{"as_of":"2026-08-15T10:42:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:5dc1cf401f52cacc169977c3b3daa0efdab6cf81c05684bfd027ffe972785f77","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":7,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":7,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-15T06:32:42.880941+00:00","state":"measured"},{"denominator":7,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":7,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-06T22:48:33.600507Z","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":"2026-07-03T16:08:37.062692Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2303.04831","last_updated":"2024-11-14T16:55:48Z","snapshot_observed_at":"2026-08-13T12:28:52.377953Z","submitted_at":"2023-03-08T19:10:01Z","title":"Richardson varieties, projected Richardson varieties and positroid varieties","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2303.04831","snapshot_observed_at":"2026-08-06T22:48:33.600507Z","title":"Richardson varieties, projected R ichardson varieties and positroid varieties","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2506.20792","last_updated":"2025-06-25T19:31:57Z","snapshot_observed_at":"2026-08-13T23:21:09.641524Z","submitted_at":"2025-06-25T19:31:57Z","title":"Richardson tableaux and components of Springer fibers equal to Richardson varieties","version":1},"reference_index":45,"source":"arxiv_source","source_observed_at":"2026-08-06T22:48:33.600507Z"},"links":{"cited_paper":"/paper/2303.04831","citing_paper":"/paper/2506.20792"},"observation_digest":"sha256:93a2b7627b30352ba3c0aaa0d435b7fd149035fab4778e4c68aa6345a8c873ea","observation_id":"721a0562-f965-4f0c-b45d-48275ee8dec1","resolution":{"observed_at":"2026-08-06T22:48:33.600507Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2303.04831","last_updated":"2024-11-14T16:55:48Z","snapshot_observed_at":"2026-08-13T12:28:52.377953Z","submitted_at":"2023-03-08T19:10:01Z","title":"Richardson varieties, projected Richardson varieties and positroid varieties","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2303.04831","snapshot_observed_at":"2026-08-05T15:23:43.992365Z","title":"Richardson varieties, projected Richardson varieties and positroid varieties","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2508.20226","last_updated":"2025-08-27T19:05:47Z","snapshot_observed_at":"2026-08-10T05:56:15.307627Z","submitted_at":"2025-08-27T19:05:47Z","title":"Decompositions of augmentation varieties via weaves and rulings","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-05T15:23:43.992365Z"},"links":{"cited_paper":"/paper/2303.04831","citing_paper":"/paper/2508.20226"},"observation_digest":"sha256:c5fce5caba9cc22a277a9f9b453928335dbd137b441e1cccde26c76d5da84d63","observation_id":"318bedac-da72-44ac-a749-18f2819c4eda","resolution":{"observed_at":"2026-08-05T15:23:43.992365Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2303.04831","last_updated":"2024-11-14T16:55:48Z","snapshot_observed_at":"2026-08-13T12:28:52.377953Z","submitted_at":"2023-03-08T19:10:01Z","title":"Richardson varieties, projected Richardson varieties and positroid varieties","version":3},"cited_work":{"arxiv_id":"2303.04831","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2303.04831","snapshot_observed_at":"2026-07-03T16:08:37.062692Z","title":"Richardson varieties, projected R ichardson varieties and positroid varieties","venue":null,"work_id":"3f8afdb3-4e35-4bf8-b422-f81be098ab46","year":2024},"citing_paper":{"arxiv_id":"2604.03484","last_updated":"2026-04-03T22:11:58Z","snapshot_observed_at":"2026-08-02T15:40:20.827790Z","submitted_at":"2026-04-03T22:11:58Z","title":"Totally nonnegative maximal tori and opposed Bruhat intervals","version":1},"reference_index":41,"source":"arxiv_source","source_observed_at":"2026-05-13T17:59:30.789563Z"},"links":{"cited_paper":"/paper/2303.04831","citing_paper":"/paper/2604.03484"},"observation_digest":"sha256:d47b19be764d942c3a5ab5e00695c2bb76a705e3d247e428f64d20995fcf06ec","observation_id":"1a75bfc6-cb57-4e3c-949e-400ee5d75375","resolution":{"observed_at":"2026-05-13T18:03:04.585642Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2303.04831","last_updated":"2024-11-14T16:55:48Z","snapshot_observed_at":"2026-08-13T12:28:52.377953Z","submitted_at":"2023-03-08T19:10:01Z","title":"Richardson varieties, projected Richardson varieties and positroid varieties","version":3},"cited_work":{"arxiv_id":"2303.04831","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2303.04831","snapshot_observed_at":"2026-07-03T16:08:37.062692Z","title":"Richardson varieties, projected R ichardson varieties and positroid varieties","venue":null,"work_id":"3f8afdb3-4e35-4bf8-b422-f81be098ab46","year":2024},"citing_paper":{"arxiv_id":"2606.12815","last_updated":"2026-06-11T02:19:45Z","snapshot_observed_at":"2026-07-06T23:51:40.528967Z","submitted_at":"2026-06-11T02:19:45Z","title":"Fence Complexes and Toric Degenerations of Positroid Varieties","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-06-27T06:09:37.234342Z"},"links":{"cited_paper":"/paper/2303.04831","citing_paper":"/paper/2606.12815"},"observation_digest":"sha256:7d808102d8fed4895822574fd5ba6fade3555a902cb755b04209282d8662f66c","observation_id":"3c76eeec-c588-4a00-bc83-d85d5b8681e7","resolution":{"observed_at":"2026-07-03T16:08:37.064589Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2303.04831","last_updated":"2024-11-14T16:55:48Z","snapshot_observed_at":"2026-08-13T12:28:52.377953Z","submitted_at":"2023-03-08T19:10:01Z","title":"Richardson varieties, projected Richardson varieties and positroid varieties","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2303.04831","snapshot_observed_at":"2026-07-14T06:49:52.281267Z","title":"arXiv preprint arXiv:2303.04831 , year=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.11133","last_updated":"2026-07-23T20:18:47Z","snapshot_observed_at":"2026-08-14T15:43:36.560426Z","submitted_at":"2026-07-13T06:12:17Z","title":"FFLV bases for covariant representations of $\\mathfrak{gl}(m|n)$","version":1},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-07-14T06:49:52.281267Z"},"links":{"cited_paper":"/paper/2303.04831","citing_paper":"/paper/2607.11133"},"observation_digest":"sha256:088ecdd3d208e0a4d30b58155331ee6e462e38d9328b7e86813de4c008e9407d","observation_id":"e1fdc6ad-503d-45f8-829a-09061fe02c52","resolution":{"observed_at":"2026-07-14T06:49:52.281267Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2303.04831","last_updated":"2024-11-14T16:55:48Z","snapshot_observed_at":"2026-08-13T12:28:52.377953Z","submitted_at":"2023-03-08T19:10:01Z","title":"Richardson varieties, projected Richardson varieties and positroid varieties","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2303.04831","snapshot_observed_at":"2026-08-02T07:14:23.307333Z","title":"arXiv preprint arXiv:2303.04831 , year=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.11133","last_updated":"2026-07-23T20:18:47Z","snapshot_observed_at":"2026-08-14T15:43:36.560426Z","submitted_at":"2026-07-13T06:12:17Z","title":"FFLV bases for covariant representations of $\\mathfrak{gl}(m|n)$","version":2},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-08-02T07:14:23.307333Z"},"links":{"cited_paper":"/paper/2303.04831","citing_paper":"/paper/2607.11133"},"observation_digest":"sha256:5d9fab9deb6f0ded15d930ef5d4fe3778598466d0f476ba044256ba0e030167a","observation_id":"0d2d4f4b-1167-4782-b192-f5596b229495","resolution":{"observed_at":"2026-08-02T07:14:23.307333Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2303.04831","last_updated":"2024-11-14T16:55:48Z","snapshot_observed_at":"2026-08-13T12:28:52.377953Z","submitted_at":"2023-03-08T19:10:01Z","title":"Richardson varieties, projected Richardson varieties and positroid varieties","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2303.04831","snapshot_observed_at":"2026-08-01T04:16:52.214752Z","title":null,"venue":null,"work_id":null,"year":1968},"citing_paper":{"arxiv_id":"2607.22920","last_updated":"2026-07-24T21:16:34Z","snapshot_observed_at":"2026-08-15T03:31:11.575174Z","submitted_at":"2026-07-24T21:16:34Z","title":"Equidistribution of currents under Anosov group actions","version":1},"reference_index":1983,"source":"pdf_text","source_observed_at":"2026-08-01T04:16:52.214752Z"},"links":{"cited_paper":"/paper/2303.04831","citing_paper":"/paper/2607.22920"},"observation_digest":"sha256:b385f6f8b3f81ab3f100b2a198e75fe612773a4ff30cb8bc6e19dab41757bce8","observation_id":"395c51b1-5bb5-42bc-acda-9b3be191ca6c","resolution":{"observed_at":"2026-08-01T04:16:52.214752Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2303.04831/citation-record","integrity":"/paper/2303.04831/integrity","json":"/paper/2303.04831/citation-record.json","paper":"/paper/2303.04831"},"outbound":[],"paper":{"arxiv_id":"2303.04831","last_updated":"2024-11-14T16:55:48Z","latest_version":3,"primary_category":"math.AG","snapshot_observed_at":"2026-08-13T12:28:52.377953Z","submitted_at":"2023-03-08T19:10:01Z","title":"Richardson varieties, projected Richardson varieties and positroid varieties"},"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":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"thesis":"As of 15 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 7 inbound Pith citation observations for arXiv:2303.04831."}