{"as_of":"2026-08-19T19:16:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:33e95646c2b2b2808057bf262006ad6d09a88b13871de11326381c5ad787f521","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":"2026-08-19T06:32:44.657259+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":"2026-08-04T17:00:43.968767Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2112.07056","last_updated":"2022-12-10T21:17:34Z","snapshot_observed_at":"2026-08-19T13:25:34.144152Z","submitted_at":"2021-12-13T22:48:30Z","title":"On rationally integrable planar dual and projective billiards","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2112.07056","snapshot_observed_at":"2026-08-04T17:00:43.968767Z","title":"Preprint https://arxiv.org/abs/2112.07056 26","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2509.11257","last_updated":"2025-09-14T12:58:25Z","snapshot_observed_at":"2026-08-09T11:57:51.542537Z","submitted_at":"2025-09-14T12:58:25Z","title":"On complex algebraic caustics in planar and projective billiards","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-04T17:00:43.968767Z"},"links":{"cited_paper":"/paper/2112.07056","citing_paper":"/paper/2509.11257"},"observation_digest":"sha256:9c2d508ace77dcb7fe820c1a3a30111c2a9cea53a5c92cf50cecf55ec4682b51","observation_id":"458b732a-c658-4425-8d84-bacb67a3ca85","resolution":{"observed_at":"2026-08-04T17:00:43.968767Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2112.07056/citation-record","integrity":"/paper/2112.07056/integrity","json":"/paper/2112.07056/citation-record.json","paper":"/paper/2112.07056"},"outbound":[],"paper":{"arxiv_id":"2112.07056","last_updated":"2022-12-10T21:17:34Z","latest_version":4,"primary_category":"math.DS","snapshot_observed_at":"2026-08-19T13:25:34.144152Z","submitted_at":"2021-12-13T22:48:30Z","title":"On rationally integrable planar dual and projective billiards"},"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":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"thesis":"As of 19 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 1 inbound Pith citation observation for arXiv:2112.07056."}