{"as_of":"2026-08-15T22:34:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:9c7ec5cb621aafc8d46b97b87616e4978e3d7da113019d6aa67e7270570799ef","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":"2026-08-15T06:32:42.880941+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":"2026-07-31T18:23:20.270432Z","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":"2107.08563","last_updated":"2021-07-19T00:15:28Z","snapshot_observed_at":"2026-08-13T18:43:59.323561Z","submitted_at":"2021-07-19T00:15:28Z","title":"The Curvature of Graph Products","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2107.08563","snapshot_observed_at":"2026-07-31T18:23:20.270432Z","title":null,"venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2607.24322","last_updated":"2026-07-27T12:02:06Z","snapshot_observed_at":"2026-08-10T19:31:15.351306Z","submitted_at":"2026-07-27T12:02:06Z","title":"Euler Characteristics of Random Manifolds","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-07-31T18:23:20.270432Z"},"links":{"cited_paper":"/paper/2107.08563","citing_paper":"/paper/2607.24322"},"observation_digest":"sha256:03408af9801b1b336cf796481e0419dad0112405852cb5d52507ae2d203d5dba","observation_id":"4f76dc14-7b46-4b50-9334-71a5e08ff647","resolution":{"observed_at":"2026-07-31T18:23:20.270432Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2107.08563/citation-record","integrity":"/paper/2107.08563/integrity","json":"/paper/2107.08563/citation-record.json","paper":"/paper/2107.08563"},"outbound":[],"paper":{"arxiv_id":"2107.08563","last_updated":"2021-07-19T00:15:28Z","latest_version":1,"primary_category":"math.CO","snapshot_observed_at":"2026-08-13T18:43:59.323561Z","submitted_at":"2021-07-19T00:15:28Z","title":"The Curvature of Graph Products"},"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":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"thesis":"As of 15 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 1 inbound Pith citation observation for arXiv:2107.08563."}