{"as_of":"2026-08-22T20:40:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:93dd9b058f1a576fe7d9f1df323c490dd0251ced37bd50b83f38217af3eb6556","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":2,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":2,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-22T06:32:14.747728+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":"2026-08-02T07:13:17.742311Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"arxiv_reference","source_observed_at":"2026-05-11T09:11:04.857353Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"1909.04772","last_updated":"2021-04-19T20:02:03Z","snapshot_observed_at":"2026-08-05T12:17:54.185833Z","submitted_at":"2019-09-10T21:55:27Z","title":"Dual linear programming bounds for sphere packing via modular forms","version":2},"cited_work":{"arxiv_id":"1909.04772","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"1909.04772","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Cohn and N","venue":null,"work_id":"688b1c81-c8ae-4cba-a96a-5e0e96cecd61","year":2022},"citing_paper":{"arxiv_id":"2604.10914","last_updated":"2026-04-13T02:32:05Z","snapshot_observed_at":"2026-08-15T01:08:53.436936Z","submitted_at":"2026-04-13T02:32:05Z","title":"Cusp Form Dimensions, Lattice Uniqueness, and LP Sharpness for Sphere Packing in Dimensions 8 and 24","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-05-10T16:11:05.165028Z"},"links":{"cited_paper":"/paper/1909.04772","citing_paper":"/paper/2604.10914"},"observation_digest":"sha256:9c4e87430233a6d44ff589ffc5c81bc69567553c6b79e52100763972d0a645b5","observation_id":"34d8405d-4cc8-4939-9093-cbb9c943c065","resolution":{"observed_at":"2026-05-11T09:11:04.915429Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1909.04772","last_updated":"2021-04-19T20:02:03Z","snapshot_observed_at":"2026-08-05T12:17:54.185833Z","submitted_at":"2019-09-10T21:55:27Z","title":"Dual linear programming bounds for sphere packing via modular forms","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1909.04772","snapshot_observed_at":"2026-08-02T07:13:17.742311Z","title":"Cohn and N","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2607.11319","last_updated":"2026-07-15T20:46:54Z","snapshot_observed_at":"2026-08-17T23:27:25.808479Z","submitted_at":"2026-07-13T09:37:13Z","title":"A dual linear programming bound for sphere packing in dimension 36","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-02T07:13:17.742311Z"},"links":{"cited_paper":"/paper/1909.04772","citing_paper":"/paper/2607.11319"},"observation_digest":"sha256:3883ea29dd869cb86e3671628375247ee36f60614608393a45c4423acc96ca75","observation_id":"05178b3c-042c-4b54-ac45-4c7660ea3490","resolution":{"observed_at":"2026-08-02T07:13:17.742311Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/1909.04772/citation-record","integrity":"/paper/1909.04772/integrity","json":"/paper/1909.04772/citation-record.json","paper":"/paper/1909.04772"},"outbound":[],"paper":{"arxiv_id":"1909.04772","last_updated":"2021-04-19T20:02:03Z","latest_version":2,"primary_category":"math.MG","snapshot_observed_at":"2026-08-05T12:17:54.185833Z","submitted_at":"2019-09-10T21:55:27Z","title":"Dual linear programming bounds for sphere packing via modular forms"},"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":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"thesis":"As of 22 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 2 inbound Pith citation observations for arXiv:1909.04772."}