{"as_of":"2026-08-10T13:47:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:711e35c6be62eca762d5c6ea85a431aaa8377b9996d0125e7d823ceb0aa3362c","coverage":[{"denominator":24,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":24,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-03T00:12:31.649100Z","state":"measured"},{"denominator":24,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":24,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-10T06:31:04.303077+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/2602.11559/citation-record","integrity":"/paper/2602.11559/integrity","json":"/paper/2602.11559/citation-record.json","paper":"/paper/2602.11559"},"outbound":[{"citation":{"cited_paper":{"arxiv_id":"2211.11168","last_updated":"2024-02-23T01:09:06Z","snapshot_observed_at":"2026-07-06T14:20:58.769163Z","submitted_at":"2022-11-21T03:51:53Z","title":"Total positivity in twisted product of flag varieties","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2211.11168","snapshot_observed_at":"2026-08-03T00:12:31.550530Z","title":"Bao and X","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2602.11559","last_updated":"2026-05-25T00:08:31Z","snapshot_observed_at":"2026-08-10T13:35:35.270308Z","submitted_at":"2026-02-12T04:26:41Z","title":"Towards Monoidal Categorifications of Twisted Products of Flag Varieties","version":5},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-03T00:12:31.550530Z"},"links":{"cited_paper":"/paper/2211.11168","citing_paper":"/paper/2602.11559"},"observation_digest":"sha256:452013dfcd32013fd9d119afcd183f52a3586e710afd1470fd9731b2796597ab","observation_id":"21da9882-428a-46dc-a855-7c395c433f2b","resolution":{"observed_at":"2026-08-03T00:12:31.550530Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2506.10382","last_updated":"2025-08-08T03:00:33Z","snapshot_observed_at":"2026-08-10T02:42:10.291094Z","submitted_at":"2025-06-12T06:18:57Z","title":"Upper cluster structure on Kac--Moody Richardson varieties","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2506.10382","snapshot_observed_at":"2026-08-03T00:12:31.555868Z","title":"Bao and J","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2602.11559","last_updated":"2026-05-25T00:08:31Z","snapshot_observed_at":"2026-08-10T13:35:35.270308Z","submitted_at":"2026-02-12T04:26:41Z","title":"Towards Monoidal Categorifications of Twisted Products of Flag Varieties","version":5},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-03T00:12:31.555868Z"},"links":{"cited_paper":"/paper/2506.10382","citing_paper":"/paper/2602.11559"},"observation_digest":"sha256:46bcd6e403dd4266b88f1aa6b1c0041ec72f5afb434368c04aab354456e88944","observation_id":"24296d17-5a05-4a9b-a038-466d0f4b5fd1","resolution":{"observed_at":"2026-08-03T00:12:31.555868Z","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":"2026-08-03T00:12:31.560190Z","title":"Bi,Monoidal categorification on open Richardson varieties, arXiv preprint arXiv:2409.04715 (2024)","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2602.11559","last_updated":"2026-05-25T00:08:31Z","snapshot_observed_at":"2026-08-10T13:35:35.270308Z","submitted_at":"2026-02-12T04:26:41Z","title":"Towards Monoidal Categorifications of Twisted Products of Flag Varieties","version":5},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-03T00:12:31.560190Z"},"links":{"citing_paper":"/paper/2602.11559"},"observation_digest":"sha256:1243d42f09cc9b49d2db20b3ca5c968a371b07cf2ecdc422e71dcc221d2c140d","observation_id":"f8276903-f096-467e-9c1b-8409021656d9","resolution":{"observed_at":"2026-08-03T00:12:31.560190Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2506.00882","last_updated":"2026-05-21T03:13:26Z","snapshot_observed_at":"2026-07-06T21:34:29.773814Z","submitted_at":"2025-06-01T07:50:06Z","title":"On cluster structures of bosonic extensions","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2506.00882","snapshot_observed_at":"2026-08-03T00:12:31.564751Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2602.11559","last_updated":"2026-05-25T00:08:31Z","snapshot_observed_at":"2026-08-10T13:35:35.270308Z","submitted_at":"2026-02-12T04:26:41Z","title":"Towards Monoidal Categorifications of Twisted Products of Flag Varieties","version":5},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-03T00:12:31.564751Z"},"links":{"cited_paper":"/paper/2506.00882","citing_paper":"/paper/2602.11559"},"observation_digest":"sha256:cbcb71420ef9afae1df4b6d5a226f66ff2efab8cad17d018a5ed7f906566f18f","observation_id":"9bbfe5b9-6ff1-41a6-9be2-805bf163679b","resolution":{"observed_at":"2026-08-03T00:12:31.564751Z","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":"2026-08-03T00:12:31.569295Z","title":"Berenstein and A","venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2602.11559","last_updated":"2026-05-25T00:08:31Z","snapshot_observed_at":"2026-08-10T13:35:35.270308Z","submitted_at":"2026-02-12T04:26:41Z","title":"Towards Monoidal Categorifications of Twisted Products of Flag Varieties","version":5},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-03T00:12:31.569295Z"},"links":{"citing_paper":"/paper/2602.11559"},"observation_digest":"sha256:6255f6e388acf2c0541dd3ea31f28f52a441106ec90662f4fdc0afb6ba416231","observation_id":"133a66f7-201c-46c5-a76f-99ac4453ce61","resolution":{"observed_at":"2026-08-03T00:12:31.569295Z","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":"2026-08-03T00:12:31.573530Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2602.11559","last_updated":"2026-05-25T00:08:31Z","snapshot_observed_at":"2026-08-10T13:35:35.270308Z","submitted_at":"2026-02-12T04:26:41Z","title":"Towards Monoidal Categorifications of Twisted Products of Flag Varieties","version":5},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-03T00:12:31.573530Z"},"links":{"citing_paper":"/paper/2602.11559"},"observation_digest":"sha256:194799117ee0282ee115ffbe395a19df3b6b356ebbdb8bd1a43eebd634f32ef8","observation_id":"390c18fb-e32c-4793-ade0-574483fe5b45","resolution":{"observed_at":"2026-08-03T00:12:31.573530Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2304.02562","last_updated":"2023-05-07T03:35:25Z","snapshot_observed_at":"2026-08-09T12:30:55.575434Z","submitted_at":"2023-04-05T16:31:25Z","title":"Isomorphisms among quantum Grothendieck rings and cluster algebras","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2304.02562","snapshot_observed_at":"2026-08-03T00:12:31.578380Z","title":"Fujita, D","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2602.11559","last_updated":"2026-05-25T00:08:31Z","snapshot_observed_at":"2026-08-10T13:35:35.270308Z","submitted_at":"2026-02-12T04:26:41Z","title":"Towards Monoidal Categorifications of Twisted Products of Flag Varieties","version":5},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-03T00:12:31.578380Z"},"links":{"cited_paper":"/paper/2304.02562","citing_paper":"/paper/2602.11559"},"observation_digest":"sha256:eafcb82099a845514b38742a699e3ca25034d1465380271a48d57dfec4ad56ed","observation_id":"929e3215-76fc-4b2f-9780-6244952ae48c","resolution":{"observed_at":"2026-08-03T00:12:31.578380Z","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":"2026-08-03T00:12:31.582713Z","title":"Fomin and A","venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2602.11559","last_updated":"2026-05-25T00:08:31Z","snapshot_observed_at":"2026-08-10T13:35:35.270308Z","submitted_at":"2026-02-12T04:26:41Z","title":"Towards Monoidal Categorifications of Twisted Products of Flag Varieties","version":5},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-03T00:12:31.582713Z"},"links":{"citing_paper":"/paper/2602.11559"},"observation_digest":"sha256:04446aacf073cecaf53c89c44d05ec43581328f11775aa0f33c421e97c6aebe3","observation_id":"3e856af9-5c60-4dcd-96da-fd6eefd18d2b","resolution":{"observed_at":"2026-08-03T00:12:31.582713Z","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":"2026-08-03T00:12:31.586721Z","title":"Galashin, T","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2602.11559","last_updated":"2026-05-25T00:08:31Z","snapshot_observed_at":"2026-08-10T13:35:35.270308Z","submitted_at":"2026-02-12T04:26:41Z","title":"Towards Monoidal Categorifications of Twisted Products of Flag Varieties","version":5},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-03T00:12:31.586721Z"},"links":{"citing_paper":"/paper/2602.11559"},"observation_digest":"sha256:7f65efa2d83c0c84cf8b99d86fcb98f904928b9bd95e7287d1f3ed5114540467","observation_id":"39146d1e-b8b1-421d-a9c9-1411baea6065","resolution":{"observed_at":"2026-08-03T00:12:31.586721Z","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":"2026-08-03T00:12:31.590639Z","title":"Hernandez and B","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2602.11559","last_updated":"2026-05-25T00:08:31Z","snapshot_observed_at":"2026-08-10T13:35:35.270308Z","submitted_at":"2026-02-12T04:26:41Z","title":"Towards Monoidal Categorifications of Twisted Products of Flag Varieties","version":5},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-03T00:12:31.590639Z"},"links":{"citing_paper":"/paper/2602.11559"},"observation_digest":"sha256:61cce35b460dee71dbb4ea7d84b7c3b7e37d3ae934b1753627de40928d5394ac","observation_id":"acbf9bbe-8d16-4688-a2cd-abd33adb1dd6","resolution":{"observed_at":"2026-08-03T00:12:31.590639Z","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":"2026-08-03T00:12:31.594642Z","title":"5, 1113–1159","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2602.11559","last_updated":"2026-05-25T00:08:31Z","snapshot_observed_at":"2026-08-10T13:35:35.270308Z","submitted_at":"2026-02-12T04:26:41Z","title":"Towards Monoidal Categorifications of Twisted Products of Flag Varieties","version":5},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-03T00:12:31.594642Z"},"links":{"citing_paper":"/paper/2602.11559"},"observation_digest":"sha256:b8dd166ac23d024e20c389af3590193b0ad84806b2d49792b631fead8b550ff6","observation_id":"86929823-7dfe-429b-a587-29d498aa8a89","resolution":{"observed_at":"2026-08-03T00:12:31.594642Z","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":"2026-08-03T00:12:31.599520Z","title":null,"venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2602.11559","last_updated":"2026-05-25T00:08:31Z","snapshot_observed_at":"2026-08-10T13:35:35.270308Z","submitted_at":"2026-02-12T04:26:41Z","title":"Towards Monoidal Categorifications of Twisted Products of Flag Varieties","version":5},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-03T00:12:31.599520Z"},"links":{"citing_paper":"/paper/2602.11559"},"observation_digest":"sha256:5304061e8578f839536b537b1326ce87259318abd3b1bc1d2b844ae623dc7294","observation_id":"7187acce-95a7-4a7d-be1a-07b9111e613a","resolution":{"observed_at":"2026-08-03T00:12:31.599520Z","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":"2026-08-03T00:12:31.603421Z","title":"Kamnitzer,Mirkovi´ c-Vilonen cycles and polytopes, Annals of Mathematics (2010), 245–294","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2602.11559","last_updated":"2026-05-25T00:08:31Z","snapshot_observed_at":"2026-08-10T13:35:35.270308Z","submitted_at":"2026-02-12T04:26:41Z","title":"Towards Monoidal Categorifications of Twisted Products of Flag Varieties","version":5},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-03T00:12:31.603421Z"},"links":{"citing_paper":"/paper/2602.11559"},"observation_digest":"sha256:0465e60ca4798d1db3039b43ddc2cb519bd51ec699bb48006a64541d3847c4b8","observation_id":"df195aa1-3970-4e7b-98ac-b7be5feb0a0d","resolution":{"observed_at":"2026-08-03T00:12:31.603421Z","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":"2026-08-03T00:12:31.607355Z","title":null,"venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2602.11559","last_updated":"2026-05-25T00:08:31Z","snapshot_observed_at":"2026-08-10T13:35:35.270308Z","submitted_at":"2026-02-12T04:26:41Z","title":"Towards Monoidal Categorifications of Twisted Products of Flag Varieties","version":5},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-03T00:12:31.607355Z"},"links":{"citing_paper":"/paper/2602.11559"},"observation_digest":"sha256:f8e2a074b472ce5da0e6663133a871af0eba840385621aaab70db5d4b307f6a2","observation_id":"4582c502-eaf8-4c60-a0f6-09f96ea8f458","resolution":{"observed_at":"2026-08-03T00:12:31.607355Z","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":"2026-08-03T00:12:31.611625Z","title":"Kashiwara, M","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2602.11559","last_updated":"2026-05-25T00:08:31Z","snapshot_observed_at":"2026-08-10T13:35:35.270308Z","submitted_at":"2026-02-12T04:26:41Z","title":"Towards Monoidal Categorifications of Twisted Products of Flag Varieties","version":5},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-03T00:12:31.611625Z"},"links":{"citing_paper":"/paper/2602.11559"},"observation_digest":"sha256:c79ac7e7f0d7f49274f985032263d3005f079c4815a4c9950e64e258d95079d4","observation_id":"0353be01-bb1d-4175-abe5-c9b80393a929","resolution":{"observed_at":"2026-08-03T00:12:31.611625Z","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":"2026-08-03T00:12:31.615486Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2602.11559","last_updated":"2026-05-25T00:08:31Z","snapshot_observed_at":"2026-08-10T13:35:35.270308Z","submitted_at":"2026-02-12T04:26:41Z","title":"Towards Monoidal Categorifications of Twisted Products of Flag Varieties","version":5},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-03T00:12:31.615486Z"},"links":{"citing_paper":"/paper/2602.11559"},"observation_digest":"sha256:045fdc11c84023e98a29367edb1cf1a47b863d2623654b9b1d9b31c031b621d7","observation_id":"340b351e-f26e-4079-84cb-cd256d0d5590","resolution":{"observed_at":"2026-08-03T00:12:31.615486Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2408.07312","last_updated":"2024-08-14T06:12:07Z","snapshot_observed_at":"2026-08-10T06:28:27.209786Z","submitted_at":"2024-08-14T06:12:07Z","title":"Braid symmetries on bosonic extensions","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2408.07312","snapshot_observed_at":"2026-08-03T00:12:31.619534Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2602.11559","last_updated":"2026-05-25T00:08:31Z","snapshot_observed_at":"2026-08-10T13:35:35.270308Z","submitted_at":"2026-02-12T04:26:41Z","title":"Towards Monoidal Categorifications of Twisted Products of Flag Varieties","version":5},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-03T00:12:31.619534Z"},"links":{"cited_paper":"/paper/2408.07312","citing_paper":"/paper/2602.11559"},"observation_digest":"sha256:85f91589d536155978243de8b80f1cef01c0c4288db0533398ebc5527f5ebece","observation_id":"3fef2220-8afa-460a-9618-84d5fe452404","resolution":{"observed_at":"2026-08-03T00:12:31.619534Z","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":"2026-08-03T00:12:31.623829Z","title":"2, e70076","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2602.11559","last_updated":"2026-05-25T00:08:31Z","snapshot_observed_at":"2026-08-10T13:35:35.270308Z","submitted_at":"2026-02-12T04:26:41Z","title":"Towards Monoidal Categorifications of Twisted Products of Flag Varieties","version":5},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-03T00:12:31.623829Z"},"links":{"citing_paper":"/paper/2602.11559"},"observation_digest":"sha256:d1e5ce6d97cef407880313c3b15da2c0379f89ea58e347e2f5eb5f904d6a81af","observation_id":"64b5e4e3-5c2a-4d86-8387-ea1e558d1d8e","resolution":{"observed_at":"2026-08-03T00:12:31.623829Z","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":"2026-08-03T00:12:31.627971Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2602.11559","last_updated":"2026-05-25T00:08:31Z","snapshot_observed_at":"2026-08-10T13:35:35.270308Z","submitted_at":"2026-02-12T04:26:41Z","title":"Towards Monoidal Categorifications of Twisted Products of Flag Varieties","version":5},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-03T00:12:31.627971Z"},"links":{"citing_paper":"/paper/2602.11559"},"observation_digest":"sha256:c3cb8c9f303a649fef4ee12d603e9039111342e5f3828d4cf499aca4658025e5","observation_id":"c160a752-1c2a-4530-a38a-529ea6cdcdc6","resolution":{"observed_at":"2026-08-03T00:12:31.627971Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2201.10292","last_updated":"2022-01-25T13:08:36Z","snapshot_observed_at":"2026-07-06T12:31:03.057583Z","submitted_at":"2022-01-25T13:08:36Z","title":"Cluster algebras associated with open Richardson varieties: an algorithm to compute initial seeds","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2201.10292","snapshot_observed_at":"2026-08-03T00:12:31.632615Z","title":"M´ enard,Cluster algebras associated with open Richardson varieties: an algorithm to compute initial seeds, arXiv preprint arXiv:2201.10292 (2022)","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2602.11559","last_updated":"2026-05-25T00:08:31Z","snapshot_observed_at":"2026-08-10T13:35:35.270308Z","submitted_at":"2026-02-12T04:26:41Z","title":"Towards Monoidal Categorifications of Twisted Products of Flag Varieties","version":5},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-03T00:12:31.632615Z"},"links":{"cited_paper":"/paper/2201.10292","citing_paper":"/paper/2602.11559"},"observation_digest":"sha256:e9e9fa22cb98392d826221420024895e6b09378b5b82645d077b7f5ee62b4510","observation_id":"c3a0f264-e61c-4cfa-90c2-67491419d859","resolution":{"observed_at":"2026-08-03T00:12:31.632615Z","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":"2026-08-03T00:12:31.636950Z","title":"Oh and E","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2602.11559","last_updated":"2026-05-25T00:08:31Z","snapshot_observed_at":"2026-08-10T13:35:35.270308Z","submitted_at":"2026-02-12T04:26:41Z","title":"Towards Monoidal Categorifications of Twisted Products of Flag Varieties","version":5},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-03T00:12:31.636950Z"},"links":{"citing_paper":"/paper/2602.11559"},"observation_digest":"sha256:321caa970ef4f932d8934971a1400007614caa95f098a9130ac3208a263d6e23","observation_id":"14c0094f-c4f9-40b3-bb92-0c10b4bd50fb","resolution":{"observed_at":"2026-08-03T00:12:31.636950Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2407.02480","last_updated":"2025-03-26T12:03:03Z","snapshot_observed_at":"2026-07-06T18:40:27.299063Z","submitted_at":"2024-07-02T17:57:31Z","title":"Analogs of the dual canonical bases for cluster algebras from Lie theory","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2407.02480","snapshot_observed_at":"2026-08-03T00:12:31.640918Z","title":"Qin,Analogs of the dual canonical bases for cluster algebras from Lie theory, arXiv preprint arXiv:2407.02480 (2024)","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2602.11559","last_updated":"2026-05-25T00:08:31Z","snapshot_observed_at":"2026-08-10T13:35:35.270308Z","submitted_at":"2026-02-12T04:26:41Z","title":"Towards Monoidal Categorifications of Twisted Products of Flag Varieties","version":5},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-03T00:12:31.640918Z"},"links":{"cited_paper":"/paper/2407.02480","citing_paper":"/paper/2602.11559"},"observation_digest":"sha256:1ee6787691892fd118b040d61d1101f988b91525f5137403f81784470d46d2da","observation_id":"9533031d-78d1-49bb-8d91-cad60fcdaddf","resolution":{"observed_at":"2026-08-03T00:12:31.640918Z","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":"2026-08-03T00:12:31.645213Z","title":"Shen and D","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2602.11559","last_updated":"2026-05-25T00:08:31Z","snapshot_observed_at":"2026-08-10T13:35:35.270308Z","submitted_at":"2026-02-12T04:26:41Z","title":"Towards Monoidal Categorifications of Twisted Products of Flag Varieties","version":5},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-03T00:12:31.645213Z"},"links":{"citing_paper":"/paper/2602.11559"},"observation_digest":"sha256:698213bbe62348d239268aada44c9654bbf2cabcde16dc35ebaa67109677c167","observation_id":"ea6cc91a-a08e-47a0-a6b6-6ca210ec80c9","resolution":{"observed_at":"2026-08-03T00:12:31.645213Z","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":"2026-08-03T00:12:31.649100Z","title":"Webster and M","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2602.11559","last_updated":"2026-05-25T00:08:31Z","snapshot_observed_at":"2026-08-10T13:35:35.270308Z","submitted_at":"2026-02-12T04:26:41Z","title":"Towards Monoidal Categorifications of Twisted Products of Flag Varieties","version":5},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-03T00:12:31.649100Z"},"links":{"citing_paper":"/paper/2602.11559"},"observation_digest":"sha256:668b54b079f4f4d7dd3441c2df85e9dfff01b9e688ff5d7e03f6e61c8b63eba0","observation_id":"8d619aba-4a73-4a8d-afad-7cc85210a8a2","resolution":{"observed_at":"2026-08-03T00:12:31.649100Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2602.11559","last_updated":"2026-05-25T00:08:31Z","latest_version":5,"primary_category":"math.RT","snapshot_observed_at":"2026-08-10T13:35:35.270308Z","submitted_at":"2026-02-12T04:26:41Z","title":"Towards Monoidal Categorifications of Twisted Products of Flag Varieties"},"reference_resolution":{"displayed":24,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":24,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":24},"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":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"thesis":"As of 10 August 2026, this Paper Citation Record lists 24 of 24 outbound references and 0 inbound Pith citation observations for arXiv:2602.11559."}