{"as_of":"2026-08-19T11:33:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:bff3244ed22dd986ec12b77f6efd81dce25181d02fd76fb067848643c2bc48e5","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":"2026-08-19T06:32:44.657259+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":"2026-06-30T16:33:24.857572Z","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":"2026-06-30T16:35:12.349881Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2209.03269","last_updated":"2022-09-07T16:19:06Z","snapshot_observed_at":"2026-08-17T21:16:20.358985Z","submitted_at":"2022-09-07T16:19:06Z","title":"Manifold Free Riemannian Optimization","version":1},"cited_work":{"arxiv_id":"2209.03269","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2209.03269","snapshot_observed_at":"2026-06-30T16:35:12.349881Z","title":"Manifold free riemannian optimization","venue":null,"work_id":"7d364ac4-9995-4b52-aaff-967808ab06c8","year":2022},"citing_paper":{"arxiv_id":"2510.21033","last_updated":"2026-08-14T22:41:31Z","snapshot_observed_at":"2026-08-19T11:12:14.239233Z","submitted_at":"2025-10-23T22:34:55Z","title":"Iso-Riemannian Optimization on Learned Data Manifolds","version":2},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-05-18T04:05:04.320292Z"},"links":{"cited_paper":"/paper/2209.03269","citing_paper":"/paper/2510.21033"},"observation_digest":"sha256:6a0449881729dd23758a815f884898dd3f969cd0e69a5a55c1e42608e6a43a35","observation_id":"073ce452-7c49-40da-a4ae-63deeb73bcfe","resolution":{"observed_at":"2026-05-18T04:05:50.841236Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2209.03269","last_updated":"2022-09-07T16:19:06Z","snapshot_observed_at":"2026-08-17T21:16:20.358985Z","submitted_at":"2022-09-07T16:19:06Z","title":"Manifold Free Riemannian Optimization","version":1},"cited_work":{"arxiv_id":"2209.03269","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2209.03269","snapshot_observed_at":"2026-06-30T16:35:12.349881Z","title":"Manifold free riemannian optimization","venue":null,"work_id":"7d364ac4-9995-4b52-aaff-967808ab06c8","year":2022},"citing_paper":{"arxiv_id":"2605.24113","last_updated":"2026-05-22T18:21:49Z","snapshot_observed_at":"2026-08-13T14:36:00.072256Z","submitted_at":"2026-05-22T18:21:49Z","title":"Riemannian Archetypal Analysis: Interpretable non-linear data analysis on deformed star distributions","version":1},"reference_index":62,"source":"pdf_text","source_observed_at":"2026-06-30T16:33:24.857572Z"},"links":{"cited_paper":"/paper/2209.03269","citing_paper":"/paper/2605.24113"},"observation_digest":"sha256:b025c88254dae29666cd14ede46a2118afe65ef476b6ac4407c55edbc4902d41","observation_id":"00310718-65dd-4de0-a58f-fbb16ff7ac64","resolution":{"observed_at":"2026-06-30T16:35:12.351265Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2209.03269/citation-record","integrity":"/paper/2209.03269/integrity","json":"/paper/2209.03269/citation-record.json","paper":"/paper/2209.03269"},"outbound":[],"paper":{"arxiv_id":"2209.03269","last_updated":"2022-09-07T16:19:06Z","latest_version":1,"primary_category":"math.OC","snapshot_observed_at":"2026-08-17T21:16:20.358985Z","submitted_at":"2022-09-07T16:19:06Z","title":"Manifold Free Riemannian Optimization"},"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":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"thesis":"As of 19 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 2 inbound Pith citation observations for arXiv:2209.03269."}