{"as_of":"2026-08-10T02:50:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:d7ab22f3f68b226b3558c58f875cec22967f36e67f9836480bc80705653407ae","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":4,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":4,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-09T06:31:02.800959+00:00","state":"measured"},{"denominator":4,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":4,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T14:36:11.692060Z","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":"2026-05-11T08:40:57.693400Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"1411.2260","last_updated":"2015-07-27T22:10:14Z","snapshot_observed_at":"2026-07-06T03:59:59.508983Z","submitted_at":"2014-11-09T18:01:42Z","title":"A Kernel-Based Approach to Data-Driven Koopman Spectral Analysis","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1411.2260","snapshot_observed_at":"2026-08-07T14:36:11.692060Z","title":"A kernel-based approach to data-driven Koopman spectral analysis.arXiv preprint arXiv:1411.2260, 2014","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2505.18671","last_updated":"2025-05-24T12:18:19Z","snapshot_observed_at":"2026-08-09T05:57:00.511284Z","submitted_at":"2025-05-24T12:18:19Z","title":"Self-Supervised Evolution Operator Learning for High-Dimensional Dynamical Systems","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-07T14:36:11.692060Z"},"links":{"cited_paper":"/paper/1411.2260","citing_paper":"/paper/2505.18671"},"observation_digest":"sha256:4be91035ff8b5d07ac4424a736b2de973f33007e9df59428dcc967d45d1c9c89","observation_id":"44bfbd5f-7343-47da-ba08-12079817299c","resolution":{"observed_at":"2026-08-07T14:36:11.692060Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1411.2260","last_updated":"2015-07-27T22:10:14Z","snapshot_observed_at":"2026-07-06T03:59:59.508983Z","submitted_at":"2014-11-09T18:01:42Z","title":"A Kernel-Based Approach to Data-Driven Koopman Spectral Analysis","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1411.2260","snapshot_observed_at":"2026-08-06T15:12:00.504650Z","title":null,"venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2507.16915","last_updated":"2025-07-22T18:01:05Z","snapshot_observed_at":"2026-08-08T19:56:29.401222Z","submitted_at":"2025-07-22T18:01:05Z","title":"Avoiding spectral pollution for transfer operators using residuals","version":1},"reference_index":80,"source":"pdf_text","source_observed_at":"2026-08-06T15:12:00.504650Z"},"links":{"cited_paper":"/paper/1411.2260","citing_paper":"/paper/2507.16915"},"observation_digest":"sha256:5a14d060a77e7e2e9d7a0d67331d56639156ea856fe6afae247ff6fa1cd35819","observation_id":"26881c93-fd7e-4356-94bb-270c95bbebd5","resolution":{"observed_at":"2026-08-06T15:12:00.504650Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1411.2260","last_updated":"2015-07-27T22:10:14Z","snapshot_observed_at":"2026-07-06T03:59:59.508983Z","submitted_at":"2014-11-09T18:01:42Z","title":"A Kernel-Based Approach to Data-Driven Koopman Spectral Analysis","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1411.2260","snapshot_observed_at":"2026-08-03T19:54:12.069832Z","title":null,"venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2511.23322","last_updated":"2026-06-26T13:15:19Z","snapshot_observed_at":"2026-08-05T18:41:36.040596Z","submitted_at":"2025-11-28T16:23:40Z","title":"Data-driven Reachability Verification with Probabilistic Guarantees under Koopman Spectral Uncertainty","version":2},"reference_index":29,"source":"arxiv_source","source_observed_at":"2026-08-03T19:54:12.069832Z"},"links":{"cited_paper":"/paper/1411.2260","citing_paper":"/paper/2511.23322"},"observation_digest":"sha256:bfe7e2240458b972c82e45480dbe5d03bfadb975acb1bc0ec29198f110279e39","observation_id":"950e5db9-42ce-4abb-8d45-5f251c0c5903","resolution":{"observed_at":"2026-08-03T19:54:12.069832Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1411.2260","last_updated":"2015-07-27T22:10:14Z","snapshot_observed_at":"2026-07-06T03:59:59.508983Z","submitted_at":"2014-11-09T18:01:42Z","title":"A Kernel-Based Approach to Data-Driven Koopman Spectral Analysis","version":4},"cited_work":{"arxiv_id":"1411.2260","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"1411.2260","snapshot_observed_at":"2026-07-04T20:29:44.878339Z","title":"A kernel-based approach to data-driven koopman spectral analysis","venue":null,"work_id":"b06e7c55-89fe-4e81-af4c-6250e161db42","year":2014},"citing_paper":{"arxiv_id":"2604.09424","last_updated":"2026-04-10T15:37:24Z","snapshot_observed_at":"2026-07-06T22:58:17.167367Z","submitted_at":"2026-04-10T15:37:24Z","title":"RKHS method for computing Koopman-based Lyapunov functions","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-05-10T16:35:07.471080Z"},"links":{"cited_paper":"/paper/1411.2260","citing_paper":"/paper/2604.09424"},"observation_digest":"sha256:78e35086ff79074fb2938d93804864c30ecd576e90f8c83f17a1b230f6d911e2","observation_id":"9d7c09cf-b256-41ca-9708-ac5093bb48ea","resolution":{"observed_at":"2026-07-04T20:29:44.878339Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/1411.2260/citation-record","integrity":"/paper/1411.2260/integrity","json":"/paper/1411.2260/citation-record.json","paper":"/paper/1411.2260"},"outbound":[],"paper":{"arxiv_id":"1411.2260","last_updated":"2015-07-27T22:10:14Z","latest_version":4,"primary_category":"math.DS","snapshot_observed_at":"2026-07-06T03:59:59.508983Z","submitted_at":"2014-11-09T18:01:42Z","title":"A Kernel-Based Approach to Data-Driven Koopman Spectral Analysis"},"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":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"thesis":"As of 10 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 4 inbound Pith citation observations for arXiv:1411.2260."}