{"as_of":"2026-08-09T20:51:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:f7b020f922b98e4b867b1d028810e6c43be0f16402ec9cbc1954673fc8cfccda","coverage":[{"denominator":17,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":17,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-04T12:47:29.545393Z","state":"measured"},{"denominator":17,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":17,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-09T06:31:02.800959+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/2510.02959/citation-record","integrity":"/paper/2510.02959/integrity","json":"/paper/2510.02959/citation-record.json","paper":"/paper/2510.02959"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T12:47:28.133519Z","title":"On a category of cluster algebras","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2510.02959","last_updated":"2026-06-10T09:09:03Z","snapshot_observed_at":"2026-08-08T18:45:34.342697Z","submitted_at":"2025-10-03T12:51:14Z","title":"Abstract Cluster Structures","version":2},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-08-04T12:47:28.133519Z"},"links":{"citing_paper":"/paper/2510.02959"},"observation_digest":"sha256:e5453352ecba0741834461dcda4e8d64dc5510aee19d3731059c20010511471e","observation_id":"15d2f93a-70b1-4450-8b4b-92c335160c01","resolution":{"observed_at":"2026-08-04T12:47:28.133519Z","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":"2026-08-04T12:47:28.180839Z","title":"Quantum cluster algebras","venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2510.02959","last_updated":"2026-06-10T09:09:03Z","snapshot_observed_at":"2026-08-08T18:45:34.342697Z","submitted_at":"2025-10-03T12:51:14Z","title":"Abstract Cluster Structures","version":2},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-08-04T12:47:28.180839Z"},"links":{"citing_paper":"/paper/2510.02959"},"observation_digest":"sha256:42dae8412dfd59d07f620141d1a92d42bd8192253e64f055760e1335120e5313","observation_id":"092ef4d5-b961-4a24-bfe0-7e0f9f77b465","resolution":{"observed_at":"2026-08-04T12:47:28.180839Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2402.16970","last_updated":"2024-03-05T17:19:12Z","snapshot_observed_at":"2026-08-03T15:11:15.658794Z","submitted_at":"2024-02-26T19:09:57Z","title":"Cluster deep loci and mirror symmetry","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2402.16970","snapshot_observed_at":"2026-08-04T12:47:28.272455Z","title":"Cluster deep loci and mirror symmetry","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2510.02959","last_updated":"2026-06-10T09:09:03Z","snapshot_observed_at":"2026-08-08T18:45:34.342697Z","submitted_at":"2025-10-03T12:51:14Z","title":"Abstract Cluster Structures","version":2},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-08-04T12:47:28.272455Z"},"links":{"cited_paper":"/paper/2402.16970","citing_paper":"/paper/2510.02959"},"observation_digest":"sha256:82687888e548056cfc5f93ec821996ca2f8bb8db678e933bbdad2a6a54242b68","observation_id":"5e833025-7d6c-494f-803c-224d13b25eef","resolution":{"observed_at":"2026-08-04T12:47:28.272455Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"math/0311245","last_updated":"2009-08-04T16:53:33Z","snapshot_observed_at":"2026-08-05T07:34:00.842403Z","submitted_at":"2003-11-14T20:49:44Z","title":"Cluster ensembles, quantization and the dilogarithm","version":7},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"math/0311245","snapshot_observed_at":"2026-08-04T12:47:28.375284Z","title":"Fock and Alexander B","venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2510.02959","last_updated":"2026-06-10T09:09:03Z","snapshot_observed_at":"2026-08-08T18:45:34.342697Z","submitted_at":"2025-10-03T12:51:14Z","title":"Abstract Cluster Structures","version":2},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-08-04T12:47:28.375284Z"},"links":{"cited_paper":"/paper/math/0311245","citing_paper":"/paper/2510.02959"},"observation_digest":"sha256:87cc35e4b326c8078c39b87f8c060a118721549ffeb46508ebdc56cab60d1e76","observation_id":"1faa8f6a-4a78-4e08-9539-a101825cb185","resolution":{"observed_at":"2026-08-04T12:47:28.375284Z","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":"2026-08-04T12:47:28.446842Z","title":"Cluster algebras and triangulated surfaces","venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2510.02959","last_updated":"2026-06-10T09:09:03Z","snapshot_observed_at":"2026-08-08T18:45:34.342697Z","submitted_at":"2025-10-03T12:51:14Z","title":"Abstract Cluster Structures","version":2},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-08-04T12:47:28.446842Z"},"links":{"citing_paper":"/paper/2510.02959"},"observation_digest":"sha256:1701b494cff85abd18c8c30e0491fd4add7bb7e862711664bd9037497e24635f","observation_id":"36cad618-0038-4c3c-8fb3-f0020fca9842","resolution":{"observed_at":"2026-08-04T12:47:28.446842Z","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":"2026-08-04T12:47:28.519101Z","title":"Cluster algebras","venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2510.02959","last_updated":"2026-06-10T09:09:03Z","snapshot_observed_at":"2026-08-08T18:45:34.342697Z","submitted_at":"2025-10-03T12:51:14Z","title":"Abstract Cluster Structures","version":2},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-08-04T12:47:28.519101Z"},"links":{"citing_paper":"/paper/2510.02959"},"observation_digest":"sha256:a28f0e63835be5a6d89476d7a062b4086c18b350c53bc56df72c7ab8b402086d","observation_id":"652aec73-176d-4254-a825-77186a22edf9","resolution":{"observed_at":"2026-08-04T12:47:28.519101Z","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":"2026-08-04T12:47:28.602696Z","title":"Cluster algebras","venue":null,"work_id":null,"year":2003},"citing_paper":{"arxiv_id":"2510.02959","last_updated":"2026-06-10T09:09:03Z","snapshot_observed_at":"2026-08-08T18:45:34.342697Z","submitted_at":"2025-10-03T12:51:14Z","title":"Abstract Cluster Structures","version":2},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-08-04T12:47:28.602696Z"},"links":{"citing_paper":"/paper/2510.02959"},"observation_digest":"sha256:d3a96348f6cadc37dfdf613dd7d58670a53e950989600a8c99b0f2081187d8b0","observation_id":"bcb60dad-f0d2-4e15-99bc-5f0dd80126a7","resolution":{"observed_at":"2026-08-04T12:47:28.602696Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"0912.4397","last_updated":"2009-12-22T13:09:20Z","snapshot_observed_at":"2026-07-06T02:05:50.100718Z","submitted_at":"2009-12-22T13:09:20Z","title":"Quantum cluster algebra structures on quantum Grassmannians and their quantum Schubert cells: the finite-type cases","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"0912.4397","snapshot_observed_at":"2026-08-04T12:47:28.698187Z","title":"Grabowski and St\\' e phane Launois","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2510.02959","last_updated":"2026-06-10T09:09:03Z","snapshot_observed_at":"2026-08-08T18:45:34.342697Z","submitted_at":"2025-10-03T12:51:14Z","title":"Abstract Cluster Structures","version":2},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-08-04T12:47:28.698187Z"},"links":{"cited_paper":"/paper/0912.4397","citing_paper":"/paper/2510.02959"},"observation_digest":"sha256:f761aa3b4feb9e98ebab9595e3196ed550c69db0a30bf6c5d9dc3550de60df21","observation_id":"2dcb3c44-0544-4042-adc4-c6180d2159d6","resolution":{"observed_at":"2026-08-04T12:47:28.698187Z","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":"2026-08-04T12:47:28.828312Z","title":"Grabowski and Matthew Pressland","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2510.02959","last_updated":"2026-06-10T09:09:03Z","snapshot_observed_at":"2026-08-08T18:45:34.342697Z","submitted_at":"2025-10-03T12:51:14Z","title":"Abstract Cluster Structures","version":2},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-08-04T12:47:28.828312Z"},"links":{"citing_paper":"/paper/2510.02959"},"observation_digest":"sha256:6cb490d0549aa50aed2eeac4a199f865710bd451fed54a90722d3879b953627c","observation_id":"e6a7e4a5-04da-4177-9689-13c282370b2b","resolution":{"observed_at":"2026-08-04T12:47:28.828312Z","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":"2026-08-04T12:47:28.903558Z","title":"Cluster algebras of infinite rank as colimits","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2510.02959","last_updated":"2026-06-10T09:09:03Z","snapshot_observed_at":"2026-08-08T18:45:34.342697Z","submitted_at":"2025-10-03T12:51:14Z","title":"Abstract Cluster Structures","version":2},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-08-04T12:47:28.903558Z"},"links":{"citing_paper":"/paper/2510.02959"},"observation_digest":"sha256:5b7e797cc1b666eede7a033024735b866ff84e42c2e52132926d0de8cfde5ab9","observation_id":"386c5fca-a732-4758-a243-d9887da5b85e","resolution":{"observed_at":"2026-08-04T12:47:28.903558Z","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":"2026-08-04T12:47:28.989927Z","title":"Cluster algebras and P oisson geometry , volume 167 of Mathematical Surveys and Monographs","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2510.02959","last_updated":"2026-06-10T09:09:03Z","snapshot_observed_at":"2026-08-08T18:45:34.342697Z","submitted_at":"2025-10-03T12:51:14Z","title":"Abstract Cluster Structures","version":2},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-08-04T12:47:28.989927Z"},"links":{"citing_paper":"/paper/2510.02959"},"observation_digest":"sha256:69bee5a2a415007e4067158e3dd2330ca5e2695c14a430472935a94371a27ce5","observation_id":"7ab810fe-fad4-4276-835e-ce25d7df80a8","resolution":{"observed_at":"2026-08-04T12:47:28.989927Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1309.7869","last_updated":"2015-05-13T06:50:30Z","snapshot_observed_at":"2026-07-06T03:24:22.271282Z","submitted_at":"2013-09-30T15:01:43Z","title":"Quantum cluster algebra structures on quantum nilpotent algebras","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1309.7869","snapshot_observed_at":"2026-08-04T12:47:29.080229Z","title":"Goodearl and Milen Yakimov","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2510.02959","last_updated":"2026-06-10T09:09:03Z","snapshot_observed_at":"2026-08-08T18:45:34.342697Z","submitted_at":"2025-10-03T12:51:14Z","title":"Abstract Cluster Structures","version":2},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-08-04T12:47:29.080229Z"},"links":{"cited_paper":"/paper/1309.7869","citing_paper":"/paper/2510.02959"},"observation_digest":"sha256:529e580a3193e82c94df4f311f45716871f8ce6e5074550c666aae31496e88b6","observation_id":"2791f8e9-8978-49a4-a100-88c247f1b7d7","resolution":{"observed_at":"2026-08-04T12:47:29.080229Z","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":"2026-08-04T12:47:29.180768Z","title":null,"venue":null,"work_id":null,"year":1965},"citing_paper":{"arxiv_id":"2510.02959","last_updated":"2026-06-10T09:09:03Z","snapshot_observed_at":"2026-08-08T18:45:34.342697Z","submitted_at":"2025-10-03T12:51:14Z","title":"Abstract Cluster Structures","version":2},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-08-04T12:47:29.180768Z"},"links":{"citing_paper":"/paper/2510.02959"},"observation_digest":"sha256:b586da99bc1fcdbf5ffa31cec3e5d8c49729d9900924928f2ebbf5809f976f58","observation_id":"26e3e584-219c-4ff7-852a-9c9cf1ce82c7","resolution":{"observed_at":"2026-08-04T12:47:29.180768Z","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":"2026-08-04T12:47:29.279998Z","title":"Quasicommuting families of quantum P l\\\"ucker coordinates","venue":null,"work_id":null,"year":1998},"citing_paper":{"arxiv_id":"2510.02959","last_updated":"2026-06-10T09:09:03Z","snapshot_observed_at":"2026-08-08T18:45:34.342697Z","submitted_at":"2025-10-03T12:51:14Z","title":"Abstract Cluster Structures","version":2},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-08-04T12:47:29.279998Z"},"links":{"citing_paper":"/paper/2510.02959"},"observation_digest":"sha256:12344ea775c3396b6483f1d64e4ba0a3542ec49d57c45b090889b1f2e5c16eda","observation_id":"bb0b3572-7e11-484f-be92-ce1c900f571f","resolution":{"observed_at":"2026-08-04T12:47:29.279998Z","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":"2026-08-04T12:47:29.351202Z","title":"Sheaves in geometry and logic","venue":null,"work_id":null,"year":1994},"citing_paper":{"arxiv_id":"2510.02959","last_updated":"2026-06-10T09:09:03Z","snapshot_observed_at":"2026-08-08T18:45:34.342697Z","submitted_at":"2025-10-03T12:51:14Z","title":"Abstract Cluster Structures","version":2},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-08-04T12:47:29.351202Z"},"links":{"citing_paper":"/paper/2510.02959"},"observation_digest":"sha256:55fc1e514786d36dcc55927e0e91ec3e84237c18ddf318cb08e9e6049b244191","observation_id":"f31234f4-7615-430f-a5ef-4ebb1ab0f1f3","resolution":{"observed_at":"2026-08-04T12:47:29.351202Z","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":"2026-08-04T12:47:29.459835Z","title":null,"venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2510.02959","last_updated":"2026-06-10T09:09:03Z","snapshot_observed_at":"2026-08-08T18:45:34.342697Z","submitted_at":"2025-10-03T12:51:14Z","title":"Abstract Cluster Structures","version":2},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-08-04T12:47:29.459835Z"},"links":{"citing_paper":"/paper/2510.02959"},"observation_digest":"sha256:4532784feef754a8426d16308cf3c2e453a290bbac099c29a77b5a8c62e849fc","observation_id":"4d1fdba0-6ce5-446c-8ee1-235e88afb95f","resolution":{"observed_at":"2026-08-04T12:47:29.459835Z","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":"2026-08-04T12:47:29.545393Z","title":"Additive Gruppen von Folgen ganzer Zahlen","venue":null,"work_id":null,"year":1950},"citing_paper":{"arxiv_id":"2510.02959","last_updated":"2026-06-10T09:09:03Z","snapshot_observed_at":"2026-08-08T18:45:34.342697Z","submitted_at":"2025-10-03T12:51:14Z","title":"Abstract Cluster Structures","version":2},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-08-04T12:47:29.545393Z"},"links":{"citing_paper":"/paper/2510.02959"},"observation_digest":"sha256:7f1fc21c168a5cc62389b931a942c3b32b416c3cf034feaec0a88a2a3f9678b0","observation_id":"7fd6af27-dab9-4c61-86a7-0bc20a453572","resolution":{"observed_at":"2026-08-04T12:47:29.545393Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2510.02959","last_updated":"2026-06-10T09:09:03Z","latest_version":2,"primary_category":"math.RA","snapshot_observed_at":"2026-08-08T18:45:34.342697Z","submitted_at":"2025-10-03T12:51:14Z","title":"Abstract Cluster Structures"},"reference_resolution":{"displayed":17,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":17,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":17},"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":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"thesis":"As of 9 August 2026, this Paper Citation Record lists 17 of 17 outbound references and 0 inbound Pith citation observations for arXiv:2510.02959."}