{"as_of":"2026-08-04T05:46:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:f41ab0316250c33c0c484def61c9f245a75273665cbbbdaf4b435f8327c309bd","coverage":[{"denominator":10,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":10,"source":"paper_references, paper_reference_links","source_observed_at":"2026-05-12T04:49:56.207874Z","state":"measured"},{"denominator":11,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":11,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-03T06:30:56.289259+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":"2026-06-27T00:06:37.507293Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"pith","source_observed_at":"2026-07-03T21:49:00.113230Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2605.10608","last_updated":"2026-05-11T14:06:31Z","snapshot_observed_at":"2026-07-06T23:22:32.858399Z","submitted_at":"2026-05-11T14:06:31Z","title":"Hidden Structure of Jack Littlewood-Richardson Coefficients","version":1},"cited_work":{"arxiv_id":"2605.10608","doi":null,"metadata_source":"pith","pith_arxiv_id":"2605.10608","snapshot_observed_at":"2026-07-03T21:49:00.113230Z","title":"Hidden Structure of Jack Littlewood-Richardson Coefficients","venue":"math.CO","work_id":"06d13692-33ee-48a6-93e3-8a971bae4d8a","year":2026},"citing_paper":{"arxiv_id":"2606.17822","last_updated":"2026-06-16T11:49:54Z","snapshot_observed_at":"2026-08-03T19:01:41.487804Z","submitted_at":"2026-06-16T11:49:54Z","title":"Congruences of shifted Jack Littlewood-Richardson coefficients","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-06-27T00:06:37.507293Z"},"links":{"cited_paper":"/paper/2605.10608","citing_paper":"/paper/2606.17822"},"observation_digest":"sha256:7749c81d23ac582b42081aba85cbcf467b540ba3b57f395eed1905b9530f9bbf","observation_id":"d3c2113f-0d16-4e26-b0d3-36038e4870aa","resolution":{"observed_at":"2026-07-03T21:49:00.114348Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-03T06:30:56.289259+00:00","source":"crossref"},{"observed_at":"2026-08-03T06:30:50.922721+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2605.10608/citation-record","integrity":"/paper/2605.10608/integrity","json":"/paper/2605.10608/citation-record.json","paper":"/paper/2605.10608"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Alexandersson,Tables of shifted Jack Littlewood-Richardson coefficients.https: // www","venue":null,"work_id":"b86170e4-d4ca-4952-8349-04e3d8abf434","year":null},"citing_paper":{"arxiv_id":"2605.10608","last_updated":"2026-05-11T14:06:31Z","snapshot_observed_at":"2026-07-06T23:22:32.858399Z","submitted_at":"2026-05-11T14:06:31Z","title":"Hidden Structure of Jack Littlewood-Richardson Coefficients","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-05-12T04:49:56.207874Z"},"links":{"citing_paper":"/paper/2605.10608"},"observation_digest":"sha256:146628c5db0d1bbf2014db14903cae9d0ad78de3a35cab51fccbc4f8b76c915a","observation_id":"37f78ab0-fed8-46ef-9a88-24b9d3055850","resolution":{"observed_at":"2026-05-12T13:21:37.272509Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-03T06:30:56.289259+00:00","source":"crossref"},{"observed_at":"2026-08-03T06:30:50.922721+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"64bdba08-c28e-4de2-b7f1-8f179498dc95","year":2019},"citing_paper":{"arxiv_id":"2605.10608","last_updated":"2026-05-11T14:06:31Z","snapshot_observed_at":"2026-07-06T23:22:32.858399Z","submitted_at":"2026-05-11T14:06:31Z","title":"Hidden Structure of Jack Littlewood-Richardson Coefficients","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-05-12T04:49:56.207874Z"},"links":{"citing_paper":"/paper/2605.10608"},"observation_digest":"sha256:46f68fc93b66945429c29a71eaa82eb08326e7f4f6a5e18a724c070bbb0e1866","observation_id":"9e29dcdc-81e4-4450-865b-dc5e02b50493","resolution":{"observed_at":"2026-05-12T13:21:37.268878Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-03T06:30:56.289259+00:00","source":"crossref"},{"observed_at":"2026-08-03T06:30:50.922721+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"058181be-2e88-4668-acec-b4729e5534be","year":1989},"citing_paper":{"arxiv_id":"2605.10608","last_updated":"2026-05-11T14:06:31Z","snapshot_observed_at":"2026-07-06T23:22:32.858399Z","submitted_at":"2026-05-11T14:06:31Z","title":"Hidden Structure of Jack Littlewood-Richardson Coefficients","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-05-12T04:49:56.207874Z"},"links":{"citing_paper":"/paper/2605.10608"},"observation_digest":"sha256:83241ce78f52e19762bf66c64b5224c647c2835c32e01e780b984f15526d56d8","observation_id":"cfa9c4bb-c658-4877-bfbf-e2306067741c","resolution":{"observed_at":"2026-05-12T13:21:37.300815Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-03T06:30:56.289259+00:00","source":"crossref"},{"observed_at":"2026-08-03T06:30:50.922721+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":"2026-06-05T21:23:00.469572Z","title":"Royle,Algebraic graph theory, Graduate Texts in Mathematics, no","venue":null,"work_id":"677c6857-e5f6-40dc-be8d-cabf1ffdc716","year":2001},"citing_paper":{"arxiv_id":"2605.10608","last_updated":"2026-05-11T14:06:31Z","snapshot_observed_at":"2026-07-06T23:22:32.858399Z","submitted_at":"2026-05-11T14:06:31Z","title":"Hidden Structure of Jack Littlewood-Richardson Coefficients","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-05-12T04:49:56.207874Z"},"links":{"citing_paper":"/paper/2605.10608"},"observation_digest":"sha256:204979a8b9c30462a7609bfdf22e026970e9c28bec70d39099ab1c77a11a7538","observation_id":"0f69e666-27e4-41e9-b37a-c52d65d94f18","resolution":{"observed_at":"2026-05-12T13:21:37.297367Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-03T06:30:56.289259+00:00","source":"crossref"},{"observed_at":"2026-08-03T06:30:50.922721+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":"2026-06-05T21:23:00.469572Z","title":"7, 1296–1303","venue":null,"work_id":"e0d7104e-53a3-4cd7-a244-b78da98b2d61","year":2008},"citing_paper":{"arxiv_id":"2605.10608","last_updated":"2026-05-11T14:06:31Z","snapshot_observed_at":"2026-07-06T23:22:32.858399Z","submitted_at":"2026-05-11T14:06:31Z","title":"Hidden Structure of Jack Littlewood-Richardson Coefficients","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-05-12T04:49:56.207874Z"},"links":{"citing_paper":"/paper/2605.10608"},"observation_digest":"sha256:ba250ce763eed1438ebe7ccd6b752cc0e1f7788c862a5b21bfe7396bede4e0fc","observation_id":"adf69d48-0aa1-4a52-a07f-6aa429d630d2","resolution":{"observed_at":"2026-05-12T13:21:37.304370Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-03T06:30:56.289259+00:00","source":"crossref"},{"observed_at":"2026-08-03T06:30:50.922721+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":"2026-06-05T21:23:00.469572Z","title":"King, Christophe Tollu, and Frédéric Toumazet,Factorisation of littlewood– richardson coefficients, Journal of Combinatorial Theory, Series A116(2009), no","venue":null,"work_id":"6e463ac5-1dd1-48c2-ae40-487e8aeb7b5c","year":2009},"citing_paper":{"arxiv_id":"2605.10608","last_updated":"2026-05-11T14:06:31Z","snapshot_observed_at":"2026-07-06T23:22:32.858399Z","submitted_at":"2026-05-11T14:06:31Z","title":"Hidden Structure of Jack Littlewood-Richardson Coefficients","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-05-12T04:49:56.207874Z"},"links":{"citing_paper":"/paper/2605.10608"},"observation_digest":"sha256:718bc4137ceccb27519e2e851f526eb5260c19739e79a22ad45fcb4b05ff31b5","observation_id":"fe26410d-1755-4dc5-bb72-954e51eaf3e0","resolution":{"observed_at":"2026-05-12T13:21:37.280336Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-03T06:30:56.289259+00:00","source":"crossref"},{"observed_at":"2026-08-03T06:30:50.922721+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2401.01582","last_updated":"2025-07-20T14:36:33Z","snapshot_observed_at":"2026-07-06T17:11:04.789413Z","submitted_at":"2024-01-03T07:18:53Z","title":"The Stanley Conjecture Revisited","version":3},"cited_work":{"arxiv_id":"2401.01582","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2401.01582","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"14d6e226-f19b-4de9-9b38-7aab0f317f3d","year":2024},"citing_paper":{"arxiv_id":"2605.10608","last_updated":"2026-05-11T14:06:31Z","snapshot_observed_at":"2026-07-06T23:22:32.858399Z","submitted_at":"2026-05-11T14:06:31Z","title":"Hidden Structure of Jack Littlewood-Richardson Coefficients","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-05-12T04:49:56.207874Z"},"links":{"cited_paper":"/paper/2401.01582","citing_paper":"/paper/2605.10608"},"observation_digest":"sha256:bd1facef0a5df722d05065baa0f87f32284fbb090e92e19bf3861d280d378fe7","observation_id":"c686c27c-2e95-410c-9fd1-8b40456678ea","resolution":{"observed_at":"2026-05-12T05:51:27.815040Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-03T06:30:56.289259+00:00","source":"crossref"},{"observed_at":"2026-08-03T06:30:50.922721+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"6ba32b90-7cf1-4d5d-bc70-17a0f32ed895","year":2026},"citing_paper":{"arxiv_id":"2605.10608","last_updated":"2026-05-11T14:06:31Z","snapshot_observed_at":"2026-07-06T23:22:32.858399Z","submitted_at":"2026-05-11T14:06:31Z","title":"Hidden Structure of Jack Littlewood-Richardson Coefficients","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-05-12T04:49:56.207874Z"},"links":{"citing_paper":"/paper/2605.10608"},"observation_digest":"sha256:e2e02472af642d9f4798b2a74c79ddf8476de884863718021027e26e850a81ad","observation_id":"df7acb1e-74d8-44b2-838f-ccaf8a6e6da8","resolution":{"observed_at":"2026-05-12T13:21:37.308152Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-03T06:30:56.289259+00:00","source":"crossref"},{"observed_at":"2026-08-03T06:30:50.922721+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":"2026-06-05T21:23:00.469572Z","title":"1, 76–115","venue":null,"work_id":"42498395-ef0f-4e15-ad11-e5b3692b6678","year":1989},"citing_paper":{"arxiv_id":"2605.10608","last_updated":"2026-05-11T14:06:31Z","snapshot_observed_at":"2026-07-06T23:22:32.858399Z","submitted_at":"2026-05-11T14:06:31Z","title":"Hidden Structure of Jack Littlewood-Richardson Coefficients","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-05-12T04:49:56.207874Z"},"links":{"citing_paper":"/paper/2605.10608"},"observation_digest":"sha256:3ed7496ebaa928e32bab439c7e5e1ba94bcf9607f83f23de10605d991aa5dd98","observation_id":"eb90e32e-1acb-44b6-bb8b-9c2ffc0f967f","resolution":{"observed_at":"2026-05-12T13:21:37.292685Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-03T06:30:56.289259+00:00","source":"crossref"},{"observed_at":"2026-08-03T06:30:50.922721+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":"2026-06-05T21:23:00.469572Z","title":"Stanley,Enumerative combinatorics, vol","venue":null,"work_id":"c8232740-8dbc-4cd0-b35b-1ecbc26b582f","year":1999},"citing_paper":{"arxiv_id":"2605.10608","last_updated":"2026-05-11T14:06:31Z","snapshot_observed_at":"2026-07-06T23:22:32.858399Z","submitted_at":"2026-05-11T14:06:31Z","title":"Hidden Structure of Jack Littlewood-Richardson Coefficients","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-05-12T04:49:56.207874Z"},"links":{"citing_paper":"/paper/2605.10608"},"observation_digest":"sha256:b2a0d826b3ffae470d68974fa13eb7503e7dd26fb42243db70b4030cf2ee9bd4","observation_id":"489effa8-7d43-4ecc-9cfa-d48c5f2c2352","resolution":{"observed_at":"2026-05-12T13:21:37.275629Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-03T06:30:56.289259+00:00","source":"crossref"},{"observed_at":"2026-08-03T06:30:50.922721+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2605.10608","last_updated":"2026-05-11T14:06:31Z","latest_version":1,"primary_category":"math.CO","snapshot_observed_at":"2026-07-06T23:22:32.858399Z","submitted_at":"2026-05-11T14:06:31Z","title":"Hidden Structure of Jack Littlewood-Richardson Coefficients"},"reference_resolution":{"displayed":10,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":3,"verified_exact":1,"verified_fuzzy":6},"total_outbound_references":10},"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":"2026-08-03T06:30:56.289259+00:00","source":"crossref"},{"observed_at":"2026-08-03T06:30:50.922721+00:00","source":"retraction_watch"}],"thesis":"As of 4 August 2026, this Paper Citation Record lists 10 of 10 outbound references and 1 inbound Pith citation observation for arXiv:2605.10608."}