{"as_of":"2026-08-07T11:52:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:fdf1e7da559cd03a155bfaa6e23efa2a8a46fc8437f140557645d5afa206dd03","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":"2026-08-07T06:34:17.273281+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":"2026-08-07T05:44:02.642509Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":1,"source":"arxiv_reference","source_observed_at":"2026-08-05T02:28:24.338817Z","state":"measured"}],"external_citation_measurements":[{"count":0,"observed_at":"2026-08-05T02:28:24.338817Z","source":"arxiv_reference"}],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2406.14299","last_updated":"2024-06-20T13:26:06Z","snapshot_observed_at":"2026-07-06T18:34:15.291938Z","submitted_at":"2024-06-20T13:26:06Z","title":"Symplectic Stiefel manifold: tractable metrics, second-order geometry and Newton's methods","version":1},"cited_work":{"arxiv_id":"2406.14299","doi":"10.48550/arxiv.2406.14299","metadata_source":"arxiv_reference","pith_arxiv_id":"2406.14299","snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":null,"venue":"arXiv (Cornell University)","work_id":"c261c739-994d-4bbe-a940-fa7049f6087e","year":2024},"citing_paper":{"arxiv_id":"2410.22068","last_updated":"2026-05-23T07:42:14Z","snapshot_observed_at":"2026-07-06T19:41:32.754401Z","submitted_at":"2024-10-29T14:27:52Z","title":"A Riemannian gradient descent method for optimization on the indefinite Stiefel manifold","version":2},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-05-23T18:44:43.277466Z"},"links":{"cited_paper":"/paper/2406.14299","citing_paper":"/paper/2410.22068"},"observation_digest":"sha256:2beaafc6d41c800558c884bbc8b76e51c751ae620f8f0367f8b9c80966bccfcc","observation_id":"24348597-1466-45f9-bcee-4a46d5e3a42c","resolution":{"observed_at":"2026-05-23T18:45:45.903533Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2406.14299","last_updated":"2024-06-20T13:26:06Z","snapshot_observed_at":"2026-07-06T18:34:15.291938Z","submitted_at":"2024-06-20T13:26:06Z","title":"Symplectic Stiefel manifold: tractable metrics, second-order geometry and Newton's methods","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2406.14299","snapshot_observed_at":"2026-08-07T05:44:02.642509Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2506.07560","last_updated":"2025-06-09T08:56:03Z","snapshot_observed_at":"2026-08-07T05:28:19.451164Z","submitted_at":"2025-06-09T08:56:03Z","title":"Brockett cost function for symplectic eigenvalues","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-07T05:44:02.642509Z"},"links":{"cited_paper":"/paper/2406.14299","citing_paper":"/paper/2506.07560"},"observation_digest":"sha256:e86160e9ab49bd5c24537595199afb066adad0d41cc580d4c88d713b5e2490b3","observation_id":"7d35dbf1-a9ee-4108-977f-7570d1adbdf3","resolution":{"observed_at":"2026-08-07T05:44:02.642509Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2406.14299","last_updated":"2024-06-20T13:26:06Z","snapshot_observed_at":"2026-07-06T18:34:15.291938Z","submitted_at":"2024-06-20T13:26:06Z","title":"Symplectic Stiefel manifold: tractable metrics, second-order geometry and Newton's methods","version":1},"cited_work":{"arxiv_id":"2406.14299","doi":"10.48550/arxiv.2406.14299","metadata_source":"arxiv_reference","pith_arxiv_id":"2406.14299","snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":null,"venue":"arXiv (Cornell University)","work_id":"c261c739-994d-4bbe-a940-fa7049f6087e","year":2024},"citing_paper":{"arxiv_id":"2509.16113","last_updated":"2026-01-25T11:25:34Z","snapshot_observed_at":"2026-08-07T03:35:51.631352Z","submitted_at":"2025-09-19T16:01:09Z","title":"A generalized canonical metric for optimization on the indefinite Stiefel manifold","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-05-18T15:29:15.351129Z"},"links":{"cited_paper":"/paper/2406.14299","citing_paper":"/paper/2509.16113"},"observation_digest":"sha256:5c24cee053df4001932c4b003910f1d9f733124ab4bf46af71a8ae4b0e545dd1","observation_id":"0c6fd352-6261-42c2-acbc-e0d1459dd82b","resolution":{"observed_at":"2026-05-18T15:31:33.489191Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2406.14299/citation-record","integrity":"/paper/2406.14299/integrity","json":"/paper/2406.14299/citation-record.json","paper":"/paper/2406.14299"},"outbound":[],"paper":{"arxiv_id":"2406.14299","last_updated":"2024-06-20T13:26:06Z","latest_version":1,"primary_category":"math.OC","snapshot_observed_at":"2026-07-06T18:34:15.291938Z","submitted_at":"2024-06-20T13:26:06Z","title":"Symplectic Stiefel manifold: tractable metrics, second-order geometry and Newton's methods"},"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":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"thesis":"As of 7 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 3 inbound Pith citation observations for arXiv:2406.14299."}