{"as_of":"2026-08-14T07:15:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:735623bed0aa44a34a3de924bba8f3b94d09a55e5aa7b3d7cb5d4f13cdc854b7","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":1,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":1,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-14T06:32:32.682623+00:00","state":"measured"},{"denominator":1,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":1,"source":"paper_references, paper_reference_links","source_observed_at":"2026-06-25T23:53:32.611593Z","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":"2026-07-04T17:09:58.999172Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2009.13482","last_updated":"2020-09-28T17:14:07Z","snapshot_observed_at":"2026-08-12T15:00:52.720239Z","submitted_at":"2020-09-28T17:14:07Z","title":"Densities of minor-closed graph classes are rational","version":1},"cited_work":{"arxiv_id":"2009.13482","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2009.13482","snapshot_observed_at":"2026-07-04T17:09:58.999172Z","title":"Densities of minor-closed graph classes are rational, 2020","venue":null,"work_id":"487b76e0-c671-46bc-9e04-f26bfb3db207","year":2020},"citing_paper":{"arxiv_id":"2606.24326","last_updated":"2026-06-24T07:44:59Z","snapshot_observed_at":"2026-08-12T07:43:16.262414Z","submitted_at":"2026-06-23T09:02:50Z","title":"Obstructions for Minor-Closed Classes of limiting Densities Below 3/2","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-06-25T23:53:32.611593Z"},"links":{"cited_paper":"/paper/2009.13482","citing_paper":"/paper/2606.24326"},"observation_digest":"sha256:8cb2f59a578fed320ee44ba0c66e2ee3e8796f7bead2d5a428df40f6355a8baf","observation_id":"3fd01b6c-c99a-44f4-b53e-ee0e4a726e3a","resolution":{"observed_at":"2026-07-04T17:09:59.000862Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2009.13482/citation-record","integrity":"/paper/2009.13482/integrity","json":"/paper/2009.13482/citation-record.json","paper":"/paper/2009.13482"},"outbound":[],"paper":{"arxiv_id":"2009.13482","last_updated":"2020-09-28T17:14:07Z","latest_version":1,"primary_category":"math.CO","snapshot_observed_at":"2026-08-12T15:00:52.720239Z","submitted_at":"2020-09-28T17:14:07Z","title":"Densities of minor-closed graph classes are rational"},"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":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"thesis":"As of 14 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 1 inbound Pith citation observation for arXiv:2009.13482."}