{"as_of":"2026-08-16T12:08:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:3f149cebdd0fd09b1fc30c107c5caeaa8f4c7edc66aed3ffb3dc6f39430f5c66","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":"2026-08-16T06:30:59.297886+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":"2026-08-05T12:16:24.332984Z","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":"2026-07-04T11:49:50.840193Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"1909.13777","last_updated":"2022-02-05T19:31:15Z","snapshot_observed_at":"2026-08-11T03:34:37.600256Z","submitted_at":"2019-09-30T15:17:01Z","title":"Schubert polynomials, pipe dreams, equivariant classes, and a co-transition formula","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1909.13777","snapshot_observed_at":"2026-08-05T12:16:24.332984Z","title":"63–83, Cambridge University Press, 2022, http://arxiv.org/abs/1909.13777 arXiv:1909.13777","venue":null,"work_id":null,"year":2022},"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":11,"source":"arxiv_source","source_observed_at":"2026-08-05T12:16:24.332984Z"},"links":{"cited_paper":"/paper/1909.13777","citing_paper":"/paper/2509.01857"},"observation_digest":"sha256:8731f87c2ea24ff7297bffd67facede21e5a724a319756b9ce55d0fa92307f48","observation_id":"394d4b43-08dd-4a7d-bccb-3d4db2babfe1","resolution":{"observed_at":"2026-08-05T12:16:24.332984Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1909.13777","last_updated":"2022-02-05T19:31:15Z","snapshot_observed_at":"2026-08-11T03:34:37.600256Z","submitted_at":"2019-09-30T15:17:01Z","title":"Schubert polynomials, pipe dreams, equivariant classes, and a co-transition formula","version":2},"cited_work":{"arxiv_id":"1909.13777","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"1909.13777","snapshot_observed_at":"2026-07-04T11:49:50.840193Z","title":"Schubert polynomials, pipe dreams, equivariant classes, and a co-transition formula","venue":null,"work_id":"8594bd75-6ccb-485f-87f9-449150fcdaa4","year":1909},"citing_paper":{"arxiv_id":"2606.23876","last_updated":"2026-06-22T19:23:04Z","snapshot_observed_at":"2026-08-16T10:15:31.730376Z","submitted_at":"2026-06-22T19:23:04Z","title":"A Littlewood-Richardson Rule for Forest Polynomials via the Schubert Bialgebra","version":1},"reference_index":69,"source":"arxiv_source","source_observed_at":"2026-06-26T07:34:59.083569Z"},"links":{"cited_paper":"/paper/1909.13777","citing_paper":"/paper/2606.23876"},"observation_digest":"sha256:dbfad00d3ac5b7643c0a3af57468e11d233adf90a3315105da3e0a7763d1844f","observation_id":"4d3d473c-2a7f-4309-9a41-55b12e277639","resolution":{"observed_at":"2026-07-04T11:49:50.841665Z","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/1909.13777/citation-record","integrity":"/paper/1909.13777/integrity","json":"/paper/1909.13777/citation-record.json","paper":"/paper/1909.13777"},"outbound":[],"paper":{"arxiv_id":"1909.13777","last_updated":"2022-02-05T19:31:15Z","latest_version":2,"primary_category":"math.CO","snapshot_observed_at":"2026-08-11T03:34:37.600256Z","submitted_at":"2019-09-30T15:17:01Z","title":"Schubert polynomials, pipe dreams, equivariant classes, and a co-transition formula"},"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 16 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 2 inbound Pith citation observations for arXiv:1909.13777."}