{"as_of":"2026-08-19T12:05:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:63885f4c5cb438162e623e20ca6b611dca7a206d502040b3c617e48b01bb6759","coverage":[{"denominator":4,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":4,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-15T20:10:37.964703Z","state":"measured"},{"denominator":5,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":5,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-19T06:32:44.657259+00:00","state":"measured"},{"denominator":1,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":1,"source":"paper_references, paper_reference_links","source_observed_at":"2026-05-07T08:23:09.084562Z","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":"2026-05-12T10:01:28.469619Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2506.13684","last_updated":"2025-06-16T16:43:57Z","snapshot_observed_at":"2026-08-15T19:55:03.718926Z","submitted_at":"2025-06-16T16:43:57Z","title":"Sums of Schubert structure constants with bounded Coxeter length","version":1},"cited_work":{"arxiv_id":"2506.13684","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2506.13684","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"a7610123-76b6-44b3-8e4d-288c278e7eed","year":2025},"citing_paper":{"arxiv_id":"2604.27107","last_updated":"2026-04-29T18:53:35Z","snapshot_observed_at":"2026-08-02T17:03:47.009133Z","submitted_at":"2026-04-29T18:53:35Z","title":"Stretched Schubert coefficients are eventually quasi-polynomial","version":1},"reference_index":54,"source":"arxiv_source","source_observed_at":"2026-05-07T08:23:09.084562Z"},"links":{"cited_paper":"/paper/2506.13684","citing_paper":"/paper/2604.27107"},"observation_digest":"sha256:9fc9f8a2728994d993a605f5b34aec5a15eaf370d7743538821ca3c36a97b3c0","observation_id":"240fb4a5-e2cd-461a-997a-eaa3c0495a4d","resolution":{"observed_at":"2026-05-12T10:01:28.472520Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2506.13684/citation-record","integrity":"/paper/2506.13684/integrity","json":"/paper/2506.13684/citation-record.json","paper":"/paper/2506.13684"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T20:10:38.131927Z","title":"Representations of quantum groups at a pth root of unity and of semisimple groups in characteristic p: independence of p , Astrisque No","venue":null,"work_id":"cdd45f0e-4fae-485b-af59-8ee617e7da32","year":1994},"citing_paper":{"arxiv_id":"2506.13684","last_updated":"2025-06-16T16:43:57Z","snapshot_observed_at":"2026-08-15T19:55:03.718926Z","submitted_at":"2025-06-16T16:43:57Z","title":"Sums of Schubert structure constants with bounded Coxeter length","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-15T20:10:37.936422Z"},"links":{"citing_paper":"/paper/2506.13684"},"observation_digest":"sha256:0044e70268d9bbfaf60cfec72ad5eab3b9c9319045682fd5537866b22e14e6ce","observation_id":"70120e0d-5c21-4f85-9682-9126d0dcdb8a","resolution":{"observed_at":"2026-08-15T20:10:38.139034Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T20:10:38.094783Z","title":"Equivariant cohomology, Koszul duality, and the localization theorem, Invent","venue":null,"work_id":"70654fba-2781-4a63-8b64-80007ba4c3a6","year":1998},"citing_paper":{"arxiv_id":"2506.13684","last_updated":"2025-06-16T16:43:57Z","snapshot_observed_at":"2026-08-15T19:55:03.718926Z","submitted_at":"2025-06-16T16:43:57Z","title":"Sums of Schubert structure constants with bounded Coxeter length","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-15T20:10:37.949384Z"},"links":{"citing_paper":"/paper/2506.13684"},"observation_digest":"sha256:2ddb9cca770358b272dc7c54bfc3f4a5556a1aa82888a525c2c4232072b55b17","observation_id":"1f1cf0c9-7fb0-4d25-815b-9ab471bc8f8e","resolution":{"observed_at":"2026-08-15T20:10:38.102686Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2504.17734","last_updated":"2026-07-10T17:29:40Z","snapshot_observed_at":"2026-08-16T10:30:09.209906Z","submitted_at":"2025-04-24T16:47:38Z","title":"Signed puzzles for Schubert coefficients","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2504.17734","snapshot_observed_at":"2026-08-15T20:10:37.957847Z","title":"Signed puzzles for Schubert coefficients, preprint, 2025","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2506.13684","last_updated":"2025-06-16T16:43:57Z","snapshot_observed_at":"2026-08-15T19:55:03.718926Z","submitted_at":"2025-06-16T16:43:57Z","title":"Sums of Schubert structure constants with bounded Coxeter length","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-15T20:10:37.957847Z"},"links":{"cited_paper":"/paper/2504.17734","citing_paper":"/paper/2506.13684"},"observation_digest":"sha256:9344eb50c9b066058c0725152fafc8609994c7827b2952fea1d86d31a0cbbaa9","observation_id":"fc2b2882-0695-429b-8a46-d5620e30fc7b","resolution":{"observed_at":"2026-08-15T20:10:37.957847Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T20:10:38.064743Z","title":"The A·B·C·Ds of Schubert calculus, S´ em","venue":null,"work_id":"89aab16d-5792-44a4-be3f-57afcccd1142","year":2020},"citing_paper":{"arxiv_id":"2506.13684","last_updated":"2025-06-16T16:43:57Z","snapshot_observed_at":"2026-08-15T19:55:03.718926Z","submitted_at":"2025-06-16T16:43:57Z","title":"Sums of Schubert structure constants with bounded Coxeter length","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-15T20:10:37.964703Z"},"links":{"citing_paper":"/paper/2506.13684"},"observation_digest":"sha256:77c3a774ec2362c80b0f2f7a5825c016c7e715205125324f81085db248a006c8","observation_id":"272aeb5f-ff78-4c3a-9c9d-6cb32d91b6ff","resolution":{"observed_at":"2026-08-15T20:10:38.075496Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2506.13684","last_updated":"2025-06-16T16:43:57Z","latest_version":1,"primary_category":"math.CO","snapshot_observed_at":"2026-08-15T19:55:03.718926Z","submitted_at":"2025-06-16T16:43:57Z","title":"Sums of Schubert structure constants with bounded Coxeter length"},"reference_resolution":{"displayed":4,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":1,"verified_exact":0,"verified_fuzzy":3},"total_outbound_references":4},"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":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"thesis":"As of 19 August 2026, this Paper Citation Record lists 4 of 4 outbound references and 1 inbound Pith citation observation for arXiv:2506.13684."}