{"as_of":"2026-08-12T21:31:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:db48ec3aeef3557f6733ed445b2d5ab613e9a80dbd00d9c7ad5679a64148d502","coverage":[{"denominator":5,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":5,"source":"paper_references, paper_reference_links","source_observed_at":"2026-05-08T13:42:35.503447Z","state":"measured"},{"denominator":7,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":7,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-12T06:34:41.77262+00:00","state":"measured"},{"denominator":2,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":2,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-12T00:29:35.580669Z","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":"2026-08-11T00:43:52.269372Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2604.21228","last_updated":"2026-04-23T02:49:27Z","snapshot_observed_at":"2026-07-06T23:07:51.979267Z","submitted_at":"2026-04-23T02:49:27Z","title":"Lean-certified four-point HRT results for three lattice points and one off-lattice point","version":1},"cited_work":{"arxiv_id":"2604.21228","doi":null,"metadata_source":"pith","pith_arxiv_id":"2604.21228","snapshot_observed_at":"2026-08-11T00:43:52.269372Z","title":"Lean-certified four-point HRT results for three lattice points and one off-lattice point","venue":"math.FA","work_id":"fa74b436-22b0-4446-829d-38a222204b50","year":2026},"citing_paper":{"arxiv_id":"2608.07604","last_updated":"2026-08-06T18:06:37Z","snapshot_observed_at":"2026-08-12T21:13:09.715953Z","submitted_at":"2026-08-06T18:06:37Z","title":"An intrinsically subcritical four-point counterexample","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-11T00:43:52.208057Z"},"links":{"cited_paper":"/paper/2604.21228","citing_paper":"/paper/2608.07604"},"observation_digest":"sha256:a88738a9ce9dd63948cfffbc594f9c70d387851cec0cbc495bf109de409b23ad","observation_id":"ac3f4a21-18e8-4d30-bd19-bee17a44f01b","resolution":{"observed_at":"2026-08-11T00:43:52.277521Z","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"}},{"citation":{"cited_paper":{"arxiv_id":"2604.21228","last_updated":"2026-04-23T02:49:27Z","snapshot_observed_at":"2026-07-06T23:07:51.979267Z","submitted_at":"2026-04-23T02:49:27Z","title":"Lean-certified four-point HRT results for three lattice points and one off-lattice point","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2604.21228","snapshot_observed_at":"2026-08-12T00:29:35.580669Z","title":null,"venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2608.08190","last_updated":"2026-08-08T15:32:24Z","snapshot_observed_at":"2026-08-12T21:15:02.022719Z","submitted_at":"2026-08-08T15:32:24Z","title":"The Minimum Cardinality of a Dependent Finite Gabor System Is Four","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-12T00:29:35.580669Z"},"links":{"cited_paper":"/paper/2604.21228","citing_paper":"/paper/2608.08190"},"observation_digest":"sha256:b8e2e96fb1c327f5effa44499902d9fb5fb990129cf89bf9d361243c8e6def44","observation_id":"489123ea-0c3e-485f-a65c-db4b2665059f","resolution":{"observed_at":"2026-08-12T00:29:35.580669Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2604.21228/citation-record","integrity":"/paper/2604.21228/integrity","json":"/paper/2604.21228/citation-record.json","paper":"/paper/2604.21228"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"42e3a28e-0094-43b5-b742-f7ebd26e65e9","year":1999},"citing_paper":{"arxiv_id":"2604.21228","last_updated":"2026-04-23T02:49:27Z","snapshot_observed_at":"2026-07-06T23:07:51.979267Z","submitted_at":"2026-04-23T02:49:27Z","title":"Lean-certified four-point HRT results for three lattice points and one off-lattice point","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-05-08T13:42:35.503447Z"},"links":{"citing_paper":"/paper/2604.21228"},"observation_digest":"sha256:a680705ab262141c768c168480175b820927fa29f7ab52a17961e198d7d4218b","observation_id":"d6110035-4576-4958-80f9-995e77ccaf0b","resolution":{"observed_at":"2026-05-26T12:12:17.679487Z","resolver_source":"raw_fallback","status":"unresolved"},"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"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Gröchenig,Foundations of Time-Frequency Analysis, Applied and Numerical Harmonic Analysis, Birkhäuser, Boston","venue":null,"work_id":"5ae96cb9-e63b-44db-84ee-da530d3d9b09","year":2001},"citing_paper":{"arxiv_id":"2604.21228","last_updated":"2026-04-23T02:49:27Z","snapshot_observed_at":"2026-07-06T23:07:51.979267Z","submitted_at":"2026-04-23T02:49:27Z","title":"Lean-certified four-point HRT results for three lattice points and one off-lattice point","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-05-08T13:42:35.503447Z"},"links":{"citing_paper":"/paper/2604.21228"},"observation_digest":"sha256:c4bf531013a4699a804a352da2cac813a2b74581cbe672ca391a026f1c67f5d1","observation_id":"fb9e5e0a-9dae-4aa3-b484-b0bf5b81012d","resolution":{"observed_at":"2026-05-26T12:12:17.675996Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"51d225b3-f57f-45eb-bb14-353321543692","year":1996},"citing_paper":{"arxiv_id":"2604.21228","last_updated":"2026-04-23T02:49:27Z","snapshot_observed_at":"2026-07-06T23:07:51.979267Z","submitted_at":"2026-04-23T02:49:27Z","title":"Lean-certified four-point HRT results for three lattice points and one off-lattice point","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-05-08T13:42:35.503447Z"},"links":{"citing_paper":"/paper/2604.21228"},"observation_digest":"sha256:12f3eacdec4d00451e548a659ac414c263b33719f5a4c9dcf299184160ae9f51","observation_id":"4fa56926-cc44-4e7f-9ecf-45b71f72272d","resolution":{"observed_at":"2026-05-26T12:12:17.682912Z","resolver_source":"raw_fallback","status":"unresolved"},"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"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"559d1418-17c2-4935-a780-ee7439981900","year":1999},"citing_paper":{"arxiv_id":"2604.21228","last_updated":"2026-04-23T02:49:27Z","snapshot_observed_at":"2026-07-06T23:07:51.979267Z","submitted_at":"2026-04-23T02:49:27Z","title":"Lean-certified four-point HRT results for three lattice points and one off-lattice point","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-05-08T13:42:35.503447Z"},"links":{"citing_paper":"/paper/2604.21228"},"observation_digest":"sha256:3c68716851d4d67c2b718a454f2cd769d56a5972025c24455047e7bc1d1aa37d","observation_id":"fed197b3-289a-46ba-b137-c54cb6355067","resolution":{"observed_at":"2026-05-26T12:12:17.686295Z","resolver_source":"raw_fallback","status":"unresolved"},"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"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Ramanathan and T","venue":null,"work_id":"45422091-cbfb-492e-a888-fc34750f6abc","year":1995},"citing_paper":{"arxiv_id":"2604.21228","last_updated":"2026-04-23T02:49:27Z","snapshot_observed_at":"2026-07-06T23:07:51.979267Z","submitted_at":"2026-04-23T02:49:27Z","title":"Lean-certified four-point HRT results for three lattice points and one off-lattice point","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-05-08T13:42:35.503447Z"},"links":{"citing_paper":"/paper/2604.21228"},"observation_digest":"sha256:39e053b2faf8293f02fc3bc9a9b993e2ecaa9a442256cff730766cbf413e9be7","observation_id":"b3cc174a-f053-4aad-ba8d-747e9a8a14e2","resolution":{"observed_at":"2026-05-26T12:12:17.689371Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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"}}],"paper":{"arxiv_id":"2604.21228","last_updated":"2026-04-23T02:49:27Z","latest_version":1,"primary_category":"math.FA","snapshot_observed_at":"2026-07-06T23:07:51.979267Z","submitted_at":"2026-04-23T02:49:27Z","title":"Lean-certified four-point HRT results for three lattice points and one off-lattice point"},"reference_resolution":{"displayed":5,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":3,"verified_exact":0,"verified_fuzzy":2},"total_outbound_references":5},"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 5 of 5 outbound references and 2 inbound Pith citation observations for arXiv:2604.21228."}