{"as_of":"2026-08-14T10:26:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:8359c802bdd7b181eb7063411b0f8aefd4821dd7b1a17c02dd9da15266818d0f","coverage":[{"denominator":27,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":27,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-10T17:52:29.615286Z","state":"measured"},{"denominator":28,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":28,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-14T06:32:32.682623+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":"2026-08-10T15:45:49.310574Z","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":"2026-08-10T15:45:49.428089Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2501.11975","last_updated":"2025-02-12T15:59:43Z","snapshot_observed_at":"2026-08-13T16:35:17.294016Z","submitted_at":"2025-01-21T08:44:09Z","title":"Matched pairs and Yang-Baxter operators","version":2},"cited_work":{"arxiv_id":"2501.11975","doi":null,"metadata_source":"pith","pith_arxiv_id":"2501.11975","snapshot_observed_at":"2026-08-10T15:45:49.428089Z","title":"Matched pairs and Yang-Baxter operators","venue":"math.QA","work_id":"8b8888d9-4bbc-4253-9ca1-e9eae5577691","year":2025},"citing_paper":{"arxiv_id":"2501.13747","last_updated":"2025-01-23T15:24:20Z","snapshot_observed_at":"2026-08-10T15:36:25.552842Z","submitted_at":"2025-01-23T15:24:20Z","title":"Matched pairs of actions on the Kac-Paljutkin algebra $H_8$","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-10T15:45:49.310574Z"},"links":{"cited_paper":"/paper/2501.11975","citing_paper":"/paper/2501.13747"},"observation_digest":"sha256:96b1367d134396eca4960ba011cce8a4150d27d8d01ddeee397da315b16dea64","observation_id":"5e5ed607-a0ad-4f1f-ac90-e35d0e294f5c","resolution":{"observed_at":"2026-08-10T15:45:49.436604Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2501.11975/citation-record","integrity":"/paper/2501.11975/integrity","json":"/paper/2501.11975/citation-record.json","paper":"/paper/2501.11975"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T17:52:29.984732Z","title":"Angiono, C","venue":null,"work_id":"1751deff-99ea-4d90-bce7-7cf2200fece8","year":2017},"citing_paper":{"arxiv_id":"2501.11975","last_updated":"2025-02-12T15:59:43Z","snapshot_observed_at":"2026-08-13T16:35:17.294016Z","submitted_at":"2025-01-21T08:44:09Z","title":"Matched pairs and Yang-Baxter operators","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-10T17:52:29.515392Z"},"links":{"citing_paper":"/paper/2501.11975"},"observation_digest":"sha256:f615848a8e25169056201f241e36d3541de2d85d6c11d3f45debb53aaa3aa1f1","observation_id":"ccd6edcc-d844-4066-b588-c2f08ec0ca4e","resolution":{"observed_at":"2026-08-10T17:52:29.988575Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T17:52:29.973001Z","title":null,"venue":null,"work_id":"17618d80-756d-4cb6-a323-6c6a55d46314","year":1992},"citing_paper":{"arxiv_id":"2501.11975","last_updated":"2025-02-12T15:59:43Z","snapshot_observed_at":"2026-08-13T16:35:17.294016Z","submitted_at":"2025-01-21T08:44:09Z","title":"Matched pairs and Yang-Baxter operators","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-10T17:52:29.519992Z"},"links":{"citing_paper":"/paper/2501.11975"},"observation_digest":"sha256:c57b05fdfbcc7df5623912a456fe29ebaeabb7c3f27981130635bf3063b22c68","observation_id":"eee2ab83-1c3e-4173-acaf-1de353fafca8","resolution":{"observed_at":"2026-08-10T17:52:29.976780Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T17:52:29.524666Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2501.11975","last_updated":"2025-02-12T15:59:43Z","snapshot_observed_at":"2026-08-13T16:35:17.294016Z","submitted_at":"2025-01-21T08:44:09Z","title":"Matched pairs and Yang-Baxter operators","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-10T17:52:29.524666Z"},"links":{"citing_paper":"/paper/2501.11975"},"observation_digest":"sha256:7b6485f1d15d02a520e530d7d0bafac4e6a7a7f1f8fe2d00a41bab4389ddb0f9","observation_id":"a9e63118-2992-4f48-b974-4801ac7478aa","resolution":{"observed_at":"2026-08-10T17:52:29.524666Z","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":"2026-08-10T17:52:29.954877Z","title":null,"venue":null,"work_id":"33369cdc-33f9-429e-8b08-1d584b40a599","year":1992},"citing_paper":{"arxiv_id":"2501.11975","last_updated":"2025-02-12T15:59:43Z","snapshot_observed_at":"2026-08-13T16:35:17.294016Z","submitted_at":"2025-01-21T08:44:09Z","title":"Matched pairs and Yang-Baxter operators","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-10T17:52:29.528878Z"},"links":{"citing_paper":"/paper/2501.11975"},"observation_digest":"sha256:bdb81c2247aaa2052320346b93230a143c63548f5da1eebcd12a20ceeba7098c","observation_id":"ea9c8666-5416-4833-8b50-6cba11111522","resolution":{"observed_at":"2026-08-10T17:52:29.958743Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T17:52:29.943355Z","title":"Ebrahimi-Fard, A","venue":null,"work_id":"5b713955-3871-4683-aad0-0af99984ffad","year":2015},"citing_paper":{"arxiv_id":"2501.11975","last_updated":"2025-02-12T15:59:43Z","snapshot_observed_at":"2026-08-13T16:35:17.294016Z","submitted_at":"2025-01-21T08:44:09Z","title":"Matched pairs and Yang-Baxter operators","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-10T17:52:29.533121Z"},"links":{"citing_paper":"/paper/2501.11975"},"observation_digest":"sha256:00fe4bf60183b1bb455efc03df16a9043533176b4a26912913d35c85e0129c4a","observation_id":"746b89e6-ddae-4ee4-a451-2dcbbb888eba","resolution":{"observed_at":"2026-08-10T17:52:29.947218Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T17:52:29.930283Z","title":"Etingof, T","venue":null,"work_id":"17420a4b-f9b3-41c5-9566-38639c1b385f","year":1999},"citing_paper":{"arxiv_id":"2501.11975","last_updated":"2025-02-12T15:59:43Z","snapshot_observed_at":"2026-08-13T16:35:17.294016Z","submitted_at":"2025-01-21T08:44:09Z","title":"Matched pairs and Yang-Baxter operators","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-10T17:52:29.537009Z"},"links":{"citing_paper":"/paper/2501.11975"},"observation_digest":"sha256:3efd0eb79c64bbc411823b61fada9f08b5543d437afcb6f5c71265312571d9ca","observation_id":"b4743bcb-c756-4745-80de-91fd0a49dffc","resolution":{"observed_at":"2026-08-10T17:52:29.935802Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2406.10009","last_updated":"2025-03-20T09:06:16Z","snapshot_observed_at":"2026-08-12T23:42:42.873107Z","submitted_at":"2024-06-14T13:21:35Z","title":"Matched pairs and Yetter-Drinfeld braces","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2406.10009","snapshot_observed_at":"2026-08-10T17:52:29.541464Z","title":"Ferri and A","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2501.11975","last_updated":"2025-02-12T15:59:43Z","snapshot_observed_at":"2026-08-13T16:35:17.294016Z","submitted_at":"2025-01-21T08:44:09Z","title":"Matched pairs and Yang-Baxter operators","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-10T17:52:29.541464Z"},"links":{"cited_paper":"/paper/2406.10009","citing_paper":"/paper/2501.11975"},"observation_digest":"sha256:844e48dc88f96f636636e9fa02f6d6024c35aa82db21c670c87b3ab85a211a16","observation_id":"8f948a69-9cd0-4c54-b5e7-de8645cc8353","resolution":{"observed_at":"2026-08-10T17:52:29.541464Z","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":"2026-08-10T17:52:29.917370Z","title":"Gateva-Ivanova and M","venue":null,"work_id":"304975cc-7375-4ea3-861f-c1a678fad674","year":1998},"citing_paper":{"arxiv_id":"2501.11975","last_updated":"2025-02-12T15:59:43Z","snapshot_observed_at":"2026-08-13T16:35:17.294016Z","submitted_at":"2025-01-21T08:44:09Z","title":"Matched pairs and Yang-Baxter operators","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-10T17:52:29.545894Z"},"links":{"citing_paper":"/paper/2501.11975"},"observation_digest":"sha256:447cc969addeb508280a41a096afe0dc72a2d93b0bd254410228b697bd41c449","observation_id":"a0abaf86-b6c2-4202-afe7-2801eb793b04","resolution":{"observed_at":"2026-08-10T17:52:29.921660Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T17:52:29.904238Z","title":"Guarnieri and L","venue":null,"work_id":"2dee31f0-cdba-427c-b793-d7c945656d18","year":2017},"citing_paper":{"arxiv_id":"2501.11975","last_updated":"2025-02-12T15:59:43Z","snapshot_observed_at":"2026-08-13T16:35:17.294016Z","submitted_at":"2025-01-21T08:44:09Z","title":"Matched pairs and Yang-Baxter operators","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-10T17:52:29.549690Z"},"links":{"citing_paper":"/paper/2501.11975"},"observation_digest":"sha256:97b7487b8335aa211db04c939542d60de4b140b5dfbe281556762209b8471744","observation_id":"e5b2d035-7bab-42a1-a373-9173cf82843b","resolution":{"observed_at":"2026-08-10T17:52:29.908361Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T17:52:29.893064Z","title":null,"venue":null,"work_id":"eb834213-bd5b-431d-a031-f4b3b7947ab7","year":2018},"citing_paper":{"arxiv_id":"2501.11975","last_updated":"2025-02-12T15:59:43Z","snapshot_observed_at":"2026-08-13T16:35:17.294016Z","submitted_at":"2025-01-21T08:44:09Z","title":"Matched pairs and Yang-Baxter operators","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-10T17:52:29.553217Z"},"links":{"citing_paper":"/paper/2501.11975"},"observation_digest":"sha256:35f945c22b06cc5d5d7a55795b56d035e702b025f5b1c2fda9a3a73593306138","observation_id":"570301d6-7441-4c7f-a58d-881f69d61824","resolution":{"observed_at":"2026-08-10T17:52:29.896862Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T17:52:29.880734Z","title":null,"venue":null,"work_id":"7f9292cc-35b5-4f30-8a6d-267938c49d18","year":2024},"citing_paper":{"arxiv_id":"2501.11975","last_updated":"2025-02-12T15:59:43Z","snapshot_observed_at":"2026-08-13T16:35:17.294016Z","submitted_at":"2025-01-21T08:44:09Z","title":"Matched pairs and Yang-Baxter operators","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-10T17:52:29.556810Z"},"links":{"citing_paper":"/paper/2501.11975"},"observation_digest":"sha256:b136b9031f93c7f10dceca810282446ce5ab0c0ad754c60248431d035c20c141","observation_id":"2fefd57f-15ba-4596-ba62-2ed2a62b9487","resolution":{"observed_at":"2026-08-10T17:52:29.884444Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2008.13494","last_updated":"2024-10-30T18:12:24Z","snapshot_observed_at":"2026-08-14T05:51:49.891604Z","submitted_at":"2020-08-31T11:22:28Z","title":"Set-theoretic type solutions of the braid equation","version":5},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2008.13494","snapshot_observed_at":"2026-08-10T17:52:29.560376Z","title":null,"venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2501.11975","last_updated":"2025-02-12T15:59:43Z","snapshot_observed_at":"2026-08-13T16:35:17.294016Z","submitted_at":"2025-01-21T08:44:09Z","title":"Matched pairs and Yang-Baxter operators","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-10T17:52:29.560376Z"},"links":{"cited_paper":"/paper/2008.13494","citing_paper":"/paper/2501.11975"},"observation_digest":"sha256:d3631b05b1803a9b3e49b091974440ff63ede500c4fed3b94c476e9fefd4bc4d","observation_id":"5812e66c-4ccd-4498-a223-16242382b195","resolution":{"observed_at":"2026-08-10T17:52:29.560376Z","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":"2026-08-10T17:52:29.869300Z","title":null,"venue":null,"work_id":"7891c463-c1c1-44f8-809d-74d99c0f6f63","year":2024},"citing_paper":{"arxiv_id":"2501.11975","last_updated":"2025-02-12T15:59:43Z","snapshot_observed_at":"2026-08-13T16:35:17.294016Z","submitted_at":"2025-01-21T08:44:09Z","title":"Matched pairs and Yang-Baxter operators","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-10T17:52:29.564584Z"},"links":{"citing_paper":"/paper/2501.11975"},"observation_digest":"sha256:b75ef95f6128071f1b3955a97fddfe6f1c826cfc0d2ed715b589c84e856144e3","observation_id":"f3ea7ec5-2f16-4894-833c-299a869698b1","resolution":{"observed_at":"2026-08-10T17:52:29.873203Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T17:52:29.857157Z","title":null,"venue":null,"work_id":"03e1c8f3-c095-481c-8754-9c11ba45e6f2","year":2000},"citing_paper":{"arxiv_id":"2501.11975","last_updated":"2025-02-12T15:59:43Z","snapshot_observed_at":"2026-08-13T16:35:17.294016Z","submitted_at":"2025-01-21T08:44:09Z","title":"Matched pairs and Yang-Baxter operators","version":2},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-10T17:52:29.568077Z"},"links":{"citing_paper":"/paper/2501.11975"},"observation_digest":"sha256:0c4845d6d47575e9a190ecbfd83a09dc6a8789b426efbb3a4c11b3ad0305b277","observation_id":"64938377-15f2-4ca3-8fe8-c73b526c79ac","resolution":{"observed_at":"2026-08-10T17:52:29.861264Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T17:52:29.844872Z","title":"Majid, Crossed products by braided groups and bosoniz ation, J","venue":null,"work_id":"3e943c7e-f695-4839-b107-43a265e3d50d","year":1994},"citing_paper":{"arxiv_id":"2501.11975","last_updated":"2025-02-12T15:59:43Z","snapshot_observed_at":"2026-08-13T16:35:17.294016Z","submitted_at":"2025-01-21T08:44:09Z","title":"Matched pairs and Yang-Baxter operators","version":2},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-10T17:52:29.571614Z"},"links":{"citing_paper":"/paper/2501.11975"},"observation_digest":"sha256:7778c905daad93c25633020774638ef1882a031dda8c9a2d326d4c2c12d839aa","observation_id":"f59a9cbc-c199-44da-b010-f923cb9901e8","resolution":{"observed_at":"2026-08-10T17:52:29.849166Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T17:52:29.829104Z","title":"Majid, Physics for algebraists: Non-commutative and non-cocommutative Hopf algebras by a bicrossprod- uct construction, J","venue":null,"work_id":"1615c117-a337-4a38-af2f-480927542f40","year":1990},"citing_paper":{"arxiv_id":"2501.11975","last_updated":"2025-02-12T15:59:43Z","snapshot_observed_at":"2026-08-13T16:35:17.294016Z","submitted_at":"2025-01-21T08:44:09Z","title":"Matched pairs and Yang-Baxter operators","version":2},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-10T17:52:29.575079Z"},"links":{"citing_paper":"/paper/2501.11975"},"observation_digest":"sha256:78a792426a1cbc27ad80633ce9a3199647d2a9f2b9665e719357b6c76ea968c9","observation_id":"00a4b1b2-608d-4c02-afc3-1638865529ec","resolution":{"observed_at":"2026-08-10T17:52:29.835214Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T17:52:29.814957Z","title":"Majid, Foundations of quantum group theory, Cambridg e University Press, 1995","venue":null,"work_id":"b00f169d-d625-4e12-89ad-a5a91d4f1f51","year":1995},"citing_paper":{"arxiv_id":"2501.11975","last_updated":"2025-02-12T15:59:43Z","snapshot_observed_at":"2026-08-13T16:35:17.294016Z","submitted_at":"2025-01-21T08:44:09Z","title":"Matched pairs and Yang-Baxter operators","version":2},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-10T17:52:29.578556Z"},"links":{"citing_paper":"/paper/2501.11975"},"observation_digest":"sha256:4d17eed7802004e38b74763b5674ff1bf9dbed12398591a78ae709d795c96f58","observation_id":"b43a3e3e-df76-49c0-9cf4-813ad98bee58","resolution":{"observed_at":"2026-08-10T17:52:29.819483Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T17:52:29.801219Z","title":null,"venue":null,"work_id":"e8f6b268-88ad-4796-b974-12d11af4e52d","year":1988},"citing_paper":{"arxiv_id":"2501.11975","last_updated":"2025-02-12T15:59:43Z","snapshot_observed_at":"2026-08-13T16:35:17.294016Z","submitted_at":"2025-01-21T08:44:09Z","title":"Matched pairs and Yang-Baxter operators","version":2},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-10T17:52:29.582338Z"},"links":{"citing_paper":"/paper/2501.11975"},"observation_digest":"sha256:8deea6f9fb3e72c900caca471d74893182db4d01071e4b83490d599a45144002","observation_id":"ff7435eb-9080-4371-8430-7fda7103a589","resolution":{"observed_at":"2026-08-10T17:52:29.805196Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T17:52:29.586278Z","title":"Montgomery, Hopf algebras and Their Actions on Rings, Amer","venue":null,"work_id":null,"year":1993},"citing_paper":{"arxiv_id":"2501.11975","last_updated":"2025-02-12T15:59:43Z","snapshot_observed_at":"2026-08-13T16:35:17.294016Z","submitted_at":"2025-01-21T08:44:09Z","title":"Matched pairs and Yang-Baxter operators","version":2},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-10T17:52:29.586278Z"},"links":{"citing_paper":"/paper/2501.11975"},"observation_digest":"sha256:33bf8259a5d62be8142f36940375dcf5b8c596331762beeb41410671acae0f78","observation_id":"5adabca1-a92e-4ca2-a00d-a84fe6766f91","resolution":{"observed_at":"2026-08-10T17:52:29.586278Z","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":"2026-08-10T17:52:29.771548Z","title":null,"venue":null,"work_id":"22c05652-86fe-4e7c-aa7d-d83bf81ca14d","year":2008},"citing_paper":{"arxiv_id":"2501.11975","last_updated":"2025-02-12T15:59:43Z","snapshot_observed_at":"2026-08-13T16:35:17.294016Z","submitted_at":"2025-01-21T08:44:09Z","title":"Matched pairs and Yang-Baxter operators","version":2},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-10T17:52:29.589839Z"},"links":{"citing_paper":"/paper/2501.11975"},"observation_digest":"sha256:1c1d831ac2de29f71c59affc5da711fd1a92dbcfd31d1d81ae94eba9f12ece8f","observation_id":"22362969-fbae-4c70-b1a8-0636a805d82d","resolution":{"observed_at":"2026-08-10T17:52:29.775666Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T17:52:29.759476Z","title":"Radford, The Structure of Hopf algebras with a project ion, J","venue":null,"work_id":"fef818eb-6879-42cf-a413-7d74985b3c34","year":1985},"citing_paper":{"arxiv_id":"2501.11975","last_updated":"2025-02-12T15:59:43Z","snapshot_observed_at":"2026-08-13T16:35:17.294016Z","submitted_at":"2025-01-21T08:44:09Z","title":"Matched pairs and Yang-Baxter operators","version":2},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-10T17:52:29.593564Z"},"links":{"citing_paper":"/paper/2501.11975"},"observation_digest":"sha256:c446b081e3837bb7068d36655033be5c30ea39042f41a776bbf532f9cd4e5d4c","observation_id":"0d16c38f-5c5a-47d1-a2ff-c656262eabd0","resolution":{"observed_at":"2026-08-10T17:52:29.763633Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T17:52:29.747466Z","title":"Rump, Braces, radical rings, and the quantum Y ang-Bax ter equation, J","venue":null,"work_id":"5dd06e0d-b450-4914-b625-e77d666d92c5","year":2007},"citing_paper":{"arxiv_id":"2501.11975","last_updated":"2025-02-12T15:59:43Z","snapshot_observed_at":"2026-08-13T16:35:17.294016Z","submitted_at":"2025-01-21T08:44:09Z","title":"Matched pairs and Yang-Baxter operators","version":2},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-10T17:52:29.597118Z"},"links":{"citing_paper":"/paper/2501.11975"},"observation_digest":"sha256:5a62a5fe3dd79fad0a535377885272cc8f7b3a0af6485d9f9d70a01627d2d478","observation_id":"d02e79d0-18c4-4f1c-a667-1fd370d67016","resolution":{"observed_at":"2026-08-10T17:52:29.751820Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2407.17922","last_updated":"2025-03-20T19:35:28Z","snapshot_observed_at":"2026-08-13T05:31:46.539319Z","submitted_at":"2024-07-25T10:16:17Z","title":"Yetter-Drinfeld post-Hopf algebras and Yetter-Drinfeld relative Rota-Baxter operators","version":2},"cited_work":{"arxiv_id":"2407.17922","doi":null,"metadata_source":"pith","pith_arxiv_id":"2407.17922","snapshot_observed_at":"2026-08-10T17:52:29.666541Z","title":"Yetter-Drinfeld post-Hopf algebras and Yetter-Drinfeld relative Rota-Baxter operators","venue":"math.QA","work_id":"e2ab4256-4b5f-4c2c-b072-baef9e2652bc","year":2024},"citing_paper":{"arxiv_id":"2501.11975","last_updated":"2025-02-12T15:59:43Z","snapshot_observed_at":"2026-08-13T16:35:17.294016Z","submitted_at":"2025-01-21T08:44:09Z","title":"Matched pairs and Yang-Baxter operators","version":2},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-10T17:52:29.600620Z"},"links":{"cited_paper":"/paper/2407.17922","citing_paper":"/paper/2501.11975"},"observation_digest":"sha256:9d79068733cfdac76fc0ca0576a4d992eae6c783fdf409aa03beeb1654502b15","observation_id":"300b6090-eade-4db2-96b4-dd2ab5ae2356","resolution":{"observed_at":"2026-08-10T17:52:29.670729Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T17:52:29.729176Z","title":"Stefan, Hopf algebras of low dimension, J","venue":null,"work_id":"2dcdfe1c-9ae0-457b-aecb-08151c841801","year":1999},"citing_paper":{"arxiv_id":"2501.11975","last_updated":"2025-02-12T15:59:43Z","snapshot_observed_at":"2026-08-13T16:35:17.294016Z","submitted_at":"2025-01-21T08:44:09Z","title":"Matched pairs and Yang-Baxter operators","version":2},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-10T17:52:29.604589Z"},"links":{"citing_paper":"/paper/2501.11975"},"observation_digest":"sha256:96db0e6d14587b2aff5c23943f927d779b896a764a3b97e00fbf5715e3091a12","observation_id":"2a48cad2-8f5a-4d92-a6a4-52d4852b59cf","resolution":{"observed_at":"2026-08-10T17:52:29.734169Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T17:52:29.714657Z","title":"Takeuchi, Matched pairs of groups and bismash product s of Hopf algebras, Comm","venue":null,"work_id":"7321ecff-a301-4d82-a5e6-62542732d629","year":1981},"citing_paper":{"arxiv_id":"2501.11975","last_updated":"2025-02-12T15:59:43Z","snapshot_observed_at":"2026-08-13T16:35:17.294016Z","submitted_at":"2025-01-21T08:44:09Z","title":"Matched pairs and Yang-Baxter operators","version":2},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-10T17:52:29.608302Z"},"links":{"citing_paper":"/paper/2501.11975"},"observation_digest":"sha256:820f9bbd406b4fe601d508e046472b19f1beb8218f9469db1099e6b1d5e72a8d","observation_id":"16a0ab98-7b2a-4d3e-b425-06167f958530","resolution":{"observed_at":"2026-08-10T17:52:29.720028Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-10T17:52:29.700604Z","title":"Takeuchi, Survey on matched pairs of groups-an elemen tary approach to the ESS-LYZ theory, Banach Center Publications 61 (2003), 305–331","venue":null,"work_id":"de84ce95-d083-4e14-930d-e3c7defbd15e","year":2003},"citing_paper":{"arxiv_id":"2501.11975","last_updated":"2025-02-12T15:59:43Z","snapshot_observed_at":"2026-08-13T16:35:17.294016Z","submitted_at":"2025-01-21T08:44:09Z","title":"Matched pairs and Yang-Baxter operators","version":2},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-10T17:52:29.611676Z"},"links":{"citing_paper":"/paper/2501.11975"},"observation_digest":"sha256:3f4fd037de72f91adccea9157fe0858f39804cd8ee878bd9cc4851af1603de1f","observation_id":"fd1a6247-c0a9-4dbb-991f-0feade009d34","resolution":{"observed_at":"2026-08-10T17:52:29.704771Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2501.13747","last_updated":"2025-01-23T15:24:20Z","snapshot_observed_at":"2026-08-10T15:36:25.552842Z","submitted_at":"2025-01-23T15:24:20Z","title":"Matched pairs of actions on the Kac-Paljutkin algebra $H_8$","version":1},"cited_work":{"arxiv_id":"2501.13747","doi":null,"metadata_source":"pith","pith_arxiv_id":"2501.13747","snapshot_observed_at":"2026-08-10T17:52:29.647195Z","title":"Matched pairs of actions on the Kac-Paljutkin algebra $H_8$","venue":"math.QA","work_id":"6de5373c-335d-452e-8c16-28eee57dd789","year":2025},"citing_paper":{"arxiv_id":"2501.11975","last_updated":"2025-02-12T15:59:43Z","snapshot_observed_at":"2026-08-13T16:35:17.294016Z","submitted_at":"2025-01-21T08:44:09Z","title":"Matched pairs and Yang-Baxter operators","version":2},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-10T17:52:29.615286Z"},"links":{"cited_paper":"/paper/2501.13747","citing_paper":"/paper/2501.11975"},"observation_digest":"sha256:1d6011d41f2005f99a2a43a10e6b1057829f8739459051345e4e9561253f059a","observation_id":"734a63ae-3d26-49aa-9eb9-a8bb144d0083","resolution":{"observed_at":"2026-08-10T17:52:29.654098Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2501.11975","last_updated":"2025-02-12T15:59:43Z","latest_version":2,"primary_category":"math.QA","snapshot_observed_at":"2026-08-13T16:35:17.294016Z","submitted_at":"2025-01-21T08:44:09Z","title":"Matched pairs and Yang-Baxter operators"},"reference_resolution":{"displayed":27,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":12,"verified_exact":2,"verified_fuzzy":13},"total_outbound_references":27},"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":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"thesis":"As of 14 August 2026, this Paper Citation Record lists 27 of 27 outbound references and 1 inbound Pith citation observation for arXiv:2501.11975."}