{"as_of":"2026-08-07T11:37:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:238d252fbe00a427793110d7dfb3b9d99690a2843a448c2d39e292b279731f6f","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":"2026-08-07T06:34:17.273281+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":"2026-08-01T12:53:22.658240Z","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":"0907.2051","last_updated":"2009-07-12T19:28:58Z","snapshot_observed_at":"2026-07-06T01:58:41.404529Z","submitted_at":"2009-07-12T19:28:58Z","title":"Slightly improved sum-product estimates in fields of prime order","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"0907.2051","snapshot_observed_at":"2026-08-01T12:53:22.658240Z","title":"arXiv preprint arXiv:0907.2051 , year=","venue":null,"work_id":null,"year":2051},"citing_paper":{"arxiv_id":"2607.19342","last_updated":"2026-07-21T17:59:04Z","snapshot_observed_at":"2026-08-06T11:24:23.738085Z","submitted_at":"2026-07-21T17:59:04Z","title":"Improved Strongly Polynomial Work-Span Tradeoffs for Directed Single Source Shortest Paths","version":1},"reference_index":49,"source":"arxiv_source","source_observed_at":"2026-08-01T12:53:22.658240Z"},"links":{"cited_paper":"/paper/0907.2051","citing_paper":"/paper/2607.19342"},"observation_digest":"sha256:27a8641bb6a299dea950caffbd26c52d022a5379aef7f7807d62531556d5ed34","observation_id":"98ae9e3d-ac94-4582-9d1b-4a3c19b9b4c2","resolution":{"observed_at":"2026-08-01T12:53:22.658240Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/0907.2051/citation-record","integrity":"/paper/0907.2051/integrity","json":"/paper/0907.2051/citation-record.json","paper":"/paper/0907.2051"},"outbound":[],"paper":{"arxiv_id":"0907.2051","last_updated":"2009-07-12T19:28:58Z","latest_version":1,"primary_category":"math.NT","snapshot_observed_at":"2026-07-06T01:58:41.404529Z","submitted_at":"2009-07-12T19:28:58Z","title":"Slightly improved sum-product estimates in fields of prime order"},"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":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"thesis":"As of 7 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 1 inbound Pith citation observation for arXiv:0907.2051."}