{"as_of":"2026-08-04T14:20:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:605be794e79c682b1cb302cde17389a40608310724aed6ded7329317f8f0890e","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":"2026-08-04T06:34:03.388597+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":"2026-05-25T19:40:44.907129Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"pith","source_observed_at":"2026-05-25T19:41:10.186920Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"1901.05133","last_updated":"2019-01-16T04:38:52Z","snapshot_observed_at":"2026-07-06T07:26:59.288200Z","submitted_at":"2019-01-16T04:38:52Z","title":"Integral Factorial Ratios","version":1},"cited_work":{"arxiv_id":"1901.05133","doi":null,"metadata_source":"pith","pith_arxiv_id":"1901.05133","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Integral Factorial Ratios","venue":"math.NT","work_id":"360ed3bb-4740-47bf-ab8e-d7388f707d4a","year":2019},"citing_paper":{"arxiv_id":"1906.08671","last_updated":"2019-06-20T14:50:31Z","snapshot_observed_at":"2026-07-06T08:01:41.630447Z","submitted_at":"2019-06-20T14:50:31Z","title":"Counting birthday collisions using partitions","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-05-25T19:40:44.907129Z"},"links":{"cited_paper":"/paper/1901.05133","citing_paper":"/paper/1906.08671"},"observation_digest":"sha256:adef8e4a0c0a394798da7e61b3af4c3e585e653113f3548f3910021a4e302b0f","observation_id":"ce25aa45-bf71-42e0-96e8-4f0945c628fa","resolution":{"observed_at":"2026-05-25T19:41:10.194486Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/1901.05133/citation-record","integrity":"/paper/1901.05133/integrity","json":"/paper/1901.05133/citation-record.json","paper":"/paper/1901.05133"},"outbound":[],"paper":{"arxiv_id":"1901.05133","last_updated":"2019-01-16T04:38:52Z","latest_version":1,"primary_category":"math.NT","snapshot_observed_at":"2026-07-06T07:26:59.288200Z","submitted_at":"2019-01-16T04:38:52Z","title":"Integral Factorial Ratios"},"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":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"thesis":"As of 4 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 1 inbound Pith citation observation for arXiv:1901.05133."}