{"as_of":"2026-08-14T15:17:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:76260b06e7d7e8be56ca8e1b58edd5ec8c2768c0afa5511842cd2c0db69b67cf","coverage":[{"denominator":38,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":38,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T04:42:07.812550Z","state":"measured"},{"denominator":41,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":41,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-14T06:32:32.682623+00:00","state":"measured"},{"denominator":3,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":3,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-03T00:12:31.555868Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"arxiv_reference","source_observed_at":"2026-07-04T20:10:07.067821Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2506.10382","last_updated":"2025-08-08T03:00:33Z","snapshot_observed_at":"2026-08-14T02:12:27.062078Z","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":"2026-08-11T06:39:13.589668Z","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:f1520e3bc9cb8e678aae1556b2027912064d2772c346f21d7c21281bc6f853b7","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":{"arxiv_id":"2506.10382","last_updated":"2025-08-08T03:00:33Z","snapshot_observed_at":"2026-08-14T02:12:27.062078Z","submitted_at":"2025-06-12T06:18:57Z","title":"Upper cluster structure on Kac--Moody Richardson varieties","version":2},"cited_work":{"arxiv_id":"2506.10382","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2506.10382","snapshot_observed_at":"2026-07-04T20:10:07.067821Z","title":"Upper cluster structure on Kac–Moody Richardson varieties.arXiv preprint arXiv:2506.10382, 2025","venue":null,"work_id":"2847ffeb-debb-4c73-8b1f-2d41082c48b3","year":2025},"citing_paper":{"arxiv_id":"2606.05184","last_updated":"2026-04-24T02:57:01Z","snapshot_observed_at":"2026-08-12T10:48:16.162069Z","submitted_at":"2026-04-24T02:57:01Z","title":"Monoidal Categories associated with Kac-Moody Open Richardson Varieties in Symmetric Type","version":1},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-07-04T20:01:15.925754Z"},"links":{"cited_paper":"/paper/2506.10382","citing_paper":"/paper/2606.05184"},"observation_digest":"sha256:47a5f8811c7bbd29d212f2a9846f9a7f37f9cf2af0b924ed7590ce62cd4344e1","observation_id":"dd9849d6-96bc-49e3-8de1-adcaedb904d8","resolution":{"observed_at":"2026-07-04T20:10:07.069956Z","resolver_source":"arxiv_id","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":{"arxiv_id":"2506.10382","last_updated":"2025-08-08T03:00:33Z","snapshot_observed_at":"2026-08-14T02:12:27.062078Z","submitted_at":"2025-06-12T06:18:57Z","title":"Upper cluster structure on Kac--Moody Richardson varieties","version":2},"cited_work":{"arxiv_id":"2506.10382","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2506.10382","snapshot_observed_at":"2026-07-04T20:10:07.067821Z","title":"Upper cluster structure on Kac–Moody Richardson varieties.arXiv preprint arXiv:2506.10382, 2025","venue":null,"work_id":"2847ffeb-debb-4c73-8b1f-2d41082c48b3","year":2025},"citing_paper":{"arxiv_id":"2606.05823","last_updated":"2026-06-04T08:01:04Z","snapshot_observed_at":"2026-08-08T15:40:21.665057Z","submitted_at":"2026-06-04T08:01:04Z","title":"Frayed Demazure weaves for Poisson-compatible cluster structures on Bott--Samelson charts","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-06-28T01:00:05.805542Z"},"links":{"cited_paper":"/paper/2506.10382","citing_paper":"/paper/2606.05823"},"observation_digest":"sha256:d350f3d3fe9b1cbe9ba9058c04989dbbf0c7492fab623e4bce67167449f46b47","observation_id":"36aaaf8b-ee2c-49d4-a268-280c5437b51f","resolution":{"observed_at":"2026-07-02T13:46:59.537869Z","resolver_source":"arxiv_id","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/2506.10382/citation-record","integrity":"/paper/2506.10382/integrity","json":"/paper/2506.10382/citation-record.json","paper":"/paper/2506.10382"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T04:42:12.918227Z","title":"Bao and X","venue":null,"work_id":"b410a7f9-36fc-405d-ae5e-e32c23a4a4f0","year":2021},"citing_paper":{"arxiv_id":"2506.10382","last_updated":"2025-08-08T03:00:33Z","snapshot_observed_at":"2026-08-14T02:12:27.062078Z","submitted_at":"2025-06-12T06:18:57Z","title":"Upper cluster structure on Kac--Moody Richardson varieties","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-07T04:42:04.433640Z"},"links":{"citing_paper":"/paper/2506.10382"},"observation_digest":"sha256:dd2056d2f4fd00741d12562e26c4b1b301d0f27873709681b1f214265ea7e526","observation_id":"a7e552f3-e2bf-4e77-906e-99c500804f35","resolution":{"observed_at":"2026-08-07T04:42:12.968144Z","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":"2026-08-07T04:42:12.789779Z","title":null,"venue":null,"work_id":"7b266024-62b7-45ae-954d-0247aa3d6742","year":2024},"citing_paper":{"arxiv_id":"2506.10382","last_updated":"2025-08-08T03:00:33Z","snapshot_observed_at":"2026-08-14T02:12:27.062078Z","submitted_at":"2025-06-12T06:18:57Z","title":"Upper cluster structure on Kac--Moody Richardson varieties","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-07T04:42:04.463551Z"},"links":{"citing_paper":"/paper/2506.10382"},"observation_digest":"sha256:36c3335657f1560215c10986773b9b59146c719460f7809997425183288c719f","observation_id":"13ace924-4bf6-4385-b480-2b64afcbf07c","resolution":{"observed_at":"2026-08-07T04:42:12.848596Z","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":"2211.11168","last_updated":"2024-02-23T01:09:06Z","snapshot_observed_at":"2026-08-13T13:38:38.884745Z","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":"2026-08-07T04:42:04.542438Z","title":null,"venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2506.10382","last_updated":"2025-08-08T03:00:33Z","snapshot_observed_at":"2026-08-14T02:12:27.062078Z","submitted_at":"2025-06-12T06:18:57Z","title":"Upper cluster structure on Kac--Moody Richardson varieties","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-07T04:42:04.542438Z"},"links":{"cited_paper":"/paper/2211.11168","citing_paper":"/paper/2506.10382"},"observation_digest":"sha256:844a4073e396a85dbea62759f322e8456776d8be5dfb2fa85cdffd1964f6885c","observation_id":"5062e82b-6c25-45b0-856d-001124ca21ba","resolution":{"observed_at":"2026-08-07T04:42:04.542438Z","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":"2026-08-07T04:42:12.684388Z","title":"Berenstein, S","venue":null,"work_id":"edf88a0c-700b-45ef-8bea-d3ccfb092375","year":2005},"citing_paper":{"arxiv_id":"2506.10382","last_updated":"2025-08-08T03:00:33Z","snapshot_observed_at":"2026-08-14T02:12:27.062078Z","submitted_at":"2025-06-12T06:18:57Z","title":"Upper cluster structure on Kac--Moody Richardson varieties","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-07T04:42:04.614098Z"},"links":{"citing_paper":"/paper/2506.10382"},"observation_digest":"sha256:4a0efb394303f1f4d17572de4afc6ad495d08e19add05332ab33257fde0542aa","observation_id":"b86fc1a2-7c4e-47f4-8a46-32b2ecddd3ea","resolution":{"observed_at":"2026-08-07T04:42:12.735415Z","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":"2026-08-07T04:42:12.557233Z","title":"Casals, E","venue":null,"work_id":"b6b70149-f3d6-4384-bf75-a3ff3bba3d2f","year":2025},"citing_paper":{"arxiv_id":"2506.10382","last_updated":"2025-08-08T03:00:33Z","snapshot_observed_at":"2026-08-14T02:12:27.062078Z","submitted_at":"2025-06-12T06:18:57Z","title":"Upper cluster structure on Kac--Moody Richardson varieties","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-07T04:42:04.728456Z"},"links":{"citing_paper":"/paper/2506.10382"},"observation_digest":"sha256:68c58b2c91a1ae1eea3cd34f0f4143fef73522371ca8513b837d7aab3f9e1266","observation_id":"045223ea-5eb7-40ef-9f54-41c64f0f87b7","resolution":{"observed_at":"2026-08-07T04:42:12.599767Z","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":"2508.03816","last_updated":"2025-08-05T18:04:16Z","snapshot_observed_at":"2026-08-06T04:14:26.400277Z","submitted_at":"2025-08-05T18:04:16Z","title":"Comparing cluster algebras on braid varieties","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2508.03816","snapshot_observed_at":"2026-08-07T04:42:04.807178Z","title":"Casals, P","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2506.10382","last_updated":"2025-08-08T03:00:33Z","snapshot_observed_at":"2026-08-14T02:12:27.062078Z","submitted_at":"2025-06-12T06:18:57Z","title":"Upper cluster structure on Kac--Moody Richardson varieties","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-07T04:42:04.807178Z"},"links":{"cited_paper":"/paper/2508.03816","citing_paper":"/paper/2506.10382"},"observation_digest":"sha256:b030a6d7dfaa2cb8a15e3275e686985dc6b6299a493df6320ea7f52da0d54f06","observation_id":"cca72710-8415-497d-b856-355aee41d395","resolution":{"observed_at":"2026-08-07T04:42:04.807178Z","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":"2026-08-07T04:42:12.425964Z","title":"Cerulli Irelli, B","venue":null,"work_id":"b5e8163b-f727-4999-b98f-fa8b118dd00b","year":2013},"citing_paper":{"arxiv_id":"2506.10382","last_updated":"2025-08-08T03:00:33Z","snapshot_observed_at":"2026-08-14T02:12:27.062078Z","submitted_at":"2025-06-12T06:18:57Z","title":"Upper cluster structure on Kac--Moody Richardson varieties","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-07T04:42:04.902688Z"},"links":{"citing_paper":"/paper/2506.10382"},"observation_digest":"sha256:e077614d79b49afb38fd351d2eba62cb95c8ffabad32ddcb04a0792a7327af9c","observation_id":"815ec3e5-8c57-473e-91df-ba1f27abaae3","resolution":{"observed_at":"2026-08-07T04:42:12.487431Z","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":"2026-08-07T04:42:12.308648Z","title":"Demonet and B","venue":null,"work_id":"7e29651f-7652-494f-ab92-d9f990d85899","year":2020},"citing_paper":{"arxiv_id":"2506.10382","last_updated":"2025-08-08T03:00:33Z","snapshot_observed_at":"2026-08-14T02:12:27.062078Z","submitted_at":"2025-06-12T06:18:57Z","title":"Upper cluster structure on Kac--Moody Richardson varieties","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-07T04:42:05.006939Z"},"links":{"citing_paper":"/paper/2506.10382"},"observation_digest":"sha256:8e1d2c24869a20473bb2f045c130620ddd2104185d06e91638868fe95658c9ce","observation_id":"7cf4e455-7d92-45c4-bd0d-7b6a092b2336","resolution":{"observed_at":"2026-08-07T04:42:12.347726Z","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":"2026-08-07T04:42:12.195771Z","title":"Deodhar, On some geometric aspects of Bruhat orderings","venue":null,"work_id":"848e26c5-2e4b-49f5-9529-c43ba0f82951","year":1985},"citing_paper":{"arxiv_id":"2506.10382","last_updated":"2025-08-08T03:00:33Z","snapshot_observed_at":"2026-08-14T02:12:27.062078Z","submitted_at":"2025-06-12T06:18:57Z","title":"Upper cluster structure on Kac--Moody Richardson varieties","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-07T04:42:05.114704Z"},"links":{"citing_paper":"/paper/2506.10382"},"observation_digest":"sha256:6603f6af5b485b4a237608552e720bf54f9bfd810648e8646912db1d8694945b","observation_id":"b30f5821-97e4-41db-af4a-1b4396fac984","resolution":{"observed_at":"2026-08-07T04:42:12.250813Z","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":"2026-08-07T04:42:12.023385Z","title":null,"venue":null,"work_id":"9e276dcf-46c4-44a4-b523-49efd19cb1b5","year":2006},"citing_paper":{"arxiv_id":"2506.10382","last_updated":"2025-08-08T03:00:33Z","snapshot_observed_at":"2026-08-14T02:12:27.062078Z","submitted_at":"2025-06-12T06:18:57Z","title":"Upper cluster structure on Kac--Moody Richardson varieties","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-07T04:42:05.188488Z"},"links":{"citing_paper":"/paper/2506.10382"},"observation_digest":"sha256:7c8eb03eb26af2ffa124501a532e054cdbe255af14bd21162331fb375a9f631b","observation_id":"0f7f1ced-665e-43dd-bf79-5ae561383467","resolution":{"observed_at":"2026-08-07T04:42:12.097830Z","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":"2026-08-07T04:42:11.858008Z","title":null,"venue":null,"work_id":"d5cc821a-89c1-4355-a6c6-5641c6fe0a0a","year":2009},"citing_paper":{"arxiv_id":"2506.10382","last_updated":"2025-08-08T03:00:33Z","snapshot_observed_at":"2026-08-14T02:12:27.062078Z","submitted_at":"2025-06-12T06:18:57Z","title":"Upper cluster structure on Kac--Moody Richardson varieties","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-07T04:42:05.266377Z"},"links":{"citing_paper":"/paper/2506.10382"},"observation_digest":"sha256:daa17ff2b4021e7ededafd7754f90703aaa4e4c946f4261016e56fe6b58328b4","observation_id":"288a8c29-e74f-4347-a3e4-d431e0a8f9ac","resolution":{"observed_at":"2026-08-07T04:42:11.944643Z","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":"2008.09189","last_updated":"2021-08-30T01:41:00Z","snapshot_observed_at":"2026-08-08T19:43:35.147043Z","submitted_at":"2020-08-20T20:09:54Z","title":"Introduction to Cluster Algebras. Chapter 6","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2008.09189","snapshot_observed_at":"2026-08-07T04:42:05.385599Z","title":"Fomin, L","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2506.10382","last_updated":"2025-08-08T03:00:33Z","snapshot_observed_at":"2026-08-14T02:12:27.062078Z","submitted_at":"2025-06-12T06:18:57Z","title":"Upper cluster structure on Kac--Moody Richardson varieties","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-07T04:42:05.385599Z"},"links":{"cited_paper":"/paper/2008.09189","citing_paper":"/paper/2506.10382"},"observation_digest":"sha256:0e2838abd2348091280a26a004ce1da2dcf3d5076735e82bdcaea0e46fe0fb20","observation_id":"046a0997-45b0-4f98-af9a-42e50cc4d098","resolution":{"observed_at":"2026-08-07T04:42:05.385599Z","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":"2026-08-07T04:42:11.686877Z","title":"Fomin and A","venue":null,"work_id":"c42ffc3c-89cc-403f-9a76-b4cdc292f5dc","year":2002},"citing_paper":{"arxiv_id":"2506.10382","last_updated":"2025-08-08T03:00:33Z","snapshot_observed_at":"2026-08-14T02:12:27.062078Z","submitted_at":"2025-06-12T06:18:57Z","title":"Upper cluster structure on Kac--Moody Richardson varieties","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-07T04:42:05.499699Z"},"links":{"citing_paper":"/paper/2506.10382"},"observation_digest":"sha256:1e9a3fe39152109aadbd3576ef4abe7a230c058b6b88788cc6e36018e32568af","observation_id":"d8384563-47d4-4836-bdc6-8080d9b63f7f","resolution":{"observed_at":"2026-08-07T04:42:11.771521Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T04:42:05.602842Z","title":null,"venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2506.10382","last_updated":"2025-08-08T03:00:33Z","snapshot_observed_at":"2026-08-14T02:12:27.062078Z","submitted_at":"2025-06-12T06:18:57Z","title":"Upper cluster structure on Kac--Moody Richardson varieties","version":2},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-07T04:42:05.602842Z"},"links":{"citing_paper":"/paper/2506.10382"},"observation_digest":"sha256:8e5d6c5800c49ecd25d16931817da798e9311f85a3ecdbf6dab15d8b03b53078","observation_id":"10c9c37d-985a-47f2-8f86-c0ac7aa3ded8","resolution":{"observed_at":"2026-08-07T04:42:05.602842Z","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":"2026-08-07T04:42:11.487407Z","title":"Fraser, Quasi-homomorphisms of cluster algebras , Adv","venue":null,"work_id":"5ad15979-c768-42a0-b224-e29ebe6cf186","year":2016},"citing_paper":{"arxiv_id":"2506.10382","last_updated":"2025-08-08T03:00:33Z","snapshot_observed_at":"2026-08-14T02:12:27.062078Z","submitted_at":"2025-06-12T06:18:57Z","title":"Upper cluster structure on Kac--Moody Richardson varieties","version":2},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-07T04:42:05.676650Z"},"links":{"citing_paper":"/paper/2506.10382"},"observation_digest":"sha256:7223c7e3ea93c234ddbbb1c95cdc0ad7a2bb80b5ef603b988e703eb742dbc71e","observation_id":"4d79dfb3-b5d0-4ef1-88f5-f194b88a9015","resolution":{"observed_at":"2026-08-07T04:42:11.574152Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T04:42:05.785360Z","title":"Galashin and T","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2506.10382","last_updated":"2025-08-08T03:00:33Z","snapshot_observed_at":"2026-08-14T02:12:27.062078Z","submitted_at":"2025-06-12T06:18:57Z","title":"Upper cluster structure on Kac--Moody Richardson varieties","version":2},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-07T04:42:05.785360Z"},"links":{"citing_paper":"/paper/2506.10382"},"observation_digest":"sha256:17667bc07c6eabc2c0aff49cd0479844793cd3545f9a9bb7aec1bf774229f118","observation_id":"f79a7309-898d-4480-8c6c-ef54c452924a","resolution":{"observed_at":"2026-08-07T04:42:05.785360Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2210.04778","last_updated":"2024-05-29T22:47:58Z","snapshot_observed_at":"2026-08-13T14:09:09.616093Z","submitted_at":"2022-10-10T15:36:51Z","title":"Braid variety cluster structures, I: 3D plabic graphs","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2210.04778","snapshot_observed_at":"2026-08-07T04:42:05.877783Z","title":"Galashin, T","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2506.10382","last_updated":"2025-08-08T03:00:33Z","snapshot_observed_at":"2026-08-14T02:12:27.062078Z","submitted_at":"2025-06-12T06:18:57Z","title":"Upper cluster structure on Kac--Moody Richardson varieties","version":2},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-07T04:42:05.877783Z"},"links":{"cited_paper":"/paper/2210.04778","citing_paper":"/paper/2506.10382"},"observation_digest":"sha256:b9169210cf939eb95490b242aaa2bae52a9dc06eba808156a6b275ee8167a342","observation_id":"ac178cea-bfdf-4291-9ce7-965552cf565c","resolution":{"observed_at":"2026-08-07T04:42:05.877783Z","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":"2026-08-07T04:42:05.961041Z","title":"Galashin, T","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2506.10382","last_updated":"2025-08-08T03:00:33Z","snapshot_observed_at":"2026-08-14T02:12:27.062078Z","submitted_at":"2025-06-12T06:18:57Z","title":"Upper cluster structure on Kac--Moody Richardson varieties","version":2},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-07T04:42:05.961041Z"},"links":{"citing_paper":"/paper/2506.10382"},"observation_digest":"sha256:530045d5fc733129177273519c11828baed781ca28da3475f4386e436267d768","observation_id":"7dddb7db-5b53-4d80-bc19-a354d66e2208","resolution":{"observed_at":"2026-08-07T04:42:05.961041Z","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":"2026-08-07T04:42:11.329037Z","title":"Geiss, B","venue":null,"work_id":"ae0b279d-215f-4a71-aa48-4f71a626f413","year":2013},"citing_paper":{"arxiv_id":"2506.10382","last_updated":"2025-08-08T03:00:33Z","snapshot_observed_at":"2026-08-14T02:12:27.062078Z","submitted_at":"2025-06-12T06:18:57Z","title":"Upper cluster structure on Kac--Moody Richardson varieties","version":2},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-07T04:42:06.101390Z"},"links":{"citing_paper":"/paper/2506.10382"},"observation_digest":"sha256:07de91de5674523397984804d3c6b2e8d2cb6fecbaa607d7fd89ef21a3771748","observation_id":"230d0dbf-4349-4b86-bbf9-a79771f216a2","resolution":{"observed_at":"2026-08-07T04:42:11.386828Z","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":"2026-08-07T04:42:11.142697Z","title":"Gross, P","venue":null,"work_id":"eb7b71f3-eb47-4f05-9a6f-48daade2bf45","year":2018},"citing_paper":{"arxiv_id":"2506.10382","last_updated":"2025-08-08T03:00:33Z","snapshot_observed_at":"2026-08-14T02:12:27.062078Z","submitted_at":"2025-06-12T06:18:57Z","title":"Upper cluster structure on Kac--Moody Richardson varieties","version":2},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-07T04:42:06.184633Z"},"links":{"citing_paper":"/paper/2506.10382"},"observation_digest":"sha256:8e19aed1e3f259924ebb437d4a749a03ca1fdc288d08e948367639bc62a7c47d","observation_id":"6ac33c36-4778-4e0c-b175-205fe1469dc1","resolution":{"observed_at":"2026-08-07T04:42:11.230484Z","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":"1904.10491","last_updated":"2024-07-31T05:06:06Z","snapshot_observed_at":"2026-08-10T03:13:06.779435Z","submitted_at":"2019-04-23T18:50:15Z","title":"Quantum geometry of moduli spaces of local systems and representation theory","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1904.10491","snapshot_observed_at":"2026-08-07T04:42:06.290009Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2506.10382","last_updated":"2025-08-08T03:00:33Z","snapshot_observed_at":"2026-08-14T02:12:27.062078Z","submitted_at":"2025-06-12T06:18:57Z","title":"Upper cluster structure on Kac--Moody Richardson varieties","version":2},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-07T04:42:06.290009Z"},"links":{"cited_paper":"/paper/1904.10491","citing_paper":"/paper/2506.10382"},"observation_digest":"sha256:bea9c8167b1701d6ba67c8988b8c74b0d769ba13d33cf0522bfb76903b3a5c00","observation_id":"a06e4211-349a-49a8-bd38-e6391caa865d","resolution":{"observed_at":"2026-08-07T04:42:06.290009Z","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":"2026-08-07T04:42:10.995581Z","title":"Gekhtman, M","venue":null,"work_id":"aa3812b5-8520-4b5a-b562-12f7e028ffe3","year":2008},"citing_paper":{"arxiv_id":"2506.10382","last_updated":"2025-08-08T03:00:33Z","snapshot_observed_at":"2026-08-14T02:12:27.062078Z","submitted_at":"2025-06-12T06:18:57Z","title":"Upper cluster structure on Kac--Moody Richardson varieties","version":2},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-07T04:42:06.368031Z"},"links":{"citing_paper":"/paper/2506.10382"},"observation_digest":"sha256:6c041e3c8276833b2c073a87527b1c13860e8e6cf8d9ce79be208e502ecbdfab","observation_id":"53970815-7db7-4e34-a5ca-f081211fdd7d","resolution":{"observed_at":"2026-08-07T04:42:11.061582Z","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":"2026-08-07T04:42:10.842387Z","title":null,"venue":null,"work_id":"9185c89d-b727-4faf-ac8f-29eb81cb9316","year":null},"citing_paper":{"arxiv_id":"2506.10382","last_updated":"2025-08-08T03:00:33Z","snapshot_observed_at":"2026-08-14T02:12:27.062078Z","submitted_at":"2025-06-12T06:18:57Z","title":"Upper cluster structure on Kac--Moody Richardson varieties","version":2},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-07T04:42:06.487351Z"},"links":{"citing_paper":"/paper/2506.10382"},"observation_digest":"sha256:c49a0da7d818f4299668283350db4c4f2023b126a0a27745dbcac7a8508a952a","observation_id":"399439e9-afd2-4e6b-8c6b-7ab26f94f610","resolution":{"observed_at":"2026-08-07T04:42:10.921076Z","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":"2026-08-07T04:42:10.697307Z","title":"Kashiwara, M","venue":null,"work_id":"0e4650a6-13e8-47ef-84ad-d8472ca87518","year":2018},"citing_paper":{"arxiv_id":"2506.10382","last_updated":"2025-08-08T03:00:33Z","snapshot_observed_at":"2026-08-14T02:12:27.062078Z","submitted_at":"2025-06-12T06:18:57Z","title":"Upper cluster structure on Kac--Moody Richardson varieties","version":2},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-07T04:42:06.602749Z"},"links":{"citing_paper":"/paper/2506.10382"},"observation_digest":"sha256:8d1cb0bfdfeaa44e6bd6da89adf8a58134fcc89128adbad4f97b35b09cdca8ea","observation_id":"4a7b659b-56f9-4367-8a57-01dfed39bd1e","resolution":{"observed_at":"2026-08-07T04:42:10.761479Z","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":"2026-08-07T04:42:10.515742Z","title":"Kazhdan and G","venue":null,"work_id":"36324ffc-80c4-46e0-aa6e-d246d6a0e9a1","year":1979},"citing_paper":{"arxiv_id":"2506.10382","last_updated":"2025-08-08T03:00:33Z","snapshot_observed_at":"2026-08-14T02:12:27.062078Z","submitted_at":"2025-06-12T06:18:57Z","title":"Upper cluster structure on Kac--Moody Richardson varieties","version":2},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-07T04:42:06.725051Z"},"links":{"citing_paper":"/paper/2506.10382"},"observation_digest":"sha256:b75dcd0c69a717a3040fb909910b05b9293ef3e252922a79214849b30373ee86","observation_id":"c0ce49d9-2f7e-486c-a04c-fed067255d6c","resolution":{"observed_at":"2026-08-07T04:42:10.608599Z","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":"2026-08-07T04:42:10.334320Z","title":"Kumar, Kac–Moody groups, their flag varieties and representation theory , Progress in Mathematics, vol","venue":null,"work_id":"12abe695-92df-45c1-bf47-9dd7fcd6a835","year":2002},"citing_paper":{"arxiv_id":"2506.10382","last_updated":"2025-08-08T03:00:33Z","snapshot_observed_at":"2026-08-14T02:12:27.062078Z","submitted_at":"2025-06-12T06:18:57Z","title":"Upper cluster structure on Kac--Moody Richardson varieties","version":2},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-07T04:42:06.813871Z"},"links":{"citing_paper":"/paper/2506.10382"},"observation_digest":"sha256:75a3cc0475fca2d3941269104124043b4963a6d48900f891a2cbeb776cd0486e","observation_id":"a396e448-9b05-4a78-a598-6565342397e6","resolution":{"observed_at":"2026-08-07T04:42:10.418510Z","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":"2026-08-07T04:42:10.054410Z","title":null,"venue":null,"work_id":"1c8d0a68-700d-405f-90aa-3408fc50d058","year":2017},"citing_paper":{"arxiv_id":"2506.10382","last_updated":"2025-08-08T03:00:33Z","snapshot_observed_at":"2026-08-14T02:12:27.062078Z","submitted_at":"2025-06-12T06:18:57Z","title":"Upper cluster structure on Kac--Moody Richardson varieties","version":2},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-07T04:42:06.896461Z"},"links":{"citing_paper":"/paper/2506.10382"},"observation_digest":"sha256:9a840997fa8e24868940b16c0cc90145cb9367f3c9eed126854c1196bf1d5dcd","observation_id":"63778259-88f7-4579-84fc-2a17118910a3","resolution":{"observed_at":"2026-08-07T04:42:10.208750Z","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":"2026-08-07T04:42:09.769635Z","title":"Knutson, A","venue":null,"work_id":"76ae3897-8e21-404a-aefe-53b0a9f317f1","year":2013},"citing_paper":{"arxiv_id":"2506.10382","last_updated":"2025-08-08T03:00:33Z","snapshot_observed_at":"2026-08-14T02:12:27.062078Z","submitted_at":"2025-06-12T06:18:57Z","title":"Upper cluster structure on Kac--Moody Richardson varieties","version":2},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-07T04:42:07.012569Z"},"links":{"citing_paper":"/paper/2506.10382"},"observation_digest":"sha256:a6e328c22876a14b71cffcaa7cb9ae6e0b3bad8d02679ba7a5971809b4a628f9","observation_id":"9d27269e-ff2e-4320-9743-07431b5cae5b","resolution":{"observed_at":"2026-08-07T04:42:09.898460Z","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":"2026-08-07T04:42:09.491187Z","title":"Leclerc, Cluster structures on strata of flag varieties , Adv","venue":null,"work_id":"8338b53c-5297-4341-9fee-91b39093c55b","year":2016},"citing_paper":{"arxiv_id":"2506.10382","last_updated":"2025-08-08T03:00:33Z","snapshot_observed_at":"2026-08-14T02:12:27.062078Z","submitted_at":"2025-06-12T06:18:57Z","title":"Upper cluster structure on Kac--Moody Richardson varieties","version":2},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-07T04:42:07.095455Z"},"links":{"citing_paper":"/paper/2506.10382"},"observation_digest":"sha256:50108e85adb1f5babf0a2c757123187f5f85db39afeedf01ffda316e0a2a9ffc","observation_id":"58f02785-e4d0-4eb1-8ebd-a86428b240fa","resolution":{"observed_at":"2026-08-07T04:42:09.627332Z","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":"2026-08-07T04:42:09.270171Z","title":"Lusztig, Total positivity in reductive groups, Lie theory and geometry, Progr","venue":null,"work_id":"cd47e9fe-02e1-40b5-8b2c-a137587cfd70","year":1994},"citing_paper":{"arxiv_id":"2506.10382","last_updated":"2025-08-08T03:00:33Z","snapshot_observed_at":"2026-08-14T02:12:27.062078Z","submitted_at":"2025-06-12T06:18:57Z","title":"Upper cluster structure on Kac--Moody Richardson varieties","version":2},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-07T04:42:07.180285Z"},"links":{"citing_paper":"/paper/2506.10382"},"observation_digest":"sha256:8ee53465c7d65a81574070ad76bfff19a7780cc4ddad3171fd5163c4ab557141","observation_id":"d09b9dcd-51cf-4904-bfca-d07e592e0c75","resolution":{"observed_at":"2026-08-07T04:42:09.364190Z","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":"2026-08-07T04:42:09.073012Z","title":null,"venue":null,"work_id":"e811eced-78f3-4a58-b3e7-f2a1c0cf8ef5","year":2004},"citing_paper":{"arxiv_id":"2506.10382","last_updated":"2025-08-08T03:00:33Z","snapshot_observed_at":"2026-08-14T02:12:27.062078Z","submitted_at":"2025-06-12T06:18:57Z","title":"Upper cluster structure on Kac--Moody Richardson varieties","version":2},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-07T04:42:07.245061Z"},"links":{"citing_paper":"/paper/2506.10382"},"observation_digest":"sha256:e6552d804b992ab6364d842817955d8f84d3b24004877554cff797dc8a6cde20","observation_id":"e3ebb8c6-24db-447f-bf64-0c535b72bc85","resolution":{"observed_at":"2026-08-07T04:42:09.174315Z","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":"2026-08-07T04:42:08.839812Z","title":"Muller, Locally acyclic cluster algebras , Adv","venue":null,"work_id":"cd0d528f-276f-432b-9a92-de828ae6dce8","year":2013},"citing_paper":{"arxiv_id":"2506.10382","last_updated":"2025-08-08T03:00:33Z","snapshot_observed_at":"2026-08-14T02:12:27.062078Z","submitted_at":"2025-06-12T06:18:57Z","title":"Upper cluster structure on Kac--Moody Richardson varieties","version":2},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-07T04:42:07.323691Z"},"links":{"citing_paper":"/paper/2506.10382"},"observation_digest":"sha256:ba130ec0f031055202277c54414823f605f5216f12c8951f62bc89f7f1d43aaa","observation_id":"e7f9d789-736d-429b-a10b-8a9dd80cc315","resolution":{"observed_at":"2026-08-07T04:42:08.961329Z","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":"2201.10292","last_updated":"2022-01-25T13:08:36Z","snapshot_observed_at":"2026-08-13T16:53:36.628049Z","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":"2026-08-07T04:42:07.371443Z","title":"M´ enard,Cluster algebras associated with open Richardson varieties: an algorithm to compute initial seeds (2022), available at arXiv:math.RT/arXiv:2201.10292","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2506.10382","last_updated":"2025-08-08T03:00:33Z","snapshot_observed_at":"2026-08-14T02:12:27.062078Z","submitted_at":"2025-06-12T06:18:57Z","title":"Upper cluster structure on Kac--Moody Richardson varieties","version":2},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-07T04:42:07.371443Z"},"links":{"cited_paper":"/paper/2201.10292","citing_paper":"/paper/2506.10382"},"observation_digest":"sha256:378cfc1b9001dec7219f1f586cb39ec48d8016ab7d5ad2363c1c3f8b616ea39a","observation_id":"82c670ef-d50c-4f80-9bde-7af91b36f01f","resolution":{"observed_at":"2026-08-07T04:42:07.371443Z","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":"2026-08-07T04:42:08.617357Z","title":"Muller, The existence of a maximal green sequence is not invariant under quiver mutation , Electron","venue":null,"work_id":"6b692d36-7475-49e8-b868-3fcad6303947","year":2016},"citing_paper":{"arxiv_id":"2506.10382","last_updated":"2025-08-08T03:00:33Z","snapshot_observed_at":"2026-08-14T02:12:27.062078Z","submitted_at":"2025-06-12T06:18:57Z","title":"Upper cluster structure on Kac--Moody Richardson varieties","version":2},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-07T04:42:07.475638Z"},"links":{"citing_paper":"/paper/2506.10382"},"observation_digest":"sha256:d4da837b451127b818d369dfd0538f65d16ccc85e1dad2df5ee8f809bb4d7685","observation_id":"f8d0c1a0-99a5-4a21-8513-390602ee5cf7","resolution":{"observed_at":"2026-08-07T04:42:08.731497Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T04:42:07.561114Z","title":"Serhiyenko and M","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2506.10382","last_updated":"2025-08-08T03:00:33Z","snapshot_observed_at":"2026-08-14T02:12:27.062078Z","submitted_at":"2025-06-12T06:18:57Z","title":"Upper cluster structure on Kac--Moody Richardson varieties","version":2},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-07T04:42:07.561114Z"},"links":{"citing_paper":"/paper/2506.10382"},"observation_digest":"sha256:80ef0f46bd5231efb0fcbcfd44b0675fd6206fae67e8bd51ed84a430b7c6e10a","observation_id":"8c5bb030-05f9-4c2f-8186-8cdcb04e7ccd","resolution":{"observed_at":"2026-08-07T04:42:07.561114Z","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":"2026-08-07T04:42:08.453039Z","title":"Shen and D","venue":null,"work_id":"a58ed087-1bec-4cf3-be92-bdc1759e4620","year":2021},"citing_paper":{"arxiv_id":"2506.10382","last_updated":"2025-08-08T03:00:33Z","snapshot_observed_at":"2026-08-14T02:12:27.062078Z","submitted_at":"2025-06-12T06:18:57Z","title":"Upper cluster structure on Kac--Moody Richardson varieties","version":2},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-07T04:42:07.641839Z"},"links":{"citing_paper":"/paper/2506.10382"},"observation_digest":"sha256:954273b54423b1a06920ac7d9cc7f1a73e6305b14e3ca4b2444151736599bdc3","observation_id":"7c14b12b-ac35-408a-99c4-7f0b0c207c11","resolution":{"observed_at":"2026-08-07T04:42:08.515692Z","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":"2026-08-07T04:42:08.264450Z","title":"Tits, Uniqueness and presentation of Kac–Moody groups over fields, J","venue":null,"work_id":"a5a5bdfc-55e7-4485-92c2-566a5e017c96","year":1987},"citing_paper":{"arxiv_id":"2506.10382","last_updated":"2025-08-08T03:00:33Z","snapshot_observed_at":"2026-08-14T02:12:27.062078Z","submitted_at":"2025-06-12T06:18:57Z","title":"Upper cluster structure on Kac--Moody Richardson varieties","version":2},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-07T04:42:07.731651Z"},"links":{"citing_paper":"/paper/2506.10382"},"observation_digest":"sha256:ff95b53d5e94c3f1c199354a2dc61257433dbfcecbc3cdda085bfd6ddbc6c47a","observation_id":"f0d0bf14-7cd3-4d30-811b-072572722b2b","resolution":{"observed_at":"2026-08-07T04:42:08.365259Z","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":"2026-08-07T04:42:08.094734Z","title":"Williams, Cluster ensembles and Kac–Moody groups , Adv","venue":null,"work_id":"98dfa030-8296-44ee-a48e-4d9fe63a4d31","year":2013},"citing_paper":{"arxiv_id":"2506.10382","last_updated":"2025-08-08T03:00:33Z","snapshot_observed_at":"2026-08-14T02:12:27.062078Z","submitted_at":"2025-06-12T06:18:57Z","title":"Upper cluster structure on Kac--Moody Richardson varieties","version":2},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-07T04:42:07.812550Z"},"links":{"citing_paper":"/paper/2506.10382"},"observation_digest":"sha256:2b8fc84f27fc966cf94c27a6dcf743d0103de268275e779bd695fd70e92ce24b","observation_id":"c0aa4f8f-a7c8-4f60-bf8c-8ad39e844fb7","resolution":{"observed_at":"2026-08-07T04:42:08.177580Z","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"}}],"paper":{"arxiv_id":"2506.10382","last_updated":"2025-08-08T03:00:33Z","latest_version":2,"primary_category":"math.RT","snapshot_observed_at":"2026-08-14T02:12:27.062078Z","submitted_at":"2025-06-12T06:18:57Z","title":"Upper cluster structure on Kac--Moody Richardson varieties"},"reference_resolution":{"displayed":38,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":16,"verified_exact":0,"verified_fuzzy":22},"total_outbound_references":38},"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 38 of 38 outbound references and 3 inbound Pith citation observations for arXiv:2506.10382."}