{"as_of":"2026-08-17T09:34:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:faadcebeff4f7c014ff58882225ab040ca1b3c859547aba66cca351172563260","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":4,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":4,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-17T06:30:58.91139+00:00","state":"measured"},{"denominator":4,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":4,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-16T11:25:44.028916Z","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":"2026-08-06T15:11:41.180027Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"1407.2087","last_updated":"2014-07-03T17:51:33Z","snapshot_observed_at":"2026-08-14T23:28:01.915538Z","submitted_at":"2014-07-03T17:51:33Z","title":"Riemannian Center of Mass and so called karcher mean","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1407.2087","snapshot_observed_at":"2026-08-14T13:57:57.774581Z","title":null,"venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"1908.04233","last_updated":"2020-10-07T13:02:41Z","snapshot_observed_at":"2026-08-17T08:32:29.620520Z","submitted_at":"2019-08-12T16:37:32Z","title":"Geometrical Smeariness -- A new Phenomenon of Fr\\'echet Means","version":3},"reference_index":30,"source":"arxiv_source","source_observed_at":"2026-08-14T13:57:57.774581Z"},"links":{"cited_paper":"/paper/1407.2087","citing_paper":"/paper/1908.04233"},"observation_digest":"sha256:7192413969eba4e633da02ee122b50a24937a12ee0a3cb31a0cc9b3e40ec915b","observation_id":"2005a012-942f-42a0-925f-7e51b3f89c6b","resolution":{"observed_at":"2026-08-14T13:57:57.774581Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1407.2087","last_updated":"2014-07-03T17:51:33Z","snapshot_observed_at":"2026-08-14T23:28:01.915538Z","submitted_at":"2014-07-03T17:51:33Z","title":"Riemannian Center of Mass and so called karcher mean","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1407.2087","snapshot_observed_at":"2026-08-14T06:04:05.285835Z","title":"Riemannian Center of Mass and so called karch er mean","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"1909.00410","last_updated":"2019-09-04T07:47:42Z","snapshot_observed_at":"2026-08-17T04:35:24.318429Z","submitted_at":"2019-09-01T14:41:56Z","title":"Stability of the Cut Locus and a Central Limit Theorem for Fr\\'echet Means of Riemannian Manifolds","version":2},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-14T06:04:05.285835Z"},"links":{"cited_paper":"/paper/1407.2087","citing_paper":"/paper/1909.00410"},"observation_digest":"sha256:149315f996d903be3ed0c07d99d0b7396b7edbb55b1aac930ca253a6329c77ad","observation_id":"4d1a948b-415b-4a45-96ab-467480a418ef","resolution":{"observed_at":"2026-08-14T06:04:05.285835Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1407.2087","last_updated":"2014-07-03T17:51:33Z","snapshot_observed_at":"2026-08-14T23:28:01.915538Z","submitted_at":"2014-07-03T17:51:33Z","title":"Riemannian Center of Mass and so called karcher mean","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1407.2087","snapshot_observed_at":"2026-08-16T11:25:44.028916Z","title":null,"venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2504.15671","last_updated":"2025-07-04T07:52:33Z","snapshot_observed_at":"2026-08-16T11:18:16.710498Z","submitted_at":"2025-04-22T07:52:10Z","title":"On the approximation of the Riemannian barycenter","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-16T11:25:44.028916Z"},"links":{"cited_paper":"/paper/1407.2087","citing_paper":"/paper/2504.15671"},"observation_digest":"sha256:b32102fbce2bb652fbcd93eb435aa0da4d9b2f9d89acb724610dfd65adb2b81e","observation_id":"942055e3-6d02-4a34-ae67-ee9db8603946","resolution":{"observed_at":"2026-08-16T11:25:44.028916Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1407.2087","last_updated":"2014-07-03T17:51:33Z","snapshot_observed_at":"2026-08-14T23:28:01.915538Z","submitted_at":"2014-07-03T17:51:33Z","title":"Riemannian Center of Mass and so called karcher mean","version":1},"cited_work":{"arxiv_id":"1407.2087","doi":null,"metadata_source":"pith","pith_arxiv_id":"1407.2087","snapshot_observed_at":"2026-08-06T15:11:41.180027Z","title":"Riemannian Center of Mass and so called karcher mean","venue":"math.HO","work_id":"941a985b-af2a-40f5-9020-8716d667ff0a","year":2014},"citing_paper":{"arxiv_id":"2507.17037","last_updated":"2025-08-05T16:44:28Z","snapshot_observed_at":"2026-08-11T08:17:58.932234Z","submitted_at":"2025-07-22T21:51:03Z","title":"Convergence of discrete conformal mappings on surfaces","version":2},"reference_index":2014,"source":"pdf_text","source_observed_at":"2026-08-06T15:11:40.742377Z"},"links":{"cited_paper":"/paper/1407.2087","citing_paper":"/paper/2507.17037"},"observation_digest":"sha256:b5731e4d980dff17531e4438fd9f8cf8dc5dcee87bf5e03d362cff34018523d8","observation_id":"62538199-3795-4820-93f7-7262b1fac8c5","resolution":{"observed_at":"2026-08-06T15:11:41.184606Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/1407.2087/citation-record","integrity":"/paper/1407.2087/integrity","json":"/paper/1407.2087/citation-record.json","paper":"/paper/1407.2087"},"outbound":[],"paper":{"arxiv_id":"1407.2087","last_updated":"2014-07-03T17:51:33Z","latest_version":1,"primary_category":"math.HO","snapshot_observed_at":"2026-08-14T23:28:01.915538Z","submitted_at":"2014-07-03T17:51:33Z","title":"Riemannian Center of Mass and so called karcher mean"},"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":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"thesis":"As of 17 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 4 inbound Pith citation observations for arXiv:1407.2087."}