{"as_of":"2026-08-11T04:35:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:a0dae96cfbcbab69d320b0cf1ae9c66acb4f35d59d3ed01137e5795e1a4e436d","coverage":[{"denominator":33,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":33,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-02T01:48:55.994852Z","state":"measured"},{"denominator":34,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":34,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-10T06:31:04.303077+00:00","state":"measured"},{"denominator":1,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":1,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-06T00:40:29.822275Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"pith","source_observed_at":"2026-08-06T00:40:29.934021Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2607.14634","last_updated":"2026-07-16T06:59:14Z","snapshot_observed_at":"2026-08-10T22:28:34.719559Z","submitted_at":"2026-07-16T06:59:14Z","title":"Cluster structures on $SL_n/SO_n$","version":1},"cited_work":{"arxiv_id":"2607.14634","doi":null,"metadata_source":"pith","pith_arxiv_id":"2607.14634","snapshot_observed_at":"2026-08-06T00:40:29.934021Z","title":"Cluster structures on $SL_n/SO_n$","venue":"math.RT","work_id":"a27874a5-f149-45d0-8137-f0f8fe4eb18b","year":2026},"citing_paper":{"arxiv_id":"2608.00963","last_updated":"2026-08-02T03:22:24Z","snapshot_observed_at":"2026-08-08T17:04:01.450172Z","submitted_at":"2026-08-02T03:22:24Z","title":"Cluster Algebras for Bosonic Plethysm","version":1},"reference_index":22,"source":"arxiv_source","source_observed_at":"2026-08-06T00:40:29.822275Z"},"links":{"cited_paper":"/paper/2607.14634","citing_paper":"/paper/2608.00963"},"observation_digest":"sha256:74bb931194425bb624b740d16c59006a9c172e251f3ff38db6e6fb3befbac754","observation_id":"3752ed57-94a2-434e-b4d7-7712b413de79","resolution":{"observed_at":"2026-08-06T00:40:30.065979Z","resolver_source":"local_arxiv","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2607.14634/citation-record","integrity":"/paper/2607.14634/integrity","json":"/paper/2607.14634/citation-record.json","paper":"/paper/2607.14634"},"outbound":[{"citation":{"cited_paper":{"arxiv_id":"2606.25516","last_updated":"2026-06-24T07:48:19Z","snapshot_observed_at":"2026-08-06T12:03:54.604657Z","submitted_at":"2026-06-24T07:48:19Z","title":"Total positivity and symmetric spaces","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2606.25516","snapshot_observed_at":"2026-08-02T01:48:53.125869Z","title":"Bao,Total positive and symmetric spaces(2026), available athttps://arxiv.org/abs/ 2606.25516","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.14634","last_updated":"2026-07-16T06:59:14Z","snapshot_observed_at":"2026-08-10T22:28:34.719559Z","submitted_at":"2026-07-16T06:59:14Z","title":"Cluster structures on $SL_n/SO_n$","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-02T01:48:53.125869Z"},"links":{"cited_paper":"/paper/2606.25516","citing_paper":"/paper/2607.14634"},"observation_digest":"sha256:eadfdbe953f0f42fb827542864c5f7597f02473ffd7867338154cb606bca61b6","observation_id":"d387ce89-a202-4fa2-af8c-ab5b5077a9cd","resolution":{"observed_at":"2026-08-02T01:48:53.125869Z","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":"2026-08-02T01:48:53.227657Z","title":"Berenstein, S","venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2607.14634","last_updated":"2026-07-16T06:59:14Z","snapshot_observed_at":"2026-08-10T22:28:34.719559Z","submitted_at":"2026-07-16T06:59:14Z","title":"Cluster structures on $SL_n/SO_n$","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-02T01:48:53.227657Z"},"links":{"citing_paper":"/paper/2607.14634"},"observation_digest":"sha256:954b39fd7fbf43cad7b5eaeb20e1af5f15efc5e7865a8653a343a2755ad83702","observation_id":"db113b79-48fe-4bb2-aa9f-8997b717abf6","resolution":{"observed_at":"2026-08-02T01:48:53.227657Z","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":"2026-08-02T01:48:53.337057Z","title":"Berenstein and A","venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2607.14634","last_updated":"2026-07-16T06:59:14Z","snapshot_observed_at":"2026-08-10T22:28:34.719559Z","submitted_at":"2026-07-16T06:59:14Z","title":"Cluster structures on $SL_n/SO_n$","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-02T01:48:53.337057Z"},"links":{"citing_paper":"/paper/2607.14634"},"observation_digest":"sha256:cf0f735bed028314af40347693939a4a702dcdc550c19d599d349eaed87e9d09","observation_id":"14fd9ee5-7280-4bfa-b54d-b379d2dfb174","resolution":{"observed_at":"2026-08-02T01:48:53.337057Z","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":"2026-08-02T01:48:53.517215Z","title":"Demonet,Alg` ebres amass´ ees et alg` ebres pr´ eprojectives: le cas non simplement lac´ e, C","venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2607.14634","last_updated":"2026-07-16T06:59:14Z","snapshot_observed_at":"2026-08-10T22:28:34.719559Z","submitted_at":"2026-07-16T06:59:14Z","title":"Cluster structures on $SL_n/SO_n$","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-02T01:48:53.517215Z"},"links":{"citing_paper":"/paper/2607.14634"},"observation_digest":"sha256:15ef4313908c62512afb430a548d82cb6f237503a6917fd8d153089cb0ac28c2","observation_id":"7c051a9b-5aed-40a0-b25e-defb4bd04291","resolution":{"observed_at":"2026-08-02T01:48:53.517215Z","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":"2026-08-02T01:48:53.735869Z","title":"Dupont,An approach to non-simply laced cluster algebras, J","venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2607.14634","last_updated":"2026-07-16T06:59:14Z","snapshot_observed_at":"2026-08-10T22:28:34.719559Z","submitted_at":"2026-07-16T06:59:14Z","title":"Cluster structures on $SL_n/SO_n$","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-02T01:48:53.735869Z"},"links":{"citing_paper":"/paper/2607.14634"},"observation_digest":"sha256:7090bfbde5dc0d9e3a74699e36492f575e0dc22f9f87951f4d7d7a3bd7517dee","observation_id":"524c52ec-99ba-42ec-af53-171180c9c23f","resolution":{"observed_at":"2026-08-02T01:48:53.735869Z","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":"2026-08-02T01:48:53.886271Z","title":"Enriquez and P","venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2607.14634","last_updated":"2026-07-16T06:59:14Z","snapshot_observed_at":"2026-08-10T22:28:34.719559Z","submitted_at":"2026-07-16T06:59:14Z","title":"Cluster structures on $SL_n/SO_n$","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-02T01:48:53.886271Z"},"links":{"citing_paper":"/paper/2607.14634"},"observation_digest":"sha256:4aea0e3792fef51e496991a541682ab99c096ceaebba7c2a536251f074167458","observation_id":"b103e19b-1d40-483c-af75-58e03f3086c2","resolution":{"observed_at":"2026-08-02T01:48:53.886271Z","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":"2026-08-02T01:48:53.981715Z","title":"Evens and J.-H","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2607.14634","last_updated":"2026-07-16T06:59:14Z","snapshot_observed_at":"2026-08-10T22:28:34.719559Z","submitted_at":"2026-07-16T06:59:14Z","title":"Cluster structures on $SL_n/SO_n$","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-02T01:48:53.981715Z"},"links":{"citing_paper":"/paper/2607.14634"},"observation_digest":"sha256:8c99fd83a32ec4af1a30dbcfbf9b5003376dbd62c4e5d38567886071a1da5de1","observation_id":"3d923f94-f990-489c-869e-61e544925394","resolution":{"observed_at":"2026-08-02T01:48:53.981715Z","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":"2026-08-02T01:48:54.061543Z","title":null,"venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2607.14634","last_updated":"2026-07-16T06:59:14Z","snapshot_observed_at":"2026-08-10T22:28:34.719559Z","submitted_at":"2026-07-16T06:59:14Z","title":"Cluster structures on $SL_n/SO_n$","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-02T01:48:54.061543Z"},"links":{"citing_paper":"/paper/2607.14634"},"observation_digest":"sha256:fadba826b10700b7eb4fa39b2100dd596844389ddf191ab057dbf92e17715051","observation_id":"68bbc2ec-9cb0-4c7a-85cd-81ed3bb43233","resolution":{"observed_at":"2026-08-02T01:48:54.061543Z","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":"2026-08-02T01:48:54.172394Z","title":"Felikson, M","venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2607.14634","last_updated":"2026-07-16T06:59:14Z","snapshot_observed_at":"2026-08-10T22:28:34.719559Z","submitted_at":"2026-07-16T06:59:14Z","title":"Cluster structures on $SL_n/SO_n$","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-02T01:48:54.172394Z"},"links":{"citing_paper":"/paper/2607.14634"},"observation_digest":"sha256:1456c4805404971b9258275d336314a2ac8776acc3ba81b5ff40d90a176080b2","observation_id":"49298cbb-ca48-466e-84f3-c36fe93d1976","resolution":{"observed_at":"2026-08-02T01:48:54.172394Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1707.07190","last_updated":"2021-08-30T01:34:51Z","snapshot_observed_at":"2026-08-10T22:31:34.864896Z","submitted_at":"2017-07-22T16:27:28Z","title":"Introduction to Cluster Algebras. Chapters 4-5","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1707.07190","snapshot_observed_at":"2026-08-02T01:48:54.269904Z","title":"Fomin, L","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2607.14634","last_updated":"2026-07-16T06:59:14Z","snapshot_observed_at":"2026-08-10T22:28:34.719559Z","submitted_at":"2026-07-16T06:59:14Z","title":"Cluster structures on $SL_n/SO_n$","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-02T01:48:54.269904Z"},"links":{"cited_paper":"/paper/1707.07190","citing_paper":"/paper/2607.14634"},"observation_digest":"sha256:30e8a8054ed9399d13d1e486be9aa3cf0adefdec41e83f168a12dce4d054229a","observation_id":"eff84377-c82c-4d40-84a9-4be7b173b1a3","resolution":{"observed_at":"2026-08-02T01:48:54.269904Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"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":"2026-08-02T01:48:54.363955Z","title":"Chapter 6(2021), available athttps://arxiv","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2607.14634","last_updated":"2026-07-16T06:59:14Z","snapshot_observed_at":"2026-08-10T22:28:34.719559Z","submitted_at":"2026-07-16T06:59:14Z","title":"Cluster structures on $SL_n/SO_n$","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-02T01:48:54.363955Z"},"links":{"cited_paper":"/paper/2008.09189","citing_paper":"/paper/2607.14634"},"observation_digest":"sha256:90f56965b4d215855eddc9facafb0d354585bee4dd444c3367bfc80ccee3a247","observation_id":"f0b7b1ca-fb58-4308-9ff7-f57ccdcac5e2","resolution":{"observed_at":"2026-08-02T01:48:54.363955Z","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":"2026-08-02T01:48:54.426449Z","title":"Fomin and A","venue":null,"work_id":null,"year":1999},"citing_paper":{"arxiv_id":"2607.14634","last_updated":"2026-07-16T06:59:14Z","snapshot_observed_at":"2026-08-10T22:28:34.719559Z","submitted_at":"2026-07-16T06:59:14Z","title":"Cluster structures on $SL_n/SO_n$","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-02T01:48:54.426449Z"},"links":{"citing_paper":"/paper/2607.14634"},"observation_digest":"sha256:a4904f6a224eb90ea58eee8e514692e7a9d4af8825994fc0f37548d8b664fb2a","observation_id":"0bb0c4d7-5900-4f23-a788-77e85a4f2670","resolution":{"observed_at":"2026-08-02T01:48:54.426449Z","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":"2026-08-02T01:48:54.499430Z","title":null,"venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2607.14634","last_updated":"2026-07-16T06:59:14Z","snapshot_observed_at":"2026-08-10T22:28:34.719559Z","submitted_at":"2026-07-16T06:59:14Z","title":"Cluster structures on $SL_n/SO_n$","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-02T01:48:54.499430Z"},"links":{"citing_paper":"/paper/2607.14634"},"observation_digest":"sha256:6a260e9c28a1c38672717022432305bcac17e99a689603449292cb3061f5bfd6","observation_id":"a35bb637-b6be-45ef-8dd1-030715185a1f","resolution":{"observed_at":"2026-08-02T01:48:54.499430Z","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":"2026-08-02T01:48:54.536045Z","title":null,"venue":null,"work_id":null,"year":2003},"citing_paper":{"arxiv_id":"2607.14634","last_updated":"2026-07-16T06:59:14Z","snapshot_observed_at":"2026-08-10T22:28:34.719559Z","submitted_at":"2026-07-16T06:59:14Z","title":"Cluster structures on $SL_n/SO_n$","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-02T01:48:54.536045Z"},"links":{"citing_paper":"/paper/2607.14634"},"observation_digest":"sha256:6b38c43a238e3daa40ef27f89089a735702bbe034cdd4384e493adb6f3d791b6","observation_id":"6798e66a-6b6d-4cec-9af2-d727da2ca9a0","resolution":{"observed_at":"2026-08-02T01:48:54.536045Z","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":"2026-08-02T01:48:54.625965Z","title":"Fraser,Quasi-homomorphisms of cluster algebras, Adv","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2607.14634","last_updated":"2026-07-16T06:59:14Z","snapshot_observed_at":"2026-08-10T22:28:34.719559Z","submitted_at":"2026-07-16T06:59:14Z","title":"Cluster structures on $SL_n/SO_n$","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-02T01:48:54.625965Z"},"links":{"citing_paper":"/paper/2607.14634"},"observation_digest":"sha256:5ffe62617eb82244911d587b2f1e7ee3fe6d89e7d7324c41013682c6d9b49261","observation_id":"4389841d-e02b-4577-a68d-9d561573c529","resolution":{"observed_at":"2026-08-02T01:48:54.625965Z","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":"2026-08-02T01:48:54.685803Z","title":"Galashin, T","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.14634","last_updated":"2026-07-16T06:59:14Z","snapshot_observed_at":"2026-08-10T22:28:34.719559Z","submitted_at":"2026-07-16T06:59:14Z","title":"Cluster structures on $SL_n/SO_n$","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-02T01:48:54.685803Z"},"links":{"citing_paper":"/paper/2607.14634"},"observation_digest":"sha256:e979dd6afcbe50356eb98f8a6c615ce9d23f706d14c0230f0305a726990cb07a","observation_id":"d89d6f73-9e88-4063-af07-8133bce9de79","resolution":{"observed_at":"2026-08-02T01:48:54.685803Z","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":"2026-08-02T01:48:54.752442Z","title":"Geck and G","venue":null,"work_id":null,"year":1993},"citing_paper":{"arxiv_id":"2607.14634","last_updated":"2026-07-16T06:59:14Z","snapshot_observed_at":"2026-08-10T22:28:34.719559Z","submitted_at":"2026-07-16T06:59:14Z","title":"Cluster structures on $SL_n/SO_n$","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-02T01:48:54.752442Z"},"links":{"citing_paper":"/paper/2607.14634"},"observation_digest":"sha256:578bee2274c534cc063f0cb839469d83f93843cd491183587960bf3cc6dc7603","observation_id":"170740f5-91b0-4af5-ad17-9ca09ef6e80e","resolution":{"observed_at":"2026-08-02T01:48:54.752442Z","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":"2026-08-02T01:48:54.824838Z","title":null,"venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2607.14634","last_updated":"2026-07-16T06:59:14Z","snapshot_observed_at":"2026-08-10T22:28:34.719559Z","submitted_at":"2026-07-16T06:59:14Z","title":"Cluster structures on $SL_n/SO_n$","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-02T01:48:54.824838Z"},"links":{"citing_paper":"/paper/2607.14634"},"observation_digest":"sha256:1d28bddb8870f6f15cff9c2d5cdf17290f01196bb0059d0dddec59eece340be7","observation_id":"2f10642e-5db9-4531-9f7e-5be0a88805a7","resolution":{"observed_at":"2026-08-02T01:48:54.824838Z","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":"2026-08-02T01:48:54.914576Z","title":"Gekhtman, M","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2607.14634","last_updated":"2026-07-16T06:59:14Z","snapshot_observed_at":"2026-08-10T22:28:34.719559Z","submitted_at":"2026-07-16T06:59:14Z","title":"Cluster structures on $SL_n/SO_n$","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-02T01:48:54.914576Z"},"links":{"citing_paper":"/paper/2607.14634"},"observation_digest":"sha256:27b83f0ca3754f0afd21fe0b8e45a34265fe80641ec8a4529094fc7aba85eb89","observation_id":"68ec0051-b0be-4c18-9463-3e5597a2d396","resolution":{"observed_at":"2026-08-02T01:48:54.914576Z","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":"2026-08-02T01:48:54.995312Z","title":"Gross, P","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2607.14634","last_updated":"2026-07-16T06:59:14Z","snapshot_observed_at":"2026-08-10T22:28:34.719559Z","submitted_at":"2026-07-16T06:59:14Z","title":"Cluster structures on $SL_n/SO_n$","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-02T01:48:54.995312Z"},"links":{"citing_paper":"/paper/2607.14634"},"observation_digest":"sha256:6db726599613aed38f3596f1239d48a7c28646515ac6c1835eec74dbd55fadac","observation_id":"fce61546-346c-4e8f-80eb-3f917b9fc588","resolution":{"observed_at":"2026-08-02T01:48:54.995312Z","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":"2026-08-02T01:48:55.058072Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.14634","last_updated":"2026-07-16T06:59:14Z","snapshot_observed_at":"2026-08-10T22:28:34.719559Z","submitted_at":"2026-07-16T06:59:14Z","title":"Cluster structures on $SL_n/SO_n$","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-02T01:48:55.058072Z"},"links":{"citing_paper":"/paper/2607.14634"},"observation_digest":"sha256:b82eeae2cabe66d1dc77970b6637377ce30860fd9f3b1279cb84d0f5f4e2beba","observation_id":"03f0c743-dd0e-4785-93ee-96c5f81705fe","resolution":{"observed_at":"2026-08-02T01:48:55.058072Z","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":"2026-08-02T01:48:55.101527Z","title":null,"venue":null,"work_id":null,"year":1983},"citing_paper":{"arxiv_id":"2607.14634","last_updated":"2026-07-16T06:59:14Z","snapshot_observed_at":"2026-08-10T22:28:34.719559Z","submitted_at":"2026-07-16T06:59:14Z","title":"Cluster structures on $SL_n/SO_n$","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-02T01:48:55.101527Z"},"links":{"citing_paper":"/paper/2607.14634"},"observation_digest":"sha256:0d4f53e9bc51dd69e1552ac8122a398aabb0e006f6693478700c0a668689505e","observation_id":"b6e77301-71db-4628-8860-6ccae7225c85","resolution":{"observed_at":"2026-08-02T01:48:55.101527Z","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":"2026-08-02T01:48:55.165362Z","title":"Lu,On theT-leaves and the ranks of a Poisson structure on twisted conjugacy classes, Indag","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2607.14634","last_updated":"2026-07-16T06:59:14Z","snapshot_observed_at":"2026-08-10T22:28:34.719559Z","submitted_at":"2026-07-16T06:59:14Z","title":"Cluster structures on $SL_n/SO_n$","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-02T01:48:55.165362Z"},"links":{"citing_paper":"/paper/2607.14634"},"observation_digest":"sha256:8f49098b15c650547b6c67cdb2e8a1e9cc0293afae124c3fc904591c3cec5e66","observation_id":"9102bfef-6016-4ae2-937f-ff6c8e452342","resolution":{"observed_at":"2026-08-02T01:48:55.165362Z","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":"2026-08-02T01:48:55.245691Z","title":"Lusztig,Introduction to quantum groups, Progress in Mathematics, vol","venue":null,"work_id":null,"year":1993},"citing_paper":{"arxiv_id":"2607.14634","last_updated":"2026-07-16T06:59:14Z","snapshot_observed_at":"2026-08-10T22:28:34.719559Z","submitted_at":"2026-07-16T06:59:14Z","title":"Cluster structures on $SL_n/SO_n$","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-02T01:48:55.245691Z"},"links":{"citing_paper":"/paper/2607.14634"},"observation_digest":"sha256:5d7e370e31b217e0759fecd51bd7245a69a35c68fc557935b1d6709137a9f294","observation_id":"41561621-a051-4db5-8b57-028fc567e6af","resolution":{"observed_at":"2026-08-02T01:48:55.245691Z","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":"2026-08-02T01:48:55.328951Z","title":"Muller,Locally acyclic cluster algebras, Adv","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2607.14634","last_updated":"2026-07-16T06:59:14Z","snapshot_observed_at":"2026-08-10T22:28:34.719559Z","submitted_at":"2026-07-16T06:59:14Z","title":"Cluster structures on $SL_n/SO_n$","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-02T01:48:55.328951Z"},"links":{"citing_paper":"/paper/2607.14634"},"observation_digest":"sha256:e72955fa427137d2394b4a4909040d586fc01225a7809940a0e6205dc5030eb7","observation_id":"865bb487-7f2a-4486-8470-258fe916d133","resolution":{"observed_at":"2026-08-02T01:48:55.328951Z","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":"2026-08-02T01:48:55.411229Z","title":"Oya,A note on a cluster structure of the coordinate ring of a simple algebraic group (2025), available athttps://arxiv.org/abs/2504.09011","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.14634","last_updated":"2026-07-16T06:59:14Z","snapshot_observed_at":"2026-08-10T22:28:34.719559Z","submitted_at":"2026-07-16T06:59:14Z","title":"Cluster structures on $SL_n/SO_n$","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-02T01:48:55.411229Z"},"links":{"citing_paper":"/paper/2607.14634"},"observation_digest":"sha256:53ccc4bdd3a59b81b7153088db648b70c03c88d83ec43def717db9d586abebee","observation_id":"ae1a9aaa-da8f-4bc8-b9a0-3d0162c71845","resolution":{"observed_at":"2026-08-02T01:48:55.411229Z","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":"2026-08-02T01:48:55.495124Z","title":"Qin,Analogs of the dual canonical bases for cluster algebras from Lie theory(2025), available athttps://arxiv.org/abs/2407.02480","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.14634","last_updated":"2026-07-16T06:59:14Z","snapshot_observed_at":"2026-08-10T22:28:34.719559Z","submitted_at":"2026-07-16T06:59:14Z","title":"Cluster structures on $SL_n/SO_n$","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-02T01:48:55.495124Z"},"links":{"cited_paper":"/paper/2407.02480","citing_paper":"/paper/2607.14634"},"observation_digest":"sha256:0d6b516a998dc626a0e342bb2b5fa6ec5685cb739f851b25540904f4984cdc2a","observation_id":"a1636794-d6db-4044-bb37-515af3aaa192","resolution":{"observed_at":"2026-08-02T01:48:55.495124Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2504.05134","last_updated":"2025-04-21T16:36:20Z","snapshot_observed_at":"2026-08-07T16:07:56.163739Z","submitted_at":"2025-04-07T14:38:54Z","title":"Partially compactified quantum cluster structures on simple algebraic groups and the full Berenstein--Zelevinsky conjecture","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2504.05134","snapshot_observed_at":"2026-08-02T01:48:55.549886Z","title":"Qin and M","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.14634","last_updated":"2026-07-16T06:59:14Z","snapshot_observed_at":"2026-08-10T22:28:34.719559Z","submitted_at":"2026-07-16T06:59:14Z","title":"Cluster structures on $SL_n/SO_n$","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-02T01:48:55.549886Z"},"links":{"cited_paper":"/paper/2504.05134","citing_paper":"/paper/2607.14634"},"observation_digest":"sha256:34fadca218935b434d325675741687c630f9fecb27863e807aa957df82e4e3b6","observation_id":"6b344987-679c-4892-872b-e8bb88fce7a7","resolution":{"observed_at":"2026-08-02T01:48:55.549886Z","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":"2026-08-02T01:48:55.618401Z","title":"Shen and D","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2607.14634","last_updated":"2026-07-16T06:59:14Z","snapshot_observed_at":"2026-08-10T22:28:34.719559Z","submitted_at":"2026-07-16T06:59:14Z","title":"Cluster structures on $SL_n/SO_n$","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-02T01:48:55.618401Z"},"links":{"citing_paper":"/paper/2607.14634"},"observation_digest":"sha256:edad7ab3ea8f5fc09a6a931df686bd3f225a1064cb1ed0d8a2c96cf0cf853a1a","observation_id":"facdcf45-cec5-452b-803e-89547fed4a77","resolution":{"observed_at":"2026-08-02T01:48:55.618401Z","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":"2026-08-02T01:48:55.716337Z","title":null,"venue":null,"work_id":null,"year":1983},"citing_paper":{"arxiv_id":"2607.14634","last_updated":"2026-07-16T06:59:14Z","snapshot_observed_at":"2026-08-10T22:28:34.719559Z","submitted_at":"2026-07-16T06:59:14Z","title":"Cluster structures on $SL_n/SO_n$","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-02T01:48:55.716337Z"},"links":{"citing_paper":"/paper/2607.14634"},"observation_digest":"sha256:f739098d5ffb79f7f17189585904607ffceeb990aa249b81b84ff8a10425df03","observation_id":"436419e6-491a-438b-a9a2-b30d65909f1d","resolution":{"observed_at":"2026-08-02T01:48:55.716337Z","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":"2026-08-02T01:48:55.786145Z","title":"Sturmfels, E","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2607.14634","last_updated":"2026-07-16T06:59:14Z","snapshot_observed_at":"2026-08-10T22:28:34.719559Z","submitted_at":"2026-07-16T06:59:14Z","title":"Cluster structures on $SL_n/SO_n$","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-02T01:48:55.786145Z"},"links":{"citing_paper":"/paper/2607.14634"},"observation_digest":"sha256:280df1e12d62fe37ac81b0e7a5242f64051144bfa6e3b7b9bfbe0b9431adf9dc","observation_id":"5fa603d2-1e8e-4bbf-8b3b-4df1dc4bc66b","resolution":{"observed_at":"2026-08-02T01:48:55.786145Z","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":"2026-08-02T01:48:55.889492Z","title":"Song and J","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.14634","last_updated":"2026-07-16T06:59:14Z","snapshot_observed_at":"2026-08-10T22:28:34.719559Z","submitted_at":"2026-07-16T06:59:14Z","title":"Cluster structures on $SL_n/SO_n$","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-02T01:48:55.889492Z"},"links":{"citing_paper":"/paper/2607.14634"},"observation_digest":"sha256:5cda19c7efe760483f5bf3eb63046d451278e49d6217497c3b33dd19c3a9300e","observation_id":"3b726056-868f-4c59-9acd-7bfeaf6a8215","resolution":{"observed_at":"2026-08-02T01:48:55.889492Z","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":"2026-08-02T01:48:55.994852Z","title":"Zhou,Cluster structures and subfans in scattering diagrams, SIGMA Symmetry Integra- bility Geom","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2607.14634","last_updated":"2026-07-16T06:59:14Z","snapshot_observed_at":"2026-08-10T22:28:34.719559Z","submitted_at":"2026-07-16T06:59:14Z","title":"Cluster structures on $SL_n/SO_n$","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-02T01:48:55.994852Z"},"links":{"citing_paper":"/paper/2607.14634"},"observation_digest":"sha256:1e586bbd34b365b6e4837a6879fd95629da8866229aa3fa6d49c68d43037b900","observation_id":"82b26a95-705e-4e3d-9049-b2b4cc081103","resolution":{"observed_at":"2026-08-02T01:48:55.994852Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2607.14634","last_updated":"2026-07-16T06:59:14Z","latest_version":1,"primary_category":"math.RT","snapshot_observed_at":"2026-08-10T22:28:34.719559Z","submitted_at":"2026-07-16T06:59:14Z","title":"Cluster structures on $SL_n/SO_n$"},"reference_resolution":{"displayed":33,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":33,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":33},"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 11 August 2026, this Paper Citation Record lists 33 of 33 outbound references and 1 inbound Pith citation observation for arXiv:2607.14634."}