{"as_of":"2026-08-20T21:22:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:5372ff5a49321aba77a8627ae39c35af69afa87526a78783fc586ac45ac72afa","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":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":"2026-08-20T06:33:59.587034+00:00","state":"measured"},{"denominator":3,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":3,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-16T11:13:37.982003Z","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":"2026-07-09T06:56:05.213905Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2009.05134","last_updated":"2022-12-26T16:53:38Z","snapshot_observed_at":"2026-08-20T11:51:10.649862Z","submitted_at":"2020-09-10T20:11:31Z","title":"Computer proofs for Property (T), and SDP duality","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2009.05134","snapshot_observed_at":"2026-08-16T11:13:37.982003Z","title":"Computer proofs for property ( T ), and sdp duality","venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2504.16625","last_updated":"2025-04-23T11:31:53Z","snapshot_observed_at":"2026-08-20T15:27:05.827662Z","submitted_at":"2025-04-23T11:31:53Z","title":"Inducing spectral gaps for the cohomological Laplacians of $\\operatorname{Sp}_{2n}(\\mathbb{Z})$","version":1},"reference_index":19,"source":"arxiv_source","source_observed_at":"2026-08-16T11:13:37.982003Z"},"links":{"cited_paper":"/paper/2009.05134","citing_paper":"/paper/2504.16625"},"observation_digest":"sha256:edd84193d1f06a49698acf80c0fb12e7567bba75551b950c46a587f2b454ceb1","observation_id":"8cf973ae-298b-424c-a8dc-1ef610317a4b","resolution":{"observed_at":"2026-08-16T11:13:37.982003Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2009.05134","last_updated":"2022-12-26T16:53:38Z","snapshot_observed_at":"2026-08-20T11:51:10.649862Z","submitted_at":"2020-09-10T20:11:31Z","title":"Computer proofs for Property (T), and SDP duality","version":3},"cited_work":{"arxiv_id":"2009.05134","doi":null,"metadata_source":"pith","pith_arxiv_id":"2009.05134","snapshot_observed_at":"2026-07-09T06:56:05.213905Z","title":"Computer proofs for Property (T), and SDP duality","venue":"math.GR","work_id":"060c3a89-05a0-41ff-876e-7d592656dd28","year":2020},"citing_paper":{"arxiv_id":"2604.24738","last_updated":"2026-04-27T17:43:58Z","snapshot_observed_at":"2026-08-17T11:53:27.466565Z","submitted_at":"2026-04-27T17:43:58Z","title":"Invariant trace simplices and relative property (T)","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-05-07T17:02:54.863445Z"},"links":{"cited_paper":"/paper/2009.05134","citing_paper":"/paper/2604.24738"},"observation_digest":"sha256:79d77d07fbccaf2b3d3a4469e6c51809afe7976dcbf7c85ae601c5300070ba6b","observation_id":"ba38ef1b-a0ae-487c-b5a4-cd0cb75c52fe","resolution":{"observed_at":"2026-05-11T23:26:13.697124Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2009.05134","last_updated":"2022-12-26T16:53:38Z","snapshot_observed_at":"2026-08-20T11:51:10.649862Z","submitted_at":"2020-09-10T20:11:31Z","title":"Computer proofs for Property (T), and SDP duality","version":3},"cited_work":{"arxiv_id":"2009.05134","doi":null,"metadata_source":"pith","pith_arxiv_id":"2009.05134","snapshot_observed_at":"2026-07-09T06:56:05.213905Z","title":"Computer proofs for Property (T), and SDP duality","venue":"math.GR","work_id":"060c3a89-05a0-41ff-876e-7d592656dd28","year":2020},"citing_paper":{"arxiv_id":"2607.07587","last_updated":"2026-07-08T16:11:11Z","snapshot_observed_at":"2026-08-08T09:59:38.509285Z","submitted_at":"2026-07-08T16:11:11Z","title":"Abelianizations of finite-index subgroups of the handlebody group","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-07-09T06:54:37.719299Z"},"links":{"cited_paper":"/paper/2009.05134","citing_paper":"/paper/2607.07587"},"observation_digest":"sha256:d2ff8ba948fb1a24f4d0f9ff80b2dfe94888f9241d32dc99cf8a7e43693297cb","observation_id":"365dba27-c4a9-4e4c-bcdd-83b798829487","resolution":{"observed_at":"2026-07-09T06:56:05.216036Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2009.05134/citation-record","integrity":"/paper/2009.05134/integrity","json":"/paper/2009.05134/citation-record.json","paper":"/paper/2009.05134"},"outbound":[],"paper":{"arxiv_id":"2009.05134","last_updated":"2022-12-26T16:53:38Z","latest_version":3,"primary_category":"math.GR","snapshot_observed_at":"2026-08-20T11:51:10.649862Z","submitted_at":"2020-09-10T20:11:31Z","title":"Computer proofs for Property (T), and SDP duality"},"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":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"thesis":"As of 20 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 3 inbound Pith citation observations for arXiv:2009.05134."}