{"as_of":"2026-08-17T05:22:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:c6c395d0c447dc8fb910cb4fc91579c9f3384a386529e4a0587f2feec6580090","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":"2026-08-16T06:30:59.297886+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":"2026-08-07T05:49:32.785018Z","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":"2026-07-03T15:58:37.948054Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2108.08370","last_updated":"2025-09-02T00:29:46Z","snapshot_observed_at":"2026-08-16T18:02:25.125943Z","submitted_at":"2021-08-18T20:07:56Z","title":"Bumpless pipe dreams encode Gr\\\"obner geometry of Schubert polynomials","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2108.08370","snapshot_observed_at":"2026-08-07T05:49:32.785018Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2506.07306","last_updated":"2025-06-08T22:39:23Z","snapshot_observed_at":"2026-08-12T01:39:38.244348Z","submitted_at":"2025-06-08T22:39:23Z","title":"Changing Bases with Pipe Dream Combinatorics","version":1},"reference_index":27,"source":"arxiv_source","source_observed_at":"2026-08-07T05:49:32.785018Z"},"links":{"cited_paper":"/paper/2108.08370","citing_paper":"/paper/2506.07306"},"observation_digest":"sha256:a63de5f827d2730c884630a2296de39abd0990bcc3ea9e2fb8c847653af335fa","observation_id":"9eb3ff15-eab3-47bf-862f-125a50c8e8b1","resolution":{"observed_at":"2026-08-07T05:49:32.785018Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2108.08370","last_updated":"2025-09-02T00:29:46Z","snapshot_observed_at":"2026-08-16T18:02:25.125943Z","submitted_at":"2021-08-18T20:07:56Z","title":"Bumpless pipe dreams encode Gr\\\"obner geometry of Schubert polynomials","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2108.08370","snapshot_observed_at":"2026-08-05T12:16:24.345937Z","title":null,"venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2509.01857","last_updated":"2025-09-02T00:52:17Z","snapshot_observed_at":"2026-08-14T23:52:34.547242Z","submitted_at":"2025-09-02T00:52:17Z","title":"Hybrid pipe dreams for the lower-upper scheme","version":1},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-08-05T12:16:24.345937Z"},"links":{"cited_paper":"/paper/2108.08370","citing_paper":"/paper/2509.01857"},"observation_digest":"sha256:b5211651d06fc5c579e4b3cc05c0581d8aacb443df3c56f0b414172b0870703f","observation_id":"abe48d34-a421-4e10-91f8-a4feb51ffd73","resolution":{"observed_at":"2026-08-05T12:16:24.345937Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2108.08370","last_updated":"2025-09-02T00:29:46Z","snapshot_observed_at":"2026-08-16T18:02:25.125943Z","submitted_at":"2021-08-18T20:07:56Z","title":"Bumpless pipe dreams encode Gr\\\"obner geometry of Schubert polynomials","version":4},"cited_work":{"arxiv_id":"2108.08370","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2108.08370","snapshot_observed_at":"2026-07-03T15:58:37.948054Z","title":null,"venue":null,"work_id":"41482744-ccd5-4397-8e34-a96573322889","year":2023},"citing_paper":{"arxiv_id":"2606.13518","last_updated":"2026-06-11T16:09:05Z","snapshot_observed_at":"2026-08-13T18:04:26.466031Z","submitted_at":"2026-06-11T16:09:05Z","title":"Weak order: Alternating sign matrices, monotone triangles, and bumpless pipe dreams","version":1},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-06-27T06:16:54.172667Z"},"links":{"cited_paper":"/paper/2108.08370","citing_paper":"/paper/2606.13518"},"observation_digest":"sha256:fba27a6d9b79869fd02b1e7b60a6e80c44e9b3bd802f4885259f18e744a32d87","observation_id":"f40551d5-fcb9-4709-853f-bcacd5756ca0","resolution":{"observed_at":"2026-07-03T15:58:37.949480Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2108.08370/citation-record","integrity":"/paper/2108.08370/integrity","json":"/paper/2108.08370/citation-record.json","paper":"/paper/2108.08370"},"outbound":[],"paper":{"arxiv_id":"2108.08370","last_updated":"2025-09-02T00:29:46Z","latest_version":4,"primary_category":"math.CO","snapshot_observed_at":"2026-08-16T18:02:25.125943Z","submitted_at":"2021-08-18T20:07:56Z","title":"Bumpless pipe dreams encode Gr\\\"obner geometry of Schubert polynomials"},"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":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"thesis":"As of 17 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 3 inbound Pith citation observations for arXiv:2108.08370."}