{"as_of":"2026-08-08T12:12:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:0a49706831a9ec2232242324d0d86725b34416a6cf20f03f8b070d2f3f00fb4e","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":"2026-08-08T06:32:00.761636+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":"2026-07-10T07:05:56.044643Z","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":"2026-07-10T07:06:52.558937Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2509.21869","last_updated":"2026-06-22T18:48:39Z","snapshot_observed_at":"2026-08-06T22:45:38.363213Z","submitted_at":"2025-09-26T04:53:55Z","title":"Two-ends Furstenberg estimates in the plane","version":3},"cited_work":{"arxiv_id":"2509.21869","doi":null,"metadata_source":"pith","pith_arxiv_id":"2509.21869","snapshot_observed_at":"2026-07-10T07:06:52.558937Z","title":"Two-ends Furstenberg estimates in the plane","venue":"math.CA","work_id":"afb8d79d-8026-4d33-906f-2ae2176a5a43","year":2025},"citing_paper":{"arxiv_id":"2607.08461","last_updated":"2026-07-09T13:20:12Z","snapshot_observed_at":"2026-08-08T01:22:27.084755Z","submitted_at":"2026-07-09T13:20:12Z","title":"Two-ends Furstenberg inequality for transversal families and applications to Fourier decay","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-07-10T07:05:56.044643Z"},"links":{"cited_paper":"/paper/2509.21869","citing_paper":"/paper/2607.08461"},"observation_digest":"sha256:33b63bd2a7213bce7fad2ab8c120df77c6de7b1001cb0dd2e323d0b8f118362e","observation_id":"ccf8f7a6-eb7b-452b-b533-e7cce7d46d6b","resolution":{"observed_at":"2026-07-10T07:06:52.560446Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2509.21869/citation-record","integrity":"/paper/2509.21869/integrity","json":"/paper/2509.21869/citation-record.json","paper":"/paper/2509.21869"},"outbound":[],"paper":{"arxiv_id":"2509.21869","last_updated":"2026-06-22T18:48:39Z","latest_version":3,"primary_category":"math.CA","snapshot_observed_at":"2026-08-06T22:45:38.363213Z","submitted_at":"2025-09-26T04:53:55Z","title":"Two-ends Furstenberg estimates in the plane"},"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":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"thesis":"As of 8 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 1 inbound Pith citation observation for arXiv:2509.21869."}