{"as_of":"2026-08-11T19:06:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:1bbf4bbfe3c7cda6285f425da6e6425b2114bec8de411fc16367876fa2f849ed","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":"2026-08-11T06:34:44.6726+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":"2026-05-13T22:27:58.747232Z","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":"2026-05-13T22:28:21.192398Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2504.06186","last_updated":"2025-04-08T16:28:07Z","snapshot_observed_at":"2026-08-07T16:07:27.584743Z","submitted_at":"2025-04-08T16:28:07Z","title":"Equivalence between the timelike Brunn-Minkowski inequality and timelike Bakry-\\'Emery-Ricci lower bound on weighted globally hyperbolic spacetimes","version":1},"cited_work":{"arxiv_id":"2504.06186","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2504.06186","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Farooqui","venue":null,"work_id":"0ff85a82-24bb-43d8-8b08-aa9244c059c6","year":2025},"citing_paper":{"arxiv_id":"2604.00562","last_updated":"2026-04-20T05:36:47Z","snapshot_observed_at":"2026-08-10T09:58:42.582359Z","submitted_at":"2026-04-01T07:12:50Z","title":"Rigidity of the Borell-Brascamp-Lieb Inequality on Weighted Riemannian Manifolds","version":2},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-05-13T22:27:58.747232Z"},"links":{"cited_paper":"/paper/2504.06186","citing_paper":"/paper/2604.00562"},"observation_digest":"sha256:ea1529961944b3bc7274326262ee49b2e6cf919b77b670619484857e8da503ec","observation_id":"0b93ae45-7a19-4b73-9d91-f78a7453d0a9","resolution":{"observed_at":"2026-05-13T22:28:21.194155Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2504.06186","last_updated":"2025-04-08T16:28:07Z","snapshot_observed_at":"2026-08-07T16:07:27.584743Z","submitted_at":"2025-04-08T16:28:07Z","title":"Equivalence between the timelike Brunn-Minkowski inequality and timelike Bakry-\\'Emery-Ricci lower bound on weighted globally hyperbolic spacetimes","version":1},"cited_work":{"arxiv_id":"2504.06186","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2504.06186","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Farooqui","venue":null,"work_id":"0ff85a82-24bb-43d8-8b08-aa9244c059c6","year":2025},"citing_paper":{"arxiv_id":"2604.11766","last_updated":"2026-04-13T17:39:18Z","snapshot_observed_at":"2026-08-11T05:05:16.679860Z","submitted_at":"2026-04-13T17:39:18Z","title":"The equivalence between timelike Ricci curvature and the timelike Brunn Minkowski inequality on synthetic Lorentzian spaces","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-05-10T15:56:39.527601Z"},"links":{"cited_paper":"/paper/2504.06186","citing_paper":"/paper/2604.11766"},"observation_digest":"sha256:b38e9049928be12387a55e750d35569c7f586ce1f83b84a78760c9a5eb91c36a","observation_id":"9f9a4469-8669-4c10-aac6-2fba2b333f38","resolution":{"observed_at":"2026-05-11T09:36:02.042839Z","resolver_source":"arxiv_id","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2504.06186/citation-record","integrity":"/paper/2504.06186/integrity","json":"/paper/2504.06186/citation-record.json","paper":"/paper/2504.06186"},"outbound":[],"paper":{"arxiv_id":"2504.06186","last_updated":"2025-04-08T16:28:07Z","latest_version":1,"primary_category":"math.MG","snapshot_observed_at":"2026-08-07T16:07:27.584743Z","submitted_at":"2025-04-08T16:28:07Z","title":"Equivalence between the timelike Brunn-Minkowski inequality and timelike Bakry-\\'Emery-Ricci lower bound on weighted globally hyperbolic spacetimes"},"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":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"thesis":"As of 11 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 2 inbound Pith citation observations for arXiv:2504.06186."}