{"as_of":"2026-08-08T11:03:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:e7c5e06db55aee057fb7beaaa2ec65a0efe9d81fc45b63b3d4fbbcd0fd714a1b","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":"2026-08-08T06:32:00.761636+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":"2026-08-07T13:43:59.104595Z","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":"2026-05-21T09:39:57.403561Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2204.13665","last_updated":"2023-11-20T23:45:51Z","snapshot_observed_at":"2026-07-06T13:04:49.115605Z","submitted_at":"2022-04-28T17:28:04Z","title":"Theory and Algorithms for Diffusion Processes on Riemannian Manifolds","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2204.13665","snapshot_observed_at":"2026-08-07T13:43:59.104595Z","title":"Theory and algorithms for diffusion processes on Riemannian manifolds.arXiv preprint arXiv:2204.13665, 2022","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2505.21640","last_updated":"2025-05-27T18:12:29Z","snapshot_observed_at":"2026-08-07T13:23:43.101984Z","submitted_at":"2025-05-27T18:12:29Z","title":"Efficient Diffusion Models for Symmetric Manifolds","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-07T13:43:59.104595Z"},"links":{"cited_paper":"/paper/2204.13665","citing_paper":"/paper/2505.21640"},"observation_digest":"sha256:b9a53a2835da10c453b68a65acf9dd0fee3d03c097d473c5d248b2df1a52bd94","observation_id":"bee96693-fa82-4bb2-a29a-25e70ad7896b","resolution":{"observed_at":"2026-08-07T13:43:59.104595Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2204.13665","last_updated":"2023-11-20T23:45:51Z","snapshot_observed_at":"2026-07-06T13:04:49.115605Z","submitted_at":"2022-04-28T17:28:04Z","title":"Theory and Algorithms for Diffusion Processes on Riemannian Manifolds","version":3},"cited_work":{"arxiv_id":"2204.13665","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2204.13665","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Theory and algorithms for diffusion processes on riemannian manifolds","venue":null,"work_id":"bb47e35e-a137-422c-a82f-560c0af007f3","year":2022},"citing_paper":{"arxiv_id":"2604.07213","last_updated":"2026-05-20T13:49:31Z","snapshot_observed_at":"2026-07-06T22:55:33.502756Z","submitted_at":"2026-04-08T15:34:21Z","title":"Diffusion Processes on Implicit Manifolds","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-05-10T19:12:47.724914Z"},"links":{"cited_paper":"/paper/2204.13665","citing_paper":"/paper/2604.07213"},"observation_digest":"sha256:d67d623772d758bf625b880b6d9c2233cb798e26caadbe6e93d9a05dae3fd2fb","observation_id":"21c9ff3b-a1b1-4c60-9ec4-a7bf1976d7f7","resolution":{"observed_at":"2026-05-10T23:20:52.703960Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2204.13665","last_updated":"2023-11-20T23:45:51Z","snapshot_observed_at":"2026-07-06T13:04:49.115605Z","submitted_at":"2022-04-28T17:28:04Z","title":"Theory and Algorithms for Diffusion Processes on Riemannian Manifolds","version":3},"cited_work":{"arxiv_id":"2204.13665","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2204.13665","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Theory and algorithms for diffusion processes on riemannian manifolds","venue":null,"work_id":"bb47e35e-a137-422c-a82f-560c0af007f3","year":2022},"citing_paper":{"arxiv_id":"2604.07213","last_updated":"2026-05-20T13:49:31Z","snapshot_observed_at":"2026-07-06T22:55:33.502756Z","submitted_at":"2026-04-08T15:34:21Z","title":"Diffusion Processes on Implicit Manifolds","version":2},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-05-21T09:37:30.479444Z"},"links":{"cited_paper":"/paper/2204.13665","citing_paper":"/paper/2604.07213"},"observation_digest":"sha256:1ced0f612cc9a2fef445d5c162013c108c927991083db208ecc3993f06f9619b","observation_id":"dc6e2cc0-a0e5-4b80-91ec-aa9e440d5530","resolution":{"observed_at":"2026-05-21T09:39:57.405391Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2204.13665","last_updated":"2023-11-20T23:45:51Z","snapshot_observed_at":"2026-07-06T13:04:49.115605Z","submitted_at":"2022-04-28T17:28:04Z","title":"Theory and Algorithms for Diffusion Processes on Riemannian Manifolds","version":3},"cited_work":{"arxiv_id":"2204.13665","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2204.13665","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Theory and algorithms for diffusion processes on riemannian manifolds","venue":null,"work_id":"bb47e35e-a137-422c-a82f-560c0af007f3","year":2022},"citing_paper":{"arxiv_id":"2605.04480","last_updated":"2026-05-06T04:08:03Z","snapshot_observed_at":"2026-07-06T23:17:13.770090Z","submitted_at":"2026-05-06T04:08:03Z","title":"Geometric Milstein Scheme for Stochastic Differential Equations on SO(n) and SE(n)","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-05-08T16:51:30.623074Z"},"links":{"cited_paper":"/paper/2204.13665","citing_paper":"/paper/2605.04480"},"observation_digest":"sha256:3c255247350fc9765a6b50ca3b1df9a4845e3e9771665f8be5af332eb6449478","observation_id":"6fc8fa5e-de8b-4a43-b7c0-4bcb7dd82e58","resolution":{"observed_at":"2026-05-11T18:01:05.455577Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2204.13665/citation-record","integrity":"/paper/2204.13665/integrity","json":"/paper/2204.13665/citation-record.json","paper":"/paper/2204.13665"},"outbound":[],"paper":{"arxiv_id":"2204.13665","last_updated":"2023-11-20T23:45:51Z","latest_version":3,"primary_category":"math.PR","snapshot_observed_at":"2026-07-06T13:04:49.115605Z","submitted_at":"2022-04-28T17:28:04Z","title":"Theory and Algorithms for Diffusion Processes on Riemannian Manifolds"},"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":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"thesis":"As of 8 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 4 inbound Pith citation observations for arXiv:2204.13665."}