{"as_of":"2026-08-04T17:01:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:5a12cc7ec9b4565100bc56547eac64cf0a4e33d04ef3224ea6f23b5a31166321","coverage":[{"denominator":12,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":12,"source":"paper_references, paper_reference_links","source_observed_at":"2026-06-28T20:11:15.453728Z","state":"measured"},{"denominator":12,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":12,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-04T06:34:03.388597+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2605.31298/citation-record","integrity":"/paper/2605.31298/integrity","json":"/paper/2605.31298/citation-record.json","paper":"/paper/2605.31298"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T20:11:15.453728Z","title":null,"venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2605.31298","last_updated":"2026-05-29T13:33:56Z","snapshot_observed_at":"2026-07-06T23:40:27.543522Z","submitted_at":"2026-05-29T13:33:56Z","title":"Multi-welded twin groups","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-06-28T20:11:15.453728Z"},"links":{"citing_paper":"/paper/2605.31298"},"observation_digest":"sha256:2f03127a6085a9313d35ce00768921998c013ef2f5b71c282cb8d4e48935bee9","observation_id":"04df7b5e-e90a-43b7-9ae3-85159816e37b","resolution":{"observed_at":"2026-06-28T20:11:15.453728Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T20:11:15.453728Z","title":null,"venue":null,"work_id":null,"year":1999},"citing_paper":{"arxiv_id":"2605.31298","last_updated":"2026-05-29T13:33:56Z","snapshot_observed_at":"2026-07-06T23:40:27.543522Z","submitted_at":"2026-05-29T13:33:56Z","title":"Multi-welded twin groups","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-06-28T20:11:15.453728Z"},"links":{"citing_paper":"/paper/2605.31298"},"observation_digest":"sha256:bc93f59ccebda050c6766211f56516f930ffb39fcf87d4f1dddd64a0522ffaf4","observation_id":"c70a8954-fdea-4a38-9d5b-43ac71104d58","resolution":{"observed_at":"2026-06-28T20:11:15.453728Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T20:11:15.453728Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2605.31298","last_updated":"2026-05-29T13:33:56Z","snapshot_observed_at":"2026-07-06T23:40:27.543522Z","submitted_at":"2026-05-29T13:33:56Z","title":"Multi-welded twin groups","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-06-28T20:11:15.453728Z"},"links":{"citing_paper":"/paper/2605.31298"},"observation_digest":"sha256:1360cb8888b7004e06756eece8bc89bcef083607406c446bc87dd34a05194bd7","observation_id":"9c878a05-de26-4049-8e42-537c780b64d0","resolution":{"observed_at":"2026-06-28T20:11:15.453728Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2508.04168","last_updated":"2025-08-06T07:48:29Z","snapshot_observed_at":"2026-07-06T22:08:36.543090Z","submitted_at":"2025-08-06T07:48:29Z","title":"On representations of the multi-virtual braid group $M_kVB_n$ and the multi-welded braid group $M_kWB_n$","version":1},"cited_work":{"arxiv_id":"2508.04168","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2508.04168","snapshot_observed_at":"2026-06-28T20:12:37.649719Z","title":"Keshari, M","venue":null,"work_id":"8ce6b241-5189-44d0-a361-50984866b225","year":2025},"citing_paper":{"arxiv_id":"2605.31298","last_updated":"2026-05-29T13:33:56Z","snapshot_observed_at":"2026-07-06T23:40:27.543522Z","submitted_at":"2026-05-29T13:33:56Z","title":"Multi-welded twin groups","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-06-28T20:11:15.453728Z"},"links":{"cited_paper":"/paper/2508.04168","citing_paper":"/paper/2605.31298"},"observation_digest":"sha256:b0b14a941afa22232adcae411161c84e3c1283df7a8844d8e54ef4c5428c3d75","observation_id":"c36f32e2-19db-4c30-9218-3120ba8555e1","resolution":{"observed_at":"2026-06-28T20:12:37.650858Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2605.13090","last_updated":"2026-05-13T07:01:00Z","snapshot_observed_at":"2026-08-02T19:53:19.543569Z","submitted_at":"2026-05-13T07:01:00Z","title":"Presentations and Representations of the Multi-Virtual Twin Group and Associated Subgroups","version":1},"cited_work":{"arxiv_id":"2605.13090","doi":null,"metadata_source":"pith","pith_arxiv_id":"2605.13090","snapshot_observed_at":"2026-06-28T20:12:37.641201Z","title":"Presentations and Representations of the Multi-Virtual Twin Group and Associated Subgroups","venue":"math.GT","work_id":"4c391f74-6428-419f-8fc4-6dee153b5b49","year":2026},"citing_paper":{"arxiv_id":"2605.31298","last_updated":"2026-05-29T13:33:56Z","snapshot_observed_at":"2026-07-06T23:40:27.543522Z","submitted_at":"2026-05-29T13:33:56Z","title":"Multi-welded twin groups","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-06-28T20:11:15.453728Z"},"links":{"cited_paper":"/paper/2605.13090","citing_paper":"/paper/2605.31298"},"observation_digest":"sha256:37a68942051d2ece1dbaa6b7237930786f873354e7399310ce82a4d41160cc1b","observation_id":"28b85c9d-0746-4b01-8e29-6e093a3381bd","resolution":{"observed_at":"2026-06-28T20:12:37.642395Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-28T20:11:15.453728Z","title":"Khovanov,RealK(π,1)arrangements from finite root systems, Math","venue":null,"work_id":null,"year":1996},"citing_paper":{"arxiv_id":"2605.31298","last_updated":"2026-05-29T13:33:56Z","snapshot_observed_at":"2026-07-06T23:40:27.543522Z","submitted_at":"2026-05-29T13:33:56Z","title":"Multi-welded twin groups","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-06-28T20:11:15.453728Z"},"links":{"citing_paper":"/paper/2605.31298"},"observation_digest":"sha256:2880d8f551f6495c0082d616c49d3300ce8a022b1029bc21be88046528053ab3","observation_id":"aeb47ad1-0107-4541-b43e-a204535744de","resolution":{"observed_at":"2026-06-28T20:11:15.453728Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T20:11:15.453728Z","title":"Khovanov,Doodle groups, Transactions of the American Mathematical Society 349, 2297–2315, (1997)","venue":null,"work_id":null,"year":1997},"citing_paper":{"arxiv_id":"2605.31298","last_updated":"2026-05-29T13:33:56Z","snapshot_observed_at":"2026-07-06T23:40:27.543522Z","submitted_at":"2026-05-29T13:33:56Z","title":"Multi-welded twin groups","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-06-28T20:11:15.453728Z"},"links":{"citing_paper":"/paper/2605.31298"},"observation_digest":"sha256:945d208d8d3df16bee0756f5825a2963dc7fd9d91fd53efc1ea9eb1ebf3cd1e0","observation_id":"69a1c4dd-e067-47a3-84bf-4307df1deeb6","resolution":{"observed_at":"2026-06-28T20:11:15.453728Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2507.15005","last_updated":"2026-04-03T15:34:53Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2025-07-20T15:17:49Z","title":"Twin groups representations","version":3},"cited_work":{"arxiv_id":"2507.15005","doi":null,"metadata_source":"pith","pith_arxiv_id":"2507.15005","snapshot_observed_at":"2026-06-28T20:12:37.645644Z","title":"Twin groups representations","venue":"math.RT","work_id":"e70fdd07-3a3b-46f7-b212-c6029e3060df","year":2025},"citing_paper":{"arxiv_id":"2605.31298","last_updated":"2026-05-29T13:33:56Z","snapshot_observed_at":"2026-07-06T23:40:27.543522Z","submitted_at":"2026-05-29T13:33:56Z","title":"Multi-welded twin groups","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-06-28T20:11:15.453728Z"},"links":{"cited_paper":"/paper/2507.15005","citing_paper":"/paper/2605.31298"},"observation_digest":"sha256:75268529813fbb0b1b694b1ed522431541ff345292c3ce2fcdd63f64e4f5210f","observation_id":"1651562b-f36a-43ed-8988-845190afcf46","resolution":{"observed_at":"2026-06-28T20:12:37.646557Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-28T20:11:15.453728Z","title":"Nasser,Attacks on local representations of the virtual and the welded braid groups, Ann","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2605.31298","last_updated":"2026-05-29T13:33:56Z","snapshot_observed_at":"2026-07-06T23:40:27.543522Z","submitted_at":"2026-05-29T13:33:56Z","title":"Multi-welded twin groups","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-06-28T20:11:15.453728Z"},"links":{"citing_paper":"/paper/2605.31298"},"observation_digest":"sha256:a61d79750f559aec28375c520554a136653b62b961f1c2226a4d18057896aec5","observation_id":"11aae19a-6b62-4871-a76f-2f8515f0ecc7","resolution":{"observed_at":"2026-06-28T20:11:15.453728Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2604.19307","last_updated":"2026-04-21T10:13:44Z","snapshot_observed_at":"2026-07-06T23:05:58.167533Z","submitted_at":"2026-04-21T10:13:44Z","title":"On Universal Virtual and Welded Braid Groups and Their Linear Representations","version":1},"cited_work":{"arxiv_id":"2604.19307","doi":null,"metadata_source":"pith","pith_arxiv_id":"2604.19307","snapshot_observed_at":"2026-07-02T15:47:06.990609Z","title":"On Universal Virtual and Welded Braid Groups and Their Linear Representations","venue":"math.RT","work_id":"61fd03a8-c9b0-41cd-9389-1883cac5fa5c","year":2026},"citing_paper":{"arxiv_id":"2605.31298","last_updated":"2026-05-29T13:33:56Z","snapshot_observed_at":"2026-07-06T23:40:27.543522Z","submitted_at":"2026-05-29T13:33:56Z","title":"Multi-welded twin groups","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-06-28T20:11:15.453728Z"},"links":{"cited_paper":"/paper/2604.19307","citing_paper":"/paper/2605.31298"},"observation_digest":"sha256:7d67eaa1038dfcbad86c409e88414551bb8d00b6bc2d186d4598028d85a9b479","observation_id":"f227086c-9f45-4a62-b887-a957e4e11df1","resolution":{"observed_at":"2026-06-28T20:12:37.644658Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2604.01633","last_updated":"2026-04-09T11:38:43Z","snapshot_observed_at":"2026-07-06T22:51:35.522923Z","submitted_at":"2026-04-02T05:23:00Z","title":"Universal virtual braid groups","version":2},"cited_work":{"arxiv_id":"2604.01633","doi":null,"metadata_source":"pith","pith_arxiv_id":"2604.01633","snapshot_observed_at":"2026-07-02T15:47:06.994168Z","title":"Universal virtual braid groups","venue":"math.GR","work_id":"58421590-c65e-4bbd-9120-01e7370736b0","year":2026},"citing_paper":{"arxiv_id":"2605.31298","last_updated":"2026-05-29T13:33:56Z","snapshot_observed_at":"2026-07-06T23:40:27.543522Z","submitted_at":"2026-05-29T13:33:56Z","title":"Multi-welded twin groups","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-06-28T20:11:15.453728Z"},"links":{"cited_paper":"/paper/2604.01633","citing_paper":"/paper/2605.31298"},"observation_digest":"sha256:63de35cd18baa75b1cbf2196166019b139f31646bce77289bf2300c182ba34d6","observation_id":"32c8606e-0c75-4d73-a084-ee6eb7fd41e8","resolution":{"observed_at":"2026-06-28T20:12:37.648724Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-28T20:11:15.453728Z","title":"Shabat and V","venue":null,"work_id":null,"year":1990},"citing_paper":{"arxiv_id":"2605.31298","last_updated":"2026-05-29T13:33:56Z","snapshot_observed_at":"2026-07-06T23:40:27.543522Z","submitted_at":"2026-05-29T13:33:56Z","title":"Multi-welded twin groups","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-06-28T20:11:15.453728Z"},"links":{"citing_paper":"/paper/2605.31298"},"observation_digest":"sha256:1dc0602e1ff2f5778ecd1fc4d777b315eae9e4db8e516531c1fc2946da2f7eb8","observation_id":"236f60dc-d5c6-4764-9089-264de41d6d89","resolution":{"observed_at":"2026-06-28T20:11:15.453728Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2605.31298","last_updated":"2026-05-29T13:33:56Z","latest_version":1,"primary_category":"math.RT","snapshot_observed_at":"2026-07-06T23:40:27.543522Z","submitted_at":"2026-05-29T13:33:56Z","title":"Multi-welded twin groups"},"reference_resolution":{"displayed":12,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":7,"verified_exact":5,"verified_fuzzy":0},"total_outbound_references":12},"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":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"thesis":"As of 4 August 2026, this Paper Citation Record lists 12 of 12 outbound references and 0 inbound Pith citation observations for arXiv:2605.31298."}