{"as_of":"2026-08-20T07:33:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:be77d1684d738045afd747cb80f332f89f580ca52bafa4bd7a7751148a1f3761","coverage":[{"denominator":27,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":27,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-12T14:55:18.243228Z","state":"measured"},{"denominator":27,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":27,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-20T06:33:59.587034+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2411.14963/citation-record","integrity":"/paper/2411.14963/integrity","json":"/paper/2411.14963/citation-record.json","paper":"/paper/2411.14963"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.4134/jkms.j210419","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T14:55:18.511748Z","title":"[Cla66] Luther Claborn","venue":null,"work_id":"1b0930aa-cee1-4dd5-8f61-6051c6c631bc","year":null},"citing_paper":{"arxiv_id":"2411.14963","last_updated":"2025-04-30T14:57:29Z","snapshot_observed_at":"2026-08-18T18:16:31.933404Z","submitted_at":"2024-11-22T14:22:29Z","title":"Every finitely generated abelian group is the class group of a generalized cluster algebra","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-12T14:55:18.148953Z"},"links":{"citing_paper":"/paper/2411.14963"},"observation_digest":"sha256:235d31b4bf31879a34b748dad245792435aa1d324cf35b6e23fd41007563e5a9","observation_id":"6b1f8c6d-79e4-4007-bcc2-4960211c9c10","resolution":{"observed_at":"2026-08-12T14:55:18.515621Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.3934/era.2022153","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T14:55:18.479596Z","title":"[FFN+24] Victor Fadinger, Sophie Frisch, Sarah Nakato, Daniel Smertnig, and Daniel Windisch","venue":null,"work_id":"167b27e4-07ba-454b-8e3e-4f782a9d8be9","year":null},"citing_paper":{"arxiv_id":"2411.14963","last_updated":"2025-04-30T14:57:29Z","snapshot_observed_at":"2026-08-18T18:16:31.933404Z","submitted_at":"2024-11-22T14:22:29Z","title":"Every finitely generated abelian group is the class group of a generalized cluster algebra","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-12T14:55:18.162811Z"},"links":{"citing_paper":"/paper/2411.14963"},"observation_digest":"sha256:ad897e4375f8db1625a2a11c8d98dbe4a5767b6da021becd08fb77ffbdd995ab","observation_id":"c2cea172-629e-4e32-8727-3b9df0b5f0d3","resolution":{"observed_at":"2026-08-12T14:55:18.483539Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2411.01051","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T14:55:18.718519Z","title":"[Fos73] Robert M","venue":null,"work_id":"bc162af8-5211-4f2e-b5e4-302739d75dff","year":null},"citing_paper":{"arxiv_id":"2411.14963","last_updated":"2025-04-30T14:57:29Z","snapshot_observed_at":"2026-08-18T18:16:31.933404Z","submitted_at":"2024-11-22T14:22:29Z","title":"Every finitely generated abelian group is the class group of a generalized cluster algebra","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-12T14:55:18.167282Z"},"links":{"citing_paper":"/paper/2411.14963"},"observation_digest":"sha256:0c7f5b04406d453d62401cc89104e8e466bdd1cda041f450dab28852e4caced5","observation_id":"acc2fe96-eddd-44f7-8572-267f9de57d1f","resolution":{"observed_at":"2026-08-12T14:55:18.725265Z","resolver_source":"raw_fallback","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/j.jnt.2024.03.001","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T14:55:18.445010Z","title":"[GLS13] Christof Geiss, Bernard Leclerc, and Jan Schr¨ oer","venue":null,"work_id":"03e3cfec-e9d1-445d-ad4a-7133e9f6b310","year":2024},"citing_paper":{"arxiv_id":"2411.14963","last_updated":"2025-04-30T14:57:29Z","snapshot_observed_at":"2026-08-18T18:16:31.933404Z","submitted_at":"2024-11-22T14:22:29Z","title":"Every finitely generated abelian group is the class group of a generalized cluster algebra","version":2},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-12T14:55:18.187689Z"},"links":{"citing_paper":"/paper/2411.14963"},"observation_digest":"sha256:1cfe728a93d599b56f2c07e808a4d0f17b68650688c3e78ddfa307ce4624addd","observation_id":"7726cc2f-e20d-4c69-97de-3f3af7d994c5","resolution":{"observed_at":"2026-08-12T14:55:18.449218Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1110.1199","last_updated":"2012-12-28T20:28:13Z","snapshot_observed_at":"2026-08-15T04:33:04.793996Z","submitted_at":"2011-10-06T09:53:00Z","title":"Factorial cluster algebras","version":4},"cited_work":{"arxiv_id":"1110.1199","doi":null,"metadata_source":"pith","pith_arxiv_id":"1110.1199","snapshot_observed_at":"2026-08-12T14:55:18.562486Z","title":"Factorial cluster algebras","venue":"math.RA","work_id":"bc354e1f-ee33-47b9-b200-dea58fac73e7","year":2011},"citing_paper":{"arxiv_id":"2411.14963","last_updated":"2025-04-30T14:57:29Z","snapshot_observed_at":"2026-08-18T18:16:31.933404Z","submitted_at":"2024-11-22T14:22:29Z","title":"Every finitely generated abelian group is the class group of a generalized cluster algebra","version":2},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-12T14:55:18.192699Z"},"links":{"cited_paper":"/paper/1110.1199","citing_paper":"/paper/2411.14963"},"observation_digest":"sha256:485a5fad23e9ec378d819d95a977eba9acd2419f84b2a5669c7b4e880aeb6843","observation_id":"4eb0bfb3-eeb6-4d75-8661-eb3f83771353","resolution":{"observed_at":"2026-08-12T14:55:18.567471Z","resolver_source":"local_arxiv","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-12T14:55:18.234516Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2411.14963","last_updated":"2025-04-30T14:57:29Z","snapshot_observed_at":"2026-08-18T18:16:31.933404Z","submitted_at":"2024-11-22T14:22:29Z","title":"Every finitely generated abelian group is the class group of a generalized cluster algebra","version":2},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-12T14:55:18.234516Z"},"links":{"citing_paper":"/paper/2411.14963"},"observation_digest":"sha256:b6f85beb2d2cf92a657464734f75df73743d1d2cd06d96a8edf35908375c433b","observation_id":"19faaf33-77d2-4d3c-99aa-18ed8f455e0e","resolution":{"observed_at":"2026-08-12T14:55:18.234516Z","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":"10.2307/1995734","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T14:55:18.414494Z","title":"[LP16] Thomas Lam and Pavlo Pylyavskyy","venue":null,"work_id":"e33b6b0f-e0d9-466c-9a14-5535b1c82c98","year":null},"citing_paper":{"arxiv_id":"2411.14963","last_updated":"2025-04-30T14:57:29Z","snapshot_observed_at":"2026-08-18T18:16:31.933404Z","submitted_at":"2024-11-22T14:22:29Z","title":"Every finitely generated abelian group is the class group of a generalized cluster algebra","version":2},"reference_index":1972,"source":"pdf_text","source_observed_at":"2026-08-12T14:55:18.205798Z"},"links":{"citing_paper":"/paper/2411.14963"},"observation_digest":"sha256:77545b3eb1af0c7dc2ca061f49f74e733559978b76ddefe3c7b96eb9ae7dabbe","observation_id":"8701cb14-a1c7-4c3a-8761-0a8178d05cb5","resolution":{"observed_at":"2026-08-12T14:55:18.418295Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/0021-8693(73)90036-7","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T14:55:18.366501Z","title":"[Ros76] Michael Rosen","venue":null,"work_id":"af7a5aa2-e64f-47c8-96e8-7c5c150dddf5","year":null},"citing_paper":{"arxiv_id":"2411.14963","last_updated":"2025-04-30T14:57:29Z","snapshot_observed_at":"2026-08-18T18:16:31.933404Z","submitted_at":"2024-11-22T14:22:29Z","title":"Every finitely generated abelian group is the class group of a generalized cluster algebra","version":2},"reference_index":1973,"source":"pdf_text","source_observed_at":"2026-08-12T14:55:18.222380Z"},"links":{"citing_paper":"/paper/2411.14963"},"observation_digest":"sha256:465670459be2da95d568a5d249ebafc1d4dafad532b2db893dd4dc54c968cc29","observation_id":"d7f7e7c9-2a76-47b4-b1dc-1470e750a372","resolution":{"observed_at":"2026-08-12T14:55:18.371694Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.2307/2041187","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T14:55:18.353161Z","title":"24 MARA POMPILI [R W21] Roswitha Rissner and Daniel Windisch","venue":null,"work_id":"4b7c197b-03a3-43d2-98c2-2a88f888b095","year":null},"citing_paper":{"arxiv_id":"2411.14963","last_updated":"2025-04-30T14:57:29Z","snapshot_observed_at":"2026-08-18T18:16:31.933404Z","submitted_at":"2024-11-22T14:22:29Z","title":"Every finitely generated abelian group is the class group of a generalized cluster algebra","version":2},"reference_index":1976,"source":"pdf_text","source_observed_at":"2026-08-12T14:55:18.225674Z"},"links":{"citing_paper":"/paper/2411.14963"},"observation_digest":"sha256:db1d54e31f3bef1e7a62988a2254d6a595e948d2677e7a8811a0e60f521902fe","observation_id":"ea6175d1-c597-45bc-b693-9b145efffe07","resolution":{"observed_at":"2026-08-12T14:55:18.357611Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.4064/cm-80-1-23-30","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T14:55:18.426256Z","title":"[Kel10] Bernhard Keller","venue":null,"work_id":"c323c7b9-3f0c-41c8-998a-f4409eac16d2","year":null},"citing_paper":{"arxiv_id":"2411.14963","last_updated":"2025-04-30T14:57:29Z","snapshot_observed_at":"2026-08-18T18:16:31.933404Z","submitted_at":"2024-11-22T14:22:29Z","title":"Every finitely generated abelian group is the class group of a generalized cluster algebra","version":2},"reference_index":1999,"source":"pdf_text","source_observed_at":"2026-08-12T14:55:18.201302Z"},"links":{"citing_paper":"/paper/2411.14963"},"observation_digest":"sha256:db3659fc8c46840c12b69f2d50099c3f1311000707d07f9bfcddbeefdda00f12","observation_id":"ce815359-4644-4afc-a2ad-8685f4747fa7","resolution":{"observed_at":"2026-08-12T14:55:18.430131Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-12T14:55:18.171465Z","title":"[FZ03] Sergey Fomin and Andrei Zelevinsky","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2411.14963","last_updated":"2025-04-30T14:57:29Z","snapshot_observed_at":"2026-08-18T18:16:31.933404Z","submitted_at":"2024-11-22T14:22:29Z","title":"Every finitely generated abelian group is the class group of a generalized cluster algebra","version":2},"reference_index":2002,"source":"pdf_text","source_observed_at":"2026-08-12T14:55:18.171465Z"},"links":{"citing_paper":"/paper/2411.14963"},"observation_digest":"sha256:3eeea8e8575d157f01fff842326b0838ae4346e3414de9732211b199f058c6db","observation_id":"98231fec-77b3-434f-8e83-70b2cbfbf769","resolution":{"observed_at":"2026-08-12T14:55:18.171465Z","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":"2026-08-12T14:55:18.175384Z","title":"[FZ07] Sergey Fomin and Andrei Zelevinsky","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2411.14963","last_updated":"2025-04-30T14:57:29Z","snapshot_observed_at":"2026-08-18T18:16:31.933404Z","submitted_at":"2024-11-22T14:22:29Z","title":"Every finitely generated abelian group is the class group of a generalized cluster algebra","version":2},"reference_index":2003,"source":"pdf_text","source_observed_at":"2026-08-12T14:55:18.175384Z"},"links":{"citing_paper":"/paper/2411.14963"},"observation_digest":"sha256:e7ba4f32d9eb06345e75795c2ec531b1ed4d58af5fc71eb5295cb31328cdd45a","observation_id":"3cb56007-6b2f-4e09-bd14-59f7aadeca71","resolution":{"observed_at":"2026-08-12T14:55:18.175384Z","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":"2026-08-12T14:55:18.140141Z","title":"EVERY F.G","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2411.14963","last_updated":"2025-04-30T14:57:29Z","snapshot_observed_at":"2026-08-18T18:16:31.933404Z","submitted_at":"2024-11-22T14:22:29Z","title":"Every finitely generated abelian group is the class group of a generalized cluster algebra","version":2},"reference_index":2005,"source":"pdf_text","source_observed_at":"2026-08-12T14:55:18.140141Z"},"links":{"citing_paper":"/paper/2411.14963"},"observation_digest":"sha256:bd5cd8d215f56e4a07218f59db6bec961ae9df03eac0b4381801fefe8b34bb57","observation_id":"61aecab1-6e8f-4ee5-88d7-a400db2e516f","resolution":{"observed_at":"2026-08-12T14:55:18.140141Z","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":"2026-08-12T14:55:18.179805Z","title":"[GELS19] Ana Garcia Elsener, Philipp Lampe, and Daniel Smertnig","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2411.14963","last_updated":"2025-04-30T14:57:29Z","snapshot_observed_at":"2026-08-18T18:16:31.933404Z","submitted_at":"2024-11-22T14:22:29Z","title":"Every finitely generated abelian group is the class group of a generalized cluster algebra","version":2},"reference_index":2007,"source":"pdf_text","source_observed_at":"2026-08-12T14:55:18.179805Z"},"links":{"citing_paper":"/paper/2411.14963"},"observation_digest":"sha256:fa90c90e159e4b6a97dc2c0ae471965b3eab30ec6ce4c7748a01537b59503231","observation_id":"ca7cd48a-f9c7-482a-b968-11c2f69dccb4","resolution":{"observed_at":"2026-08-12T14:55:18.179805Z","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":"10.4171/lem/55-3-1","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T14:55:18.499338Z","title":"[CS13] Leonid Chekhov and Michael Shapiro","venue":null,"work_id":"b4778179-f8ef-4cb2-aeb7-9a4abaff08f3","year":2014},"citing_paper":{"arxiv_id":"2411.14963","last_updated":"2025-04-30T14:57:29Z","snapshot_observed_at":"2026-08-18T18:16:31.933404Z","submitted_at":"2024-11-22T14:22:29Z","title":"Every finitely generated abelian group is the class group of a generalized cluster algebra","version":2},"reference_index":2009,"source":"pdf_text","source_observed_at":"2026-08-12T14:55:18.152961Z"},"links":{"citing_paper":"/paper/2411.14963"},"observation_digest":"sha256:5f58d8b4284301c8c2d1a7a5757d6e62f1e6440a8bbeaa9555ce1fb02834498b","observation_id":"dd368233-3bce-4e7c-bc1f-808a6be2678b","resolution":{"observed_at":"2026-08-12T14:55:18.503344Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-12T14:55:18.158487Z","title":"[DL22] Qiuning Du and Fang Li","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2411.14963","last_updated":"2025-04-30T14:57:29Z","snapshot_observed_at":"2026-08-18T18:16:31.933404Z","submitted_at":"2024-11-22T14:22:29Z","title":"Every finitely generated abelian group is the class group of a generalized cluster algebra","version":2},"reference_index":2013,"source":"pdf_text","source_observed_at":"2026-08-12T14:55:18.158487Z"},"links":{"citing_paper":"/paper/2411.14963"},"observation_digest":"sha256:16703f81005f9db315ec7ad583c36c0cc70755171c26df8cdcbb6d70ee2be49d","observation_id":"ed1a4ab8-2b32-43cc-9507-be9e5faa58d5","resolution":{"observed_at":"2026-08-12T14:55:18.158487Z","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":"10.1090/s0273-0979-2013-01417-4","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T14:55:18.291330Z","title":"University of Graz, Department of Mathematics and Scientific Computing, NA WI Graz, Heinrichstrasse 36, 8010 Graz, Austria Email address : mara.pompili@uni-graz.at","venue":null,"work_id":"1711a6ef-0a5d-47f4-8fa9-0783b4a95bb8","year":2013},"citing_paper":{"arxiv_id":"2411.14963","last_updated":"2025-04-30T14:57:29Z","snapshot_observed_at":"2026-08-18T18:16:31.933404Z","submitted_at":"2024-11-22T14:22:29Z","title":"Every finitely generated abelian group is the class group of a generalized cluster algebra","version":2},"reference_index":2014,"source":"pdf_text","source_observed_at":"2026-08-12T14:55:18.243228Z"},"links":{"citing_paper":"/paper/2411.14963"},"observation_digest":"sha256:5d5cfc0395cae0b31230148bff0b9f3638610d08cb642ca6ec4cc85e9b998bc5","observation_id":"b39639ec-3730-4697-bfdb-a81a61ed7d98","resolution":{"observed_at":"2026-08-12T14:55:18.301148Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-12T14:55:18.209772Z","title":"[Per23] Giulio Peruginelli","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2411.14963","last_updated":"2025-04-30T14:57:29Z","snapshot_observed_at":"2026-08-18T18:16:31.933404Z","submitted_at":"2024-11-22T14:22:29Z","title":"Every finitely generated abelian group is the class group of a generalized cluster algebra","version":2},"reference_index":2016,"source":"pdf_text","source_observed_at":"2026-08-12T14:55:18.209772Z"},"links":{"citing_paper":"/paper/2411.14963"},"observation_digest":"sha256:156dccdb145daa547d07ceb15be7924bbc476bff11d06667196d9cade5a6e302","observation_id":"f4e3898d-517c-481a-9fba-17b2ecfc2116","resolution":{"observed_at":"2026-08-12T14:55:18.209772Z","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":"10.1090/tran/6868","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T14:55:18.318108Z","title":"[Wil14] Lauren K","venue":null,"work_id":"4ee16201-606c-4a73-b5b1-d668d886c43d","year":null},"citing_paper":{"arxiv_id":"2411.14963","last_updated":"2025-04-30T14:57:29Z","snapshot_observed_at":"2026-08-18T18:16:31.933404Z","submitted_at":"2024-11-22T14:22:29Z","title":"Every finitely generated abelian group is the class group of a generalized cluster algebra","version":2},"reference_index":2017,"source":"pdf_text","source_observed_at":"2026-08-12T14:55:18.238654Z"},"links":{"citing_paper":"/paper/2411.14963"},"observation_digest":"sha256:f334b2b87dc8a6483de8f64d1a8bab110d0fd0c1f3857678e5130abd1533b193","observation_id":"68f0b2c7-e01b-4e4c-a5ca-ebef461555e2","resolution":{"observed_at":"2026-08-12T14:55:18.322574Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-12T14:55:18.197178Z","title":"[Kai99] Florian Kainrath","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2411.14963","last_updated":"2025-04-30T14:57:29Z","snapshot_observed_at":"2026-08-18T18:16:31.933404Z","submitted_at":"2024-11-22T14:22:29Z","title":"Every finitely generated abelian group is the class group of a generalized cluster algebra","version":2},"reference_index":2018,"source":"pdf_text","source_observed_at":"2026-08-12T14:55:18.197178Z"},"links":{"citing_paper":"/paper/2411.14963"},"observation_digest":"sha256:ddacb194f07de8775cd844b117a63f8c40d611823037d4f605c0a05f613d43ac","observation_id":"53f59688-0ba1-460a-ba6b-b380795390c8","resolution":{"observed_at":"2026-08-12T14:55:18.197178Z","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":"2019.10685","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T14:55:18.639094Z","title":"[GHK06] Alfred Geroldinger and Franz Halter-Koch","venue":null,"work_id":"0f51e779-495f-4ce5-9697-e5f730ea5b99","year":2019},"citing_paper":{"arxiv_id":"2411.14963","last_updated":"2025-04-30T14:57:29Z","snapshot_observed_at":"2026-08-18T18:16:31.933404Z","submitted_at":"2024-11-22T14:22:29Z","title":"Every finitely generated abelian group is the class group of a generalized cluster algebra","version":2},"reference_index":2019,"source":"pdf_text","source_observed_at":"2026-08-12T14:55:18.183754Z"},"links":{"citing_paper":"/paper/2411.14963"},"observation_digest":"sha256:bff06866f3d5d429bc9e9583dd7bc0a54dcc98db84eed5773fa6baf3bec0804b","observation_id":"5678cbc1-3aec-4f45-a158-4eeda129db79","resolution":{"observed_at":"2026-08-12T14:55:18.646087Z","resolver_source":"raw_fallback","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-12T14:55:18.135563Z","title":"[BFZ05] Arkady Berenstein, Sergey Fomin, and Andrei Zelevinsky","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2411.14963","last_updated":"2025-04-30T14:57:29Z","snapshot_observed_at":"2026-08-18T18:16:31.933404Z","submitted_at":"2024-11-22T14:22:29Z","title":"Every finitely generated abelian group is the class group of a generalized cluster algebra","version":2},"reference_index":2020,"source":"pdf_text","source_observed_at":"2026-08-12T14:55:18.135563Z"},"links":{"citing_paper":"/paper/2411.14963"},"observation_digest":"sha256:4192bfd95bc5843ad4911abe085627998f85b922ea144b926b7ee9489ae0fc4a","observation_id":"0d20d1e1-258d-459d-9b63-26af28100a3d","resolution":{"observed_at":"2026-08-12T14:55:18.135563Z","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":"10.1016/j.jalgebra.2021.03.007","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T14:55:18.342281Z","title":"[Sch16] W","venue":null,"work_id":"310c1928-c820-4b69-a14b-8fc137c5836f","year":2021},"citing_paper":{"arxiv_id":"2411.14963","last_updated":"2025-04-30T14:57:29Z","snapshot_observed_at":"2026-08-18T18:16:31.933404Z","submitted_at":"2024-11-22T14:22:29Z","title":"Every finitely generated abelian group is the class group of a generalized cluster algebra","version":2},"reference_index":2021,"source":"pdf_text","source_observed_at":"2026-08-12T14:55:18.229714Z"},"links":{"citing_paper":"/paper/2411.14963"},"observation_digest":"sha256:152702b83003d2a3d93d611cc59800bc9ce55f2600523df7c452e670bbe77906","observation_id":"da53e900-eea7-43af-9cb8-01f21b05c9ae","resolution":{"observed_at":"2026-08-12T14:55:18.345699Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s00233-021-10231-9","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-18T11:03:46.223893Z","title":"[BCDX20] Liqian Bai, Xueqing Chen, Ming Ding, and Fan Xu","venue":"Semigroup Forum","work_id":"8d314847-c1e5-438c-b620-e0dbad71ed43","year":null},"citing_paper":{"arxiv_id":"2411.14963","last_updated":"2025-04-30T14:57:29Z","snapshot_observed_at":"2026-08-18T18:16:31.933404Z","submitted_at":"2024-11-22T14:22:29Z","title":"Every finitely generated abelian group is the class group of a generalized cluster algebra","version":2},"reference_index":2022,"source":"pdf_text","source_observed_at":"2026-08-12T14:55:18.130037Z"},"links":{"citing_paper":"/paper/2411.14963"},"observation_digest":"sha256:1aa8f4d46be3f3e6e89bbc68620d071c9637d395a56146cf93371c9abec0ba6b","observation_id":"1658e7f9-8192-46b7-bcea-dec64bcc1e37","resolution":{"observed_at":"2026-08-12T14:55:18.548733Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[{"edge_observation":{"observed_at":"2026-08-12T18:18:04.257148+00:00","source":"paper_reference_links","state":"open"},"event_date":"2021-11-29","event_type":"correction","notice_doi":"10.1007/s00233-021-10243-5","provenance":{"observed_at":"2026-07-11T03:01:55.460606+00:00","source":"crossref","source_record_id":"10.1007/s00233-021-10243-5->10.1007/s00233-021-10231-9:correction"}}],"reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.2140/pjm.2023.324.333","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T14:55:18.393279Z","title":"[Pom25] Mara Pompili","venue":null,"work_id":"f23111ff-42cd-4d0c-a4a1-b40360fa89fe","year":2023},"citing_paper":{"arxiv_id":"2411.14963","last_updated":"2025-04-30T14:57:29Z","snapshot_observed_at":"2026-08-18T18:16:31.933404Z","submitted_at":"2024-11-22T14:22:29Z","title":"Every finitely generated abelian group is the class group of a generalized cluster algebra","version":2},"reference_index":2023,"source":"pdf_text","source_observed_at":"2026-08-12T14:55:18.214446Z"},"links":{"citing_paper":"/paper/2411.14963"},"observation_digest":"sha256:604ae6810646c137c205cb3f84c5df334c1b9ba2bf2b39f5fee678b5a445a74e","observation_id":"ea1cfe53-d4c4-458d-880f-a41e79e6faa8","resolution":{"observed_at":"2026-08-12T14:55:18.397667Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-12T14:55:18.144248Z","title":"[Cha22] Gyu Whan Chang","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2411.14963","last_updated":"2025-04-30T14:57:29Z","snapshot_observed_at":"2026-08-18T18:16:31.933404Z","submitted_at":"2024-11-22T14:22:29Z","title":"Every finitely generated abelian group is the class group of a generalized cluster algebra","version":2},"reference_index":2024,"source":"pdf_text","source_observed_at":"2026-08-12T14:55:18.144248Z"},"links":{"citing_paper":"/paper/2411.14963"},"observation_digest":"sha256:b82ae232e9e6e6d13b1b8a40bdbdebb2437d6211e38425d8af4d181d500e04b3","observation_id":"9a6c0f12-cc32-4439-9003-e8a783164257","resolution":{"observed_at":"2026-08-12T14:55:18.144248Z","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":"10.4153/s0008414x25000033","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T14:55:18.380601Z","title":"[Ros73] Michael Rosen","venue":null,"work_id":"0308d711-0e16-4401-bfbb-23c2b67f912e","year":null},"citing_paper":{"arxiv_id":"2411.14963","last_updated":"2025-04-30T14:57:29Z","snapshot_observed_at":"2026-08-18T18:16:31.933404Z","submitted_at":"2024-11-22T14:22:29Z","title":"Every finitely generated abelian group is the class group of a generalized cluster algebra","version":2},"reference_index":2025,"source":"pdf_text","source_observed_at":"2026-08-12T14:55:18.218578Z"},"links":{"citing_paper":"/paper/2411.14963"},"observation_digest":"sha256:47408ea1649408ae7a65ac575c85138725710cd02e9a58014be45c4e39108640","observation_id":"987955ad-9840-4079-a4b7-f860eadfae4f","resolution":{"observed_at":"2026-08-12T14:55:18.384831Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2411.14963","last_updated":"2025-04-30T14:57:29Z","latest_version":2,"primary_category":"math.AC","snapshot_observed_at":"2026-08-18T18:16:31.933404Z","submitted_at":"2024-11-22T14:22:29Z","title":"Every finitely generated abelian group is the class group of a generalized cluster algebra"},"reference_resolution":{"displayed":27,"state_counts":{"malformed_identifier":0,"metadata_mismatch":2,"parse_uncertain":0,"unresolved":10,"verified_exact":15,"verified_fuzzy":0},"total_outbound_references":27},"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":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"thesis":"As of 20 August 2026, this Paper Citation Record lists 27 of 27 outbound references and 0 inbound Pith citation observations for arXiv:2411.14963."}