{"as_of":"2026-08-10T06:19:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:13fcfc1d58dbbedc7853dcc384899a0d98bcd8051e7cbfc8de22b7c515debb16","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":"2026-08-09T06:31:02.800959+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":"2026-08-07T15:01:09.896282Z","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":"2026-05-14T21:58:04.014002Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"1804.10738","last_updated":"2019-10-01T18:30:23Z","snapshot_observed_at":"2026-08-05T10:39:56.093180Z","submitted_at":"2018-04-28T03:57:45Z","title":"A Riemannian Corollary of Helly's Theorem","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1804.10738","snapshot_observed_at":"2026-08-07T15:01:09.896282Z","title":"Rusciano","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2505.16970","last_updated":"2025-05-22T17:50:10Z","snapshot_observed_at":"2026-08-08T01:02:59.562855Z","submitted_at":"2025-05-22T17:50:10Z","title":"Horospherically Convex Optimization on Hadamard Manifolds Part I: Analysis and Algorithms","version":1},"reference_index":93,"source":"pdf_text","source_observed_at":"2026-08-07T15:01:09.896282Z"},"links":{"cited_paper":"/paper/1804.10738","citing_paper":"/paper/2505.16970"},"observation_digest":"sha256:e84028144d7e415771cccda5f23a75b4db57fe6f99695ce4af0ae3b85cf42a5c","observation_id":"246703d8-2538-44f4-b620-6031b5b2f00d","resolution":{"observed_at":"2026-08-07T15:01:09.896282Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1804.10738","last_updated":"2019-10-01T18:30:23Z","snapshot_observed_at":"2026-08-05T10:39:56.093180Z","submitted_at":"2018-04-28T03:57:45Z","title":"A Riemannian Corollary of Helly's Theorem","version":2},"cited_work":{"arxiv_id":"1804.10738","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"1804.10738","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"A Riemannian Corollary of Helly’s theorem","venue":null,"work_id":"19910fc8-5972-4726-ac9e-01c43e4f3793","year":2018},"citing_paper":{"arxiv_id":"2604.18242","last_updated":"2026-05-13T09:53:29Z","snapshot_observed_at":"2026-08-08T15:51:07.984272Z","submitted_at":"2026-04-20T13:23:57Z","title":"Horospherical Depth and Busemann Median on Hadamard Manifolds","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-05-10T03:32:41.493738Z"},"links":{"cited_paper":"/paper/1804.10738","citing_paper":"/paper/2604.18242"},"observation_digest":"sha256:b752e1d1af8099a2973a81b4c3906ea8481e7a7eb2bbf931be40e774b4fb635c","observation_id":"9c73d89b-1e8b-4272-82f0-448827940660","resolution":{"observed_at":"2026-05-11T12:31:03.829981Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1804.10738","last_updated":"2019-10-01T18:30:23Z","snapshot_observed_at":"2026-08-05T10:39:56.093180Z","submitted_at":"2018-04-28T03:57:45Z","title":"A Riemannian Corollary of Helly's Theorem","version":2},"cited_work":{"arxiv_id":"1804.10738","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"1804.10738","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"A Riemannian Corollary of Helly’s theorem","venue":null,"work_id":"19910fc8-5972-4726-ac9e-01c43e4f3793","year":2018},"citing_paper":{"arxiv_id":"2604.18242","last_updated":"2026-05-13T09:53:29Z","snapshot_observed_at":"2026-08-08T15:51:07.984272Z","submitted_at":"2026-04-20T13:23:57Z","title":"Horospherical Depth and Busemann Median on Hadamard Manifolds","version":2},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-05-14T21:50:20.941853Z"},"links":{"cited_paper":"/paper/1804.10738","citing_paper":"/paper/2604.18242"},"observation_digest":"sha256:d4485dd09a883c35de978d32f9b7364af00714ad2933aecb2932a39371d65922","observation_id":"8fb41d42-2e3c-4a51-a79d-60027c23800d","resolution":{"observed_at":"2026-05-14T21:58:04.017706Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/1804.10738/citation-record","integrity":"/paper/1804.10738/integrity","json":"/paper/1804.10738/citation-record.json","paper":"/paper/1804.10738"},"outbound":[],"paper":{"arxiv_id":"1804.10738","last_updated":"2019-10-01T18:30:23Z","latest_version":2,"primary_category":"math.MG","snapshot_observed_at":"2026-08-05T10:39:56.093180Z","submitted_at":"2018-04-28T03:57:45Z","title":"A Riemannian Corollary of Helly's Theorem"},"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":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"thesis":"As of 10 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 3 inbound Pith citation observations for arXiv:1804.10738."}