{"as_of":"2026-08-12T09:32:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:2f819167f53cd95506193c6e16d7f757cf85d8a64038924d1c361aa5568fc53b","coverage":[{"denominator":2,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":2,"source":"paper_references, paper_reference_links","source_observed_at":"2026-07-15T11:43:56.243427Z","state":"measured"},{"denominator":3,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":3,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-12T06:34:41.77262+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":"2026-08-07T10:44:07.921961Z","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":"2026-08-07T10:44:11.532663Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2604.01316","last_updated":"2026-07-14T00:44:20Z","snapshot_observed_at":"2026-08-09T18:08:33.248675Z","submitted_at":"2026-04-01T18:42:20Z","title":"Non-vanishing for quartic Hecke $L$-functions and ranks of elliptic curves","version":2},"cited_work":{"arxiv_id":"2604.01316","doi":null,"metadata_source":"pith","pith_arxiv_id":"2604.01316","snapshot_observed_at":"2026-08-07T10:44:11.532663Z","title":"Non-vanishing for quartic Hecke $L$-functions and ranks of elliptic curves","venue":"math.NT","work_id":"b9d2abfd-a250-4f7e-a93d-c2979a95203f","year":2026},"citing_paper":{"arxiv_id":"2608.06286","last_updated":"2026-08-06T17:12:01Z","snapshot_observed_at":"2026-08-12T04:02:27.726748Z","submitted_at":"2026-08-06T17:12:01Z","title":"Average analytic rank for the $L$-functions of the elliptic curves $y^2=x^3-dx$","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-07T10:44:07.921961Z"},"links":{"cited_paper":"/paper/2604.01316","citing_paper":"/paper/2608.06286"},"observation_digest":"sha256:3e04e33cc6226a9e35f3c9526f4ce0e881afe7085e468b17453af981e60f6e0e","observation_id":"6c9c957f-fee4-497d-8082-66d1597dc3b0","resolution":{"observed_at":"2026-08-07T10:44:11.572026Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2604.01316/citation-record","integrity":"/paper/2604.01316/integrity","json":"/paper/2604.01316/citation-record.json","paper":"/paper/2604.01316"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-15T11:43:56.243427Z","title":"Miskolc Math","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2604.01316","last_updated":"2026-07-14T00:44:20Z","snapshot_observed_at":"2026-08-09T18:08:33.248675Z","submitted_at":"2026-04-01T18:42:20Z","title":"Non-vanishing for quartic Hecke $L$-functions and ranks of elliptic curves","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-07-15T11:43:56.243427Z"},"links":{"citing_paper":"/paper/2604.01316"},"observation_digest":"sha256:fb0d2b1e64fd4b1a97b10e5cc5d14434a744dccd29befc650fc5f050182e12cd","observation_id":"26c7d338-d229-40c1-9c3b-98c75c318828","resolution":{"observed_at":"2026-07-15T11:43:56.243427Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-15T11:43:56.243427Z","title":"Milan J Math.83, 237–278 (2015)","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2604.01316","last_updated":"2026-07-14T00:44:20Z","snapshot_observed_at":"2026-08-09T18:08:33.248675Z","submitted_at":"2026-04-01T18:42:20Z","title":"Non-vanishing for quartic Hecke $L$-functions and ranks of elliptic curves","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-07-15T11:43:56.243427Z"},"links":{"citing_paper":"/paper/2604.01316"},"observation_digest":"sha256:67c7152152715d59c149d850234e1e18e11e591eef718af6de0d098e52b47eb0","observation_id":"0119f29b-50b6-42ed-b54a-1c3bcee7f76d","resolution":{"observed_at":"2026-07-15T11:43:56.243427Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2604.01316","last_updated":"2026-07-14T00:44:20Z","latest_version":2,"primary_category":"math.NT","snapshot_observed_at":"2026-08-09T18:08:33.248675Z","submitted_at":"2026-04-01T18:42:20Z","title":"Non-vanishing for quartic Hecke $L$-functions and ranks of elliptic curves"},"reference_resolution":{"displayed":2,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":2,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":2},"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":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"thesis":"As of 12 August 2026, this Paper Citation Record lists 2 of 2 outbound references and 1 inbound Pith citation observation for arXiv:2604.01316."}