{"as_of":"2026-07-31T18:48:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:1566cefbf181c3e91b9c0ebe122f6fd1c25eae0fd04d97f404c1c5d96aa0bde7","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":"2026-07-31T06:34:12.847434+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":"2026-05-20T17:20:29.589792Z","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":"2026-07-10T12:15:01.137692Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2505.18443","last_updated":"2025-05-24T00:56:07Z","snapshot_observed_at":"2026-07-06T21:29:40.876235Z","submitted_at":"2025-05-24T00:56:07Z","title":"An Early History of Toric Ideals","version":1},"cited_work":{"arxiv_id":"2505.18443","doi":"10.48550/arxiv.2505.18443","metadata_source":"arxiv_reference","pith_arxiv_id":"2505.18443","snapshot_observed_at":"2026-07-10T12:15:01.137692Z","title":null,"venue":null,"work_id":"f86f4a86-e882-442f-990f-b5da248f3ba2","year":null},"citing_paper":{"arxiv_id":"2605.15970","last_updated":"2026-05-15T14:00:47Z","snapshot_observed_at":"2026-07-06T23:27:11.118592Z","submitted_at":"2026-05-15T14:00:47Z","title":"Copositive Matrices with Ordered Off-Diagonal Entries","version":1},"reference_index":193,"source":"arxiv_source","source_observed_at":"2026-05-20T17:20:29.589792Z"},"links":{"cited_paper":"/paper/2505.18443","citing_paper":"/paper/2605.15970"},"observation_digest":"sha256:ecef43152bd650c27d5442cca383813fc89ac0fd84b6eb85d67406614614c0fd","observation_id":"a35292d0-5715-4c49-a908-8a7290c97b84","resolution":{"observed_at":"2026-05-20T17:23:36.364462Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-07-31T06:34:12.847434+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-07-31T06:34:12.847434+00:00","source":"crossref"},{"observed_at":"2026-05-24T04:55:22.169501+00:00","source":"crossref_status_cache"},{"observed_at":"2026-05-24T04:55:22.169501+00:00","source":"openalex_status_cache"},{"observed_at":"2026-07-31T06:34:08.642788+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2505.18443/citation-record","integrity":"/paper/2505.18443/integrity","json":"/paper/2505.18443/citation-record.json","paper":"/paper/2505.18443"},"outbound":[],"paper":{"arxiv_id":"2505.18443","last_updated":"2025-05-24T00:56:07Z","latest_version":1,"primary_category":"math.AC","snapshot_observed_at":"2026-07-06T21:29:40.876235Z","submitted_at":"2025-05-24T00:56:07Z","title":"An Early History of Toric Ideals"},"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":"2026-07-31T06:34:12.847434+00:00","source":"crossref"},{"observed_at":"2026-07-31T06:34:08.642788+00:00","source":"retraction_watch"}],"thesis":"As of 31 July 2026, this Paper Citation Record lists 0 of 0 outbound references and 1 inbound Pith citation observation for arXiv:2505.18443."}