{"as_of":"2026-08-17T04:00:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:8b997b5f6b3f1e9dbc30c51ae8980d8a8c31545c5a1a8e9f6b31632d458c8958","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":"2026-08-16T06:30:59.297886+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":"2026-08-14T15:12:26.901311Z","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":"2026-08-14T15:12:27.070950Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"1412.7640","last_updated":"2014-12-24T10:46:16Z","snapshot_observed_at":"2026-08-14T23:06:11.804630Z","submitted_at":"2014-12-24T10:46:16Z","title":"Ergodic theorems with arithmetical weights","version":1},"cited_work":{"arxiv_id":"1412.7640","doi":null,"metadata_source":"pith","pith_arxiv_id":"1412.7640","snapshot_observed_at":"2026-08-14T15:12:27.070950Z","title":"Ergodic theorems with arithmetical weights","venue":"math.DS","work_id":"9d7d89b4-986e-4f30-b0e2-1943de0b6537","year":2014},"citing_paper":{"arxiv_id":"1908.02281","last_updated":"2019-08-05T18:11:44Z","snapshot_observed_at":"2026-08-16T08:19:21.410153Z","submitted_at":"2019-08-05T18:11:44Z","title":"Simple proof of Bourgain bilinear ergodic theorem and its extension to polynomials and polynomials in primes","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-14T15:12:26.901311Z"},"links":{"cited_paper":"/paper/1412.7640","citing_paper":"/paper/1908.02281"},"observation_digest":"sha256:def735b45c58769b269c91e9d495c00f87a4de3e78c9590edc43df36758b5239","observation_id":"e015392c-7e01-494d-a369-3d6d1e2a869f","resolution":{"observed_at":"2026-08-14T15:12:27.079422Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/1412.7640/citation-record","integrity":"/paper/1412.7640/integrity","json":"/paper/1412.7640/citation-record.json","paper":"/paper/1412.7640"},"outbound":[],"paper":{"arxiv_id":"1412.7640","last_updated":"2014-12-24T10:46:16Z","latest_version":1,"primary_category":"math.DS","snapshot_observed_at":"2026-08-14T23:06:11.804630Z","submitted_at":"2014-12-24T10:46:16Z","title":"Ergodic theorems with arithmetical weights"},"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":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"thesis":"As of 17 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 1 inbound Pith citation observation for arXiv:1412.7640."}