{"as_of":"2026-08-10T03:33:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:bd68296ea5976da0a8dce7f0c019cb4eec4e1b27e0c11540b604927ff03a0765","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":2,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":2,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-09T06:31:02.800959+00:00","state":"measured"},{"denominator":2,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":2,"source":"paper_references, paper_reference_links","source_observed_at":"2026-07-14T04:38:57.571931Z","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":"2026-05-20T18:28:53.158417Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2004.10074","last_updated":"2020-11-29T10:16:39Z","snapshot_observed_at":"2026-08-10T01:13:37.476781Z","submitted_at":"2020-04-21T15:01:57Z","title":"Spectral Analysis of the Koopman Operator for Partial Differential Equations","version":2},"cited_work":{"arxiv_id":"2004.10074","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2004.10074","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Nakao and I","venue":null,"work_id":"66d3c751-76c1-4344-a735-212a532f2157","year":2020},"citing_paper":{"arxiv_id":"2605.15969","last_updated":"2026-05-15T14:00:43Z","snapshot_observed_at":"2026-07-06T23:27:11.118592Z","submitted_at":"2026-05-15T14:00:43Z","title":"Quantum mechanics for classical transport equations","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-05-20T18:24:01.160627Z"},"links":{"cited_paper":"/paper/2004.10074","citing_paper":"/paper/2605.15969"},"observation_digest":"sha256:ea5fde06370c38c5c1cf016d35de62eb6338bd4d1100755d965bcc63444cd6fc","observation_id":"7d74809c-7337-4a42-b0f6-88dd34fd03dd","resolution":{"observed_at":"2026-05-20T18:28:53.159855Z","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"}},{"citation":{"cited_paper":{"arxiv_id":"2004.10074","last_updated":"2020-11-29T10:16:39Z","snapshot_observed_at":"2026-08-10T01:13:37.476781Z","submitted_at":"2020-04-21T15:01:57Z","title":"Spectral Analysis of the Koopman Operator for Partial Differential Equations","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2004.10074","snapshot_observed_at":"2026-07-14T04:38:57.571931Z","title":"Nakao and I","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2607.11580","last_updated":"2026-07-13T14:00:03Z","snapshot_observed_at":"2026-08-08T04:29:48.669438Z","submitted_at":"2026-07-13T14:00:03Z","title":"Classical probabilistic realisation of quantum double-slit interference","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-07-14T04:38:57.571931Z"},"links":{"cited_paper":"/paper/2004.10074","citing_paper":"/paper/2607.11580"},"observation_digest":"sha256:64ba750d63e5bc08c1985b3c60ae8b591696d3f6c58cd8d81dc9c05a4ec556bc","observation_id":"51c705f9-3961-4295-b85c-be4d564ee217","resolution":{"observed_at":"2026-07-14T04:38:57.571931Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2004.10074/citation-record","integrity":"/paper/2004.10074/integrity","json":"/paper/2004.10074/citation-record.json","paper":"/paper/2004.10074"},"outbound":[],"paper":{"arxiv_id":"2004.10074","last_updated":"2020-11-29T10:16:39Z","latest_version":2,"primary_category":"nlin.PS","snapshot_observed_at":"2026-08-10T01:13:37.476781Z","submitted_at":"2020-04-21T15:01:57Z","title":"Spectral Analysis of the Koopman Operator for Partial Differential Equations"},"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 2 inbound Pith citation observations for arXiv:2004.10074."}