{"as_of":"2026-08-17T09:19:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:ac6b5a7d2c5a8fe0ce199997702c9616f8d79cd605caf41bdd49f40deb2974a3","coverage":[{"denominator":20,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":20,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-06T22:37:23.444077Z","state":"measured"},{"denominator":20,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":20,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-17T06:30:58.91139+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/2506.21856/citation-record","integrity":"/paper/2506.21856/integrity","json":"/paper/2506.21856/citation-record.json","paper":"/paper/2506.21856"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T22:37:27.017731Z","title":"Two-parameter quantum groups of exceptional type E-series and convex PBW-type basis.Algebra Colloq., 15(4):619–636, 2008","venue":null,"work_id":"32096dda-e942-4ed3-b5e7-eefebc5529a0","year":2008},"citing_paper":{"arxiv_id":"2506.21856","last_updated":"2025-07-27T14:51:37Z","snapshot_observed_at":"2026-08-06T22:15:04.095547Z","submitted_at":"2025-06-27T02:20:03Z","title":"Simple Modules and PI Structure of the Two-Parameter Quantized Algebra $U^+_{r,s}(B_2)$","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-06T22:37:21.875711Z"},"links":{"citing_paper":"/paper/2506.21856"},"observation_digest":"sha256:2da24addc8b7de2978b7a1c056c7ce314015afcf5ee211750cbca4be2dcfff99","observation_id":"b4e925ee-a467-4387-b16b-18bbb630e011","resolution":{"observed_at":"2026-08-06T22:37:27.107696Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-06T22:37:26.812330Z","title":null,"venue":null,"work_id":"4bf4862c-f83c-4181-82ef-1391e9c0352b","year":1994},"citing_paper":{"arxiv_id":"2506.21856","last_updated":"2025-07-27T14:51:37Z","snapshot_observed_at":"2026-08-06T22:15:04.095547Z","submitted_at":"2025-06-27T02:20:03Z","title":"Simple Modules and PI Structure of the Two-Parameter Quantized Algebra $U^+_{r,s}(B_2)$","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-06T22:37:21.953054Z"},"links":{"citing_paper":"/paper/2506.21856"},"observation_digest":"sha256:4d6a830f1f24f701115ec2b6343b0fdaec5fcb48aa777150d419df6040ca855a","observation_id":"7a2f5774-8b74-48d0-8a02-9ac7b84b4110","resolution":{"observed_at":"2026-08-06T22:37:26.930413Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-06T22:37:26.593197Z","title":"Representations of two-parameter quantum groups and Schur-Weyl duality","venue":null,"work_id":"454a64dc-f4de-457d-8dd8-941ca589597c","year":2004},"citing_paper":{"arxiv_id":"2506.21856","last_updated":"2025-07-27T14:51:37Z","snapshot_observed_at":"2026-08-06T22:15:04.095547Z","submitted_at":"2025-06-27T02:20:03Z","title":"Simple Modules and PI Structure of the Two-Parameter Quantized Algebra $U^+_{r,s}(B_2)$","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-06T22:37:22.040311Z"},"links":{"citing_paper":"/paper/2506.21856"},"observation_digest":"sha256:a563fd5f982733a9f28293b5edfc0a3ebdae8e87b25f349b70c5bdea412d5030","observation_id":"3ce807de-799a-4739-9a80-e0d385447cd1","resolution":{"observed_at":"2026-08-06T22:37:26.721561Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-06T22:37:26.360646Z","title":"Two-parameter quantum groups and drinfeld doubles","venue":null,"work_id":"bbb86921-4037-4937-b3eb-7fac005ea994","year":2004},"citing_paper":{"arxiv_id":"2506.21856","last_updated":"2025-07-27T14:51:37Z","snapshot_observed_at":"2026-08-06T22:15:04.095547Z","submitted_at":"2025-06-27T02:20:03Z","title":"Simple Modules and PI Structure of the Two-Parameter Quantized Algebra $U^+_{r,s}(B_2)$","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-06T22:37:22.127231Z"},"links":{"citing_paper":"/paper/2506.21856"},"observation_digest":"sha256:901560604df0200f4e4b443347b10b89143a6711261f13e8ce928ddbbc38c43a","observation_id":"bacd4160-929d-436c-8785-fc382f5fc50b","resolution":{"observed_at":"2026-08-06T22:37:26.427050Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-06T22:37:26.185798Z","title":"Quantum Heisenberg enveloping algebras at roots of unity.J","venue":null,"work_id":"73f4797c-14be-458a-a35f-136aeb44b21a","year":2024},"citing_paper":{"arxiv_id":"2506.21856","last_updated":"2025-07-27T14:51:37Z","snapshot_observed_at":"2026-08-06T22:15:04.095547Z","submitted_at":"2025-06-27T02:20:03Z","title":"Simple Modules and PI Structure of the Two-Parameter Quantized Algebra $U^+_{r,s}(B_2)$","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-06T22:37:22.226233Z"},"links":{"citing_paper":"/paper/2506.21856"},"observation_digest":"sha256:cc1728b6756f1cf9cc26096a046cc36d9252dbdd31696b02dd191d28036965c6","observation_id":"59002cc6-b57b-4e25-9e04-63ffaf3779a2","resolution":{"observed_at":"2026-08-06T22:37:26.288821Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2503.21170","last_updated":"2025-03-27T05:44:45Z","snapshot_observed_at":"2026-08-16T12:46:25.228045Z","submitted_at":"2025-03-27T05:44:45Z","title":"$U_q^+(B_2)$ and its representations","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2503.21170","snapshot_observed_at":"2026-08-06T22:37:22.232890Z","title":"U + q (B2) and its representations","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2506.21856","last_updated":"2025-07-27T14:51:37Z","snapshot_observed_at":"2026-08-06T22:15:04.095547Z","submitted_at":"2025-06-27T02:20:03Z","title":"Simple Modules and PI Structure of the Two-Parameter Quantized Algebra $U^+_{r,s}(B_2)$","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-06T22:37:22.232890Z"},"links":{"cited_paper":"/paper/2503.21170","citing_paper":"/paper/2506.21856"},"observation_digest":"sha256:b4b4e01b2bc9de355fe6e4194e4dcdd0dbd86d77c1a0de5491d5f686c2497bc0","observation_id":"0ee29ebd-6ebd-4184-924c-a044e2e86ab4","resolution":{"observed_at":"2026-08-06T22:37:22.232890Z","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":"2026-08-06T22:37:26.010131Z","title":"Drinfeld doubles and lusztig’s symme- tries of two-parameter quantum groups.J","venue":null,"work_id":"08c09c74-946a-494d-9f6c-bcd0abcd17ba","year":2006},"citing_paper":{"arxiv_id":"2506.21856","last_updated":"2025-07-27T14:51:37Z","snapshot_observed_at":"2026-08-06T22:15:04.095547Z","submitted_at":"2025-06-27T02:20:03Z","title":"Simple Modules and PI Structure of the Two-Parameter Quantized Algebra $U^+_{r,s}(B_2)$","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-06T22:37:22.288071Z"},"links":{"citing_paper":"/paper/2506.21856"},"observation_digest":"sha256:cfaee6c772810c9ba70d20cb6790d68dfc97600ecb1b0f0094524a2d52105c44","observation_id":"3d80952e-d7c8-49fe-bffe-1313d687ba2f","resolution":{"observed_at":"2026-08-06T22:37:26.100398Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-06T22:37:25.795948Z","title":"Brown and Ken R","venue":null,"work_id":"b6c46a69-6818-406c-bb9b-ce3c01b7f1ac","year":2002},"citing_paper":{"arxiv_id":"2506.21856","last_updated":"2025-07-27T14:51:37Z","snapshot_observed_at":"2026-08-06T22:15:04.095547Z","submitted_at":"2025-06-27T02:20:03Z","title":"Simple Modules and PI Structure of the Two-Parameter Quantized Algebra $U^+_{r,s}(B_2)$","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-06T22:37:22.370980Z"},"links":{"citing_paper":"/paper/2506.21856"},"observation_digest":"sha256:37c0292a21a97967b44d0a582120fa4d6e60703c94ba3638be0586fd40460b2e","observation_id":"35b3b26c-84ae-4c96-8fc2-779871df8078","resolution":{"observed_at":"2026-08-06T22:37:25.888440Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-06T22:37:25.624611Z","title":"De Concini and C","venue":null,"work_id":"d5770e7b-5f87-499c-b34e-eae12bf1a9f7","year":1992},"citing_paper":{"arxiv_id":"2506.21856","last_updated":"2025-07-27T14:51:37Z","snapshot_observed_at":"2026-08-06T22:15:04.095547Z","submitted_at":"2025-06-27T02:20:03Z","title":"Simple Modules and PI Structure of the Two-Parameter Quantized Algebra $U^+_{r,s}(B_2)$","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-06T22:37:22.455038Z"},"links":{"citing_paper":"/paper/2506.21856"},"observation_digest":"sha256:d8d388f384daaf067c19988cd310be6af4695174a0f8404d33ad817205a9a510","observation_id":"0d8cc017-7b62-425a-aa95-69946d3df789","resolution":{"observed_at":"2026-08-06T22:37:25.670597Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-06T22:37:25.451875Z","title":"Two-parameter quantum affine algebra Ur,s(ˆsln), Drinfeld realization and quantum affine Lyndon basis.Comm","venue":null,"work_id":"730ed338-a5a1-43f4-8dfc-ad2daa00ad2a","year":2008},"citing_paper":{"arxiv_id":"2506.21856","last_updated":"2025-07-27T14:51:37Z","snapshot_observed_at":"2026-08-06T22:15:04.095547Z","submitted_at":"2025-06-27T02:20:03Z","title":"Simple Modules and PI Structure of the Two-Parameter Quantized Algebra $U^+_{r,s}(B_2)$","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-06T22:37:22.533758Z"},"links":{"citing_paper":"/paper/2506.21856"},"observation_digest":"sha256:798ec966bad3941d87a90b6ec39d7faa3f3d9a7fed5c0416cd6da501d0761178","observation_id":"93c8e7fa-59d9-4c89-955e-4b5c73b5aba3","resolution":{"observed_at":"2026-08-06T22:37:25.532961Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-06T22:37:25.239255Z","title":"The two-parameter quantum group of exceptional type G2 and Lusztig’s symmetries.Pacific J","venue":null,"work_id":"db8fba49-7b1e-4123-a863-6380efd3547e","year":2007},"citing_paper":{"arxiv_id":"2506.21856","last_updated":"2025-07-27T14:51:37Z","snapshot_observed_at":"2026-08-06T22:15:04.095547Z","submitted_at":"2025-06-27T02:20:03Z","title":"Simple Modules and PI Structure of the Two-Parameter Quantized Algebra $U^+_{r,s}(B_2)$","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-06T22:37:22.614638Z"},"links":{"citing_paper":"/paper/2506.21856"},"observation_digest":"sha256:726e11139cb5da98d5c57316f729e396d29bf16f00ef8232960bdb29169b57ce","observation_id":"821248fc-e5a6-4440-bd68-5b3ddd5d5147","resolution":{"observed_at":"2026-08-06T22:37:25.352474Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-06T22:37:25.034356Z","title":"On the centre of two-parameter quantum groupsUr,s(g) for typeBn with n even","venue":null,"work_id":"82906224-6849-43a9-93e7-439918baa11d","year":2014},"citing_paper":{"arxiv_id":"2506.21856","last_updated":"2025-07-27T14:51:37Z","snapshot_observed_at":"2026-08-06T22:15:04.095547Z","submitted_at":"2025-06-27T02:20:03Z","title":"Simple Modules and PI Structure of the Two-Parameter Quantized Algebra $U^+_{r,s}(B_2)$","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-06T22:37:22.674124Z"},"links":{"citing_paper":"/paper/2506.21856"},"observation_digest":"sha256:33369fbf5e7138177828eed21d86eec31ac0f1bb7053c79019a25d4ed0cb8fd3","observation_id":"a844d9b4-107f-4816-8c38-ce4d0f9d635d","resolution":{"observed_at":"2026-08-06T22:37:25.169143Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-06T22:37:24.827670Z","title":"Convex PBW-type Lyndon basis and restricted two-parameter quantum groups of typeG2","venue":null,"work_id":"1ff0c658-4c81-4f94-8551-8881e50efedd","year":2009},"citing_paper":{"arxiv_id":"2506.21856","last_updated":"2025-07-27T14:51:37Z","snapshot_observed_at":"2026-08-06T22:15:04.095547Z","submitted_at":"2025-06-27T02:20:03Z","title":"Simple Modules and PI Structure of the Two-Parameter Quantized Algebra $U^+_{r,s}(B_2)$","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-06T22:37:22.820987Z"},"links":{"citing_paper":"/paper/2506.21856"},"observation_digest":"sha256:0a207d1a1953d8130781f84b6b0011856c122d7be3701e18bb4d3cbb638e0ab2","observation_id":"fadf64d4-452a-4dd3-85c9-a46d962c3061","resolution":{"observed_at":"2026-08-06T22:37:24.908110Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-06T22:37:24.600699Z","title":"Convex PBW-type Lyndon bases and restricted two-parameter quantum groups of typeB","venue":null,"work_id":"3a83c84b-50e2-4e48-b642-f162f4b4c811","year":2010},"citing_paper":{"arxiv_id":"2506.21856","last_updated":"2025-07-27T14:51:37Z","snapshot_observed_at":"2026-08-06T22:15:04.095547Z","submitted_at":"2025-06-27T02:20:03Z","title":"Simple Modules and PI Structure of the Two-Parameter Quantized Algebra $U^+_{r,s}(B_2)$","version":2},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-06T22:37:22.967103Z"},"links":{"citing_paper":"/paper/2506.21856"},"observation_digest":"sha256:9e72b8d3ab7d6643dd5a7003d95c01b1731b4e4386654fef4339d07a3bd4047d","observation_id":"1752ccc9-692f-42b9-9ab9-0ebdcf96b04e","resolution":{"observed_at":"2026-08-06T22:37:24.701628Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-06T22:37:24.368912Z","title":"Lopes, and Alexandra Rogers","venue":null,"work_id":"9914c2d6-1f62-482d-ad6b-0382c15ca52f","year":2024},"citing_paper":{"arxiv_id":"2506.21856","last_updated":"2025-07-27T14:51:37Z","snapshot_observed_at":"2026-08-06T22:15:04.095547Z","submitted_at":"2025-06-27T02:20:03Z","title":"Simple Modules and PI Structure of the Two-Parameter Quantized Algebra $U^+_{r,s}(B_2)$","version":2},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-06T22:37:23.033582Z"},"links":{"citing_paper":"/paper/2506.21856"},"observation_digest":"sha256:64dc813efe61fc9d0ece00049c86e58fa4a7facc47976e71ae90e9b2e5507f7b","observation_id":"db19cf43-ee81-4d83-9b43-947274cc9463","resolution":{"observed_at":"2026-08-06T22:37:24.469471Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-06T22:37:24.158815Z","title":null,"venue":null,"work_id":"a2bbfd9b-2d4f-40bc-ad8d-2c953a34243a","year":2001},"citing_paper":{"arxiv_id":"2506.21856","last_updated":"2025-07-27T14:51:37Z","snapshot_observed_at":"2026-08-06T22:15:04.095547Z","submitted_at":"2025-06-27T02:20:03Z","title":"Simple Modules and PI Structure of the Two-Parameter Quantized Algebra $U^+_{r,s}(B_2)$","version":2},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-06T22:37:23.106315Z"},"links":{"citing_paper":"/paper/2506.21856"},"observation_digest":"sha256:fcd4ddecfe1f1ac716c63ff44eb1004d3c8ecc62dcf672652c61d9416a7e5b56","observation_id":"9e6cfdfc-39c7-4f96-9d16-4cb37ad929f2","resolution":{"observed_at":"2026-08-06T22:37:24.221793Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-06T22:37:24.018505Z","title":"Construction of simple modules over the quantum affine space.Algebra Colloq., 31(1):1–10, 2024","venue":null,"work_id":"9227dd75-8b32-4f2c-9e59-68ad00624a86","year":2024},"citing_paper":{"arxiv_id":"2506.21856","last_updated":"2025-07-27T14:51:37Z","snapshot_observed_at":"2026-08-06T22:15:04.095547Z","submitted_at":"2025-06-27T02:20:03Z","title":"Simple Modules and PI Structure of the Two-Parameter Quantized Algebra $U^+_{r,s}(B_2)$","version":2},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-06T22:37:23.173948Z"},"links":{"citing_paper":"/paper/2506.21856"},"observation_digest":"sha256:4365b2bbb53b3653f2e9b4b0d5ef56c5e080b8e08b92deffa0bf7e9210b56c8c","observation_id":"5e68d4e6-1df3-41fd-9ce9-461a088e1231","resolution":{"observed_at":"2026-08-06T22:37:24.086284Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-06T22:37:23.868825Z","title":"Representations of quantum nilpotent algebras at roots of unity and their completely prime quotients.PhD Thesis, Univ","venue":null,"work_id":"ac51c2d0-8f19-430c-98e7-8d7a39f64fe8","year":2019},"citing_paper":{"arxiv_id":"2506.21856","last_updated":"2025-07-27T14:51:37Z","snapshot_observed_at":"2026-08-06T22:15:04.095547Z","submitted_at":"2025-06-27T02:20:03Z","title":"Simple Modules and PI Structure of the Two-Parameter Quantized Algebra $U^+_{r,s}(B_2)$","version":2},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-06T22:37:23.248500Z"},"links":{"citing_paper":"/paper/2506.21856"},"observation_digest":"sha256:cc1014941c26bf348af5a8b546e3a9dcd29d064d403e7f69af26060997b7df5e","observation_id":"f2817780-1016-46e2-ab52-266283ada5a7","resolution":{"observed_at":"2026-08-06T22:37:23.938688Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-06T22:37:23.742895Z","title":"The prime ideal stratification and the automorphism group ofU + r,s(B2)","venue":null,"work_id":"dd644161-7ce7-4d77-a342-e167303e1a51","year":2011},"citing_paper":{"arxiv_id":"2506.21856","last_updated":"2025-07-27T14:51:37Z","snapshot_observed_at":"2026-08-06T22:15:04.095547Z","submitted_at":"2025-06-27T02:20:03Z","title":"Simple Modules and PI Structure of the Two-Parameter Quantized Algebra $U^+_{r,s}(B_2)$","version":2},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-06T22:37:23.364848Z"},"links":{"citing_paper":"/paper/2506.21856"},"observation_digest":"sha256:d9333f3ef2ed4d3845b72250664375d9b55ba077f5fc40b85fcb70f15f13a3c7","observation_id":"43ec4edb-8e51-40ff-8b70-0db03a1b11e8","resolution":{"observed_at":"2026-08-06T22:37:23.797423Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+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":"2026-08-06T22:37:23.562557Z","title":"Derivations of the two-parameter quantized enveloping algebraU + r,s(B2)","venue":null,"work_id":"33d95a74-3d82-4c55-b76d-1ce0fb40c465","year":2013},"citing_paper":{"arxiv_id":"2506.21856","last_updated":"2025-07-27T14:51:37Z","snapshot_observed_at":"2026-08-06T22:15:04.095547Z","submitted_at":"2025-06-27T02:20:03Z","title":"Simple Modules and PI Structure of the Two-Parameter Quantized Algebra $U^+_{r,s}(B_2)$","version":2},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-06T22:37:23.444077Z"},"links":{"citing_paper":"/paper/2506.21856"},"observation_digest":"sha256:084a3bf262ca37688a02dd74e197cc8109423847467319ebbcc141cfe0cf395a","observation_id":"b3d4167f-9706-44f8-8a00-4353cf4714a8","resolution":{"observed_at":"2026-08-06T22:37:23.620798Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2506.21856","last_updated":"2025-07-27T14:51:37Z","latest_version":2,"primary_category":"math.RT","snapshot_observed_at":"2026-08-06T22:15:04.095547Z","submitted_at":"2025-06-27T02:20:03Z","title":"Simple Modules and PI Structure of the Two-Parameter Quantized Algebra $U^+_{r,s}(B_2)$"},"reference_resolution":{"displayed":20,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":3,"verified_exact":0,"verified_fuzzy":17},"total_outbound_references":20},"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":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"thesis":"As of 17 August 2026, this Paper Citation Record lists 20 of 20 outbound references and 0 inbound Pith citation observations for arXiv:2506.21856."}