13033."}