{"as_of":"2026-08-18T00:45:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:507bb8137c3ed2fd90943077ba11f14884f36a92a5478211d17ff8283969a7cc","coverage":[{"denominator":37,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":37,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-11T22:16:01.966754Z","state":"measured"},{"denominator":38,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":38,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-17T06:30:58.91139+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":"2026-08-16T06:08:35.218760Z","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":"2026-08-16T06:08:36.988863Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2412.03750","last_updated":"2025-02-03T18:44:35Z","snapshot_observed_at":"2026-08-15T02:30:19.775240Z","submitted_at":"2024-12-04T22:40:39Z","title":"Alternating snake modules and a determinantal formula","version":2},"cited_work":{"arxiv_id":"2412.03750","doi":null,"metadata_source":"pith","pith_arxiv_id":"2412.03750","snapshot_observed_at":"2026-08-16T06:08:36.988863Z","title":"Alternating snake modules and a determinantal formula","venue":"math.RT","work_id":"08661dd3-cb54-4a44-99ca-1830e2a8e620","year":2024},"citing_paper":{"arxiv_id":"2504.19313","last_updated":"2025-04-27T17:28:52Z","snapshot_observed_at":"2026-08-16T05:53:11.149814Z","submitted_at":"2025-04-27T17:28:52Z","title":"On dominant $\\ell$--weights and maps between Weyl modules for quantum affine $A_n$","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-16T06:08:35.218760Z"},"links":{"cited_paper":"/paper/2412.03750","citing_paper":"/paper/2504.19313"},"observation_digest":"sha256:911627b39235b507bdcef5119cfd947b9be158bb613f17c756a930ef771740a1","observation_id":"412c2332-5e57-4df6-8b15-a81975504e5b","resolution":{"observed_at":"2026-08-16T06:08:37.022539Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2412.03750/citation-record","integrity":"/paper/2412.03750/integrity","json":"/paper/2412.03750/citation-record.json","paper":"/paper/2412.03750"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T22:16:02.382298Z","title":"Duality between sln(C) and the Degenerate Aﬃne Hecke Algebra","venue":null,"work_id":"cd2fd4a8-0df9-4e37-b212-a406da7d0893","year":1998},"citing_paper":{"arxiv_id":"2412.03750","last_updated":"2025-02-03T18:44:35Z","snapshot_observed_at":"2026-08-15T02:30:19.775240Z","submitted_at":"2024-12-04T22:40:39Z","title":"Alternating snake modules and a determinantal formula","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-11T22:16:01.846881Z"},"links":{"citing_paper":"/paper/2412.03750"},"observation_digest":"sha256:1ebd0dd9fe33b182c76fe060e4d9c878a0ee915a3f146e4a2b1c9ec4eaf0ded2","observation_id":"107eacad-100a-4284-8321-85d042dac5ec","resolution":{"observed_at":"2026-08-11T22:16:02.386064Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T22:16:02.374158Z","title":"Ladder representations of GL(n, Qp), pages 117–137","venue":null,"work_id":"6d53999f-3bd2-499d-98f1-d8b25743977f","year":2015},"citing_paper":{"arxiv_id":"2412.03750","last_updated":"2025-02-03T18:44:35Z","snapshot_observed_at":"2026-08-15T02:30:19.775240Z","submitted_at":"2024-12-04T22:40:39Z","title":"Alternating snake modules and a determinantal formula","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-11T22:16:01.850583Z"},"links":{"citing_paper":"/paper/2412.03750"},"observation_digest":"sha256:fce531e808cb8e0b0290307f24d3ebbb66ad8a7624ac1adab35d38936611b847","observation_id":"54fca017-a25b-4697-bbcb-4831ba83b6a9","resolution":{"observed_at":"2026-08-11T22:16:02.377160Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T22:16:02.365727Z","title":"Tensor products and q-characters of HL-modules and monoidal categoriﬁcations","venue":null,"work_id":"c0e701ac-bf5e-477a-95b8-11ce354b3455","year":2019},"citing_paper":{"arxiv_id":"2412.03750","last_updated":"2025-02-03T18:44:35Z","snapshot_observed_at":"2026-08-15T02:30:19.775240Z","submitted_at":"2024-12-04T22:40:39Z","title":"Alternating snake modules and a determinantal formula","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-11T22:16:01.854275Z"},"links":{"citing_paper":"/paper/2412.03750"},"observation_digest":"sha256:7267d01ae6f88e4b88f62561394a1f1d3b11c9579585df7d90f0739c06322c0a","observation_id":"a8b21b28-7367-47bb-83cc-a570a759b9f4","resolution":{"observed_at":"2026-08-11T22:16:02.368707Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T22:16:02.357322Z","title":"Higher order Kirill ov–Reshetikhin modules for Uq(A(1) n ), imagi- nary modules and monoidal categoriﬁcation","venue":null,"work_id":"3420f3f0-65fd-4674-8bd4-1e869faa1450","year":2023},"citing_paper":{"arxiv_id":"2412.03750","last_updated":"2025-02-03T18:44:35Z","snapshot_observed_at":"2026-08-15T02:30:19.775240Z","submitted_at":"2024-12-04T22:40:39Z","title":"Alternating snake modules and a determinantal formula","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-11T22:16:01.857824Z"},"links":{"citing_paper":"/paper/2412.03750"},"observation_digest":"sha256:abb8579ad2547048cb08f8553e6d3c9cf701d28bd4cff06e22e540151db9a56f","observation_id":"5e191bb2-e825-4848-b222-99b7bf87881f","resolution":{"observed_at":"2026-08-11T22:16:02.360450Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2406.06970","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T22:16:02.064268Z","title":"Realit y determining subgraphs and strongly real mod- ules","venue":null,"work_id":"bc00debd-7180-45d1-8c9f-3709da35adb4","year":2024},"citing_paper":{"arxiv_id":"2412.03750","last_updated":"2025-02-03T18:44:35Z","snapshot_observed_at":"2026-08-15T02:30:19.775240Z","submitted_at":"2024-12-04T22:40:39Z","title":"Alternating snake modules and a determinantal formula","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-11T22:16:01.861703Z"},"links":{"citing_paper":"/paper/2412.03750"},"observation_digest":"sha256:3e3168b22872c2f9a7903a86f0ad68dc604d7c4e74b83bd5f52bdbc0841d51a1","observation_id":"0b8121e0-fc84-4281-81b9-357aeabb4d40","resolution":{"observed_at":"2026-08-11T22:16:02.071855Z","resolver_source":"raw_fallback","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T22:16:02.349077Z","title":"Braid group actions and tensor produc ts","venue":null,"work_id":"881fc925-99bf-455f-b2ac-eee0051eeb75","year":2002},"citing_paper":{"arxiv_id":"2412.03750","last_updated":"2025-02-03T18:44:35Z","snapshot_observed_at":"2026-08-15T02:30:19.775240Z","submitted_at":"2024-12-04T22:40:39Z","title":"Alternating snake modules and a determinantal formula","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-11T22:16:01.865234Z"},"links":{"citing_paper":"/paper/2412.03750"},"observation_digest":"sha256:a700c94d0301052fb6e727cf1ba02d6ab824a71428a22c468580fda94231df80","observation_id":"ea7a69aa-ef14-40dc-a0bf-e4647f45a74e","resolution":{"observed_at":"2026-08-11T22:16:02.352168Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T22:16:02.341182Z","title":null,"venue":null,"work_id":"738f5940-0486-42b4-9171-b0cf70453588","year":2005},"citing_paper":{"arxiv_id":"2412.03750","last_updated":"2025-02-03T18:44:35Z","snapshot_observed_at":"2026-08-15T02:30:19.775240Z","submitted_at":"2024-12-04T22:40:39Z","title":"Alternating snake modules and a determinantal formula","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-11T22:16:01.869652Z"},"links":{"citing_paper":"/paper/2412.03750"},"observation_digest":"sha256:baa360728b67ad2031540952af2afe2c5c33d3bc377d98414cdd71209e1322b3","observation_id":"560cf8e8-fd6c-4e29-893d-195a0624ee67","resolution":{"observed_at":"2026-08-11T22:16:02.344032Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T22:16:02.333184Z","title":"Quantum aﬃne alge bras","venue":null,"work_id":"b3ce6513-e19c-4366-92df-901168ef7a92","year":1991},"citing_paper":{"arxiv_id":"2412.03750","last_updated":"2025-02-03T18:44:35Z","snapshot_observed_at":"2026-08-15T02:30:19.775240Z","submitted_at":"2024-12-04T22:40:39Z","title":"Alternating snake modules and a determinantal formula","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-11T22:16:01.872955Z"},"links":{"citing_paper":"/paper/2412.03750"},"observation_digest":"sha256:3ea4cae458e2e2c3491624c51b0edbf4895f6fbe8ef02d7df193beca3be2fa87","observation_id":"6b77ebbc-2baf-4430-ba27-47311fc4b997","resolution":{"observed_at":"2026-08-11T22:16:02.336042Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T22:16:02.324846Z","title":"Minimal aﬃnizati ons of representations of quantum groups: the nonsimply-laced case","venue":null,"work_id":"dec1719e-3939-4f95-891a-3692ee14fc1b","year":1995},"citing_paper":{"arxiv_id":"2412.03750","last_updated":"2025-02-03T18:44:35Z","snapshot_observed_at":"2026-08-15T02:30:19.775240Z","submitted_at":"2024-12-04T22:40:39Z","title":"Alternating snake modules and a determinantal formula","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-11T22:16:01.876201Z"},"links":{"citing_paper":"/paper/2412.03750"},"observation_digest":"sha256:f3c778dd7095a1edcedacc4f7e8693382f650144fa0561cfa5bac0c6024a8b0d","observation_id":"8b4fdb74-dfe5-48e8-9205-2dfc26592dae","resolution":{"observed_at":"2026-08-11T22:16:02.327959Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T22:16:02.316639Z","title":"Quantum aﬃne alg ebras and aﬃne hecke algebras","venue":null,"work_id":"96937784-b6fa-4174-969c-23de7ccef4bc","year":1995},"citing_paper":{"arxiv_id":"2412.03750","last_updated":"2025-02-03T18:44:35Z","snapshot_observed_at":"2026-08-15T02:30:19.775240Z","submitted_at":"2024-12-04T22:40:39Z","title":"Alternating snake modules and a determinantal formula","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-11T22:16:01.879409Z"},"links":{"citing_paper":"/paper/2412.03750"},"observation_digest":"sha256:86d2cc5afc5faf88eb24a6714003da02fe66ea1b88413521e80eaf5b6339af5d","observation_id":"10e52f62-ffee-4d1a-8da9-fa5c79edcd12","resolution":{"observed_at":"2026-08-11T22:16:02.319630Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T22:16:02.308243Z","title":"Quantum aﬃne alg ebras and their representations","venue":null,"work_id":"285ca4a0-ecf6-42a0-b002-86f4abc802b3","year":1994},"citing_paper":{"arxiv_id":"2412.03750","last_updated":"2025-02-03T18:44:35Z","snapshot_observed_at":"2026-08-15T02:30:19.775240Z","submitted_at":"2024-12-04T22:40:39Z","title":"Alternating snake modules and a determinantal formula","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-11T22:16:01.882648Z"},"links":{"citing_paper":"/paper/2412.03750"},"observation_digest":"sha256:de5dca5cdf014c4a7bf26f46b6a44ad63c9021e024b56274e61eccf76a607325","observation_id":"eb8421d9-b3f9-46c4-82de-f7733cc6a53a","resolution":{"observed_at":"2026-08-11T22:16:02.311351Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T22:16:02.299706Z","title":"Minimal aﬃnizat ions of representations of quantum groups: the simply laced case","venue":null,"work_id":"18570196-1996-4bdd-a8e7-f5f167627da1","year":1996},"citing_paper":{"arxiv_id":"2412.03750","last_updated":"2025-02-03T18:44:35Z","snapshot_observed_at":"2026-08-15T02:30:19.775240Z","submitted_at":"2024-12-04T22:40:39Z","title":"Alternating snake modules and a determinantal formula","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-11T22:16:01.886088Z"},"links":{"citing_paper":"/paper/2412.03750"},"observation_digest":"sha256:6d2c740acf4da5950081309f8ad3ba64fd4cc0367a093c3a0b151246d0bbdb1e","observation_id":"b9c7884e-af8c-47cc-974c-f56ed2d4de98","resolution":{"observed_at":"2026-08-11T22:16:02.302812Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T22:16:02.291704Z","title":"Weyl modules for classical and quantum aﬃne algebras","venue":null,"work_id":"0a1344c1-bb07-47c6-b7e7-4bbbba7463be","year":2001},"citing_paper":{"arxiv_id":"2412.03750","last_updated":"2025-02-03T18:44:35Z","snapshot_observed_at":"2026-08-15T02:30:19.775240Z","submitted_at":"2024-12-04T22:40:39Z","title":"Alternating snake modules and a determinantal formula","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-11T22:16:01.889446Z"},"links":{"citing_paper":"/paper/2412.03750"},"observation_digest":"sha256:3bce0439b6ee3aec4e1f41186d1a6763633c8ce7ee12529ca4b0ceb12a93eb6e","observation_id":"9f64a881-2271-4825-b41d-6257b8c6a050","resolution":{"observed_at":"2026-08-11T22:16:02.294569Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T22:16:02.282938Z","title":"Cluster alge bras and snake modules","venue":null,"work_id":"3d69fa10-2541-49d9-950f-2eb0081ac26d","year":2019},"citing_paper":{"arxiv_id":"2412.03750","last_updated":"2025-02-03T18:44:35Z","snapshot_observed_at":"2026-08-15T02:30:19.775240Z","submitted_at":"2024-12-04T22:40:39Z","title":"Alternating snake modules and a determinantal formula","version":2},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-11T22:16:01.892832Z"},"links":{"citing_paper":"/paper/2412.03750"},"observation_digest":"sha256:7aee1e3582459c579485ba7845eff3adef4965ced2dc80f961f586d0ffe8e6bd","observation_id":"3c089a81-f52e-40e3-8234-3fe53e245f56","resolution":{"observed_at":"2026-08-11T22:16:02.286595Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T22:16:02.274721Z","title":"Tropical geometry, quantu m aﬃne algebras, and scattering amplitudes","venue":null,"work_id":"8a2cd62f-064c-4949-a6a5-55752d406918","year":2024},"citing_paper":{"arxiv_id":"2412.03750","last_updated":"2025-02-03T18:44:35Z","snapshot_observed_at":"2026-08-15T02:30:19.775240Z","submitted_at":"2024-12-04T22:40:39Z","title":"Alternating snake modules and a determinantal formula","version":2},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-11T22:16:01.896125Z"},"links":{"citing_paper":"/paper/2412.03750"},"observation_digest":"sha256:7dab839a3bc7cc079f318c578aaaf69f91d5a8aaa44d994dd7ee415f052ffad4","observation_id":"fe74df99-554a-4ffd-9a44-387adc295f04","resolution":{"observed_at":"2026-08-11T22:16:02.277810Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T22:16:02.266555Z","title":"The q-characters of representations of quantum aﬃne algebras and deformations of W-algebras","venue":null,"work_id":"ad9faf31-2f11-4284-b66e-db0d601a523b","year":1998},"citing_paper":{"arxiv_id":"2412.03750","last_updated":"2025-02-03T18:44:35Z","snapshot_observed_at":"2026-08-15T02:30:19.775240Z","submitted_at":"2024-12-04T22:40:39Z","title":"Alternating snake modules and a determinantal formula","version":2},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-11T22:16:01.899497Z"},"links":{"citing_paper":"/paper/2412.03750"},"observation_digest":"sha256:a4b5a5c55968de66c229cc58f374ecea5aa6fdd35a7c18b2eeb8abb0fe43482f","observation_id":"cb93e568-472a-45b8-8eeb-77f071d1b1fd","resolution":{"observed_at":"2026-08-11T22:16:02.269541Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T22:16:02.257974Z","title":"Quantum invariants for decomposition problems in type a rings of representations","venue":null,"work_id":"54a69579-a28a-43d5-94fa-81cf6fd67d9a","year":2021},"citing_paper":{"arxiv_id":"2412.03750","last_updated":"2025-02-03T18:44:35Z","snapshot_observed_at":"2026-08-15T02:30:19.775240Z","submitted_at":"2024-12-04T22:40:39Z","title":"Alternating snake modules and a determinantal formula","version":2},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-11T22:16:01.902843Z"},"links":{"citing_paper":"/paper/2412.03750"},"observation_digest":"sha256:cdbf273872b33e86c3072001b73a066bcaee3249297f0f8491aab5b60461414b","observation_id":"55c7c0bf-2739-435a-b293-f5061ca91588","resolution":{"observed_at":"2026-08-11T22:16:02.261139Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T22:16:02.249619Z","title":"Cluster algebras and quantum aﬃne algebras","venue":null,"work_id":"7e9c906d-7375-4e7c-84ca-a500a807ebff","year":2010},"citing_paper":{"arxiv_id":"2412.03750","last_updated":"2025-02-03T18:44:35Z","snapshot_observed_at":"2026-08-15T02:30:19.775240Z","submitted_at":"2024-12-04T22:40:39Z","title":"Alternating snake modules and a determinantal formula","version":2},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-11T22:16:01.906025Z"},"links":{"citing_paper":"/paper/2412.03750"},"observation_digest":"sha256:e7f88f8bff9437d72628e33fbd6e615f170f028d21e3234e9d50c7608c56c55a","observation_id":"215e8a77-abb5-4589-9dbe-7f1e3b5d3b6e","resolution":{"observed_at":"2026-08-11T22:16:02.252772Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T22:16:02.241038Z","title":"A cluster algebra approach to q-characters of Kirillov-Reshetikhin modules","venue":null,"work_id":"d3bc7741-5422-4e9c-ba08-957514fbb6dd","year":2013},"citing_paper":{"arxiv_id":"2412.03750","last_updated":"2025-02-03T18:44:35Z","snapshot_observed_at":"2026-08-15T02:30:19.775240Z","submitted_at":"2024-12-04T22:40:39Z","title":"Alternating snake modules and a determinantal formula","version":2},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-11T22:16:01.909081Z"},"links":{"citing_paper":"/paper/2412.03750"},"observation_digest":"sha256:af9a98622261f482d2fd7739e53b1807b1b9f68c2d39c69bc41d1b5f2ab29858","observation_id":"25ec817b-3da4-4304-9f3a-fe118b3fcf65","resolution":{"observed_at":"2026-08-11T22:16:02.244157Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T22:16:02.233013Z","title":"Monoidal categor iﬁcations of cluster algebras of type A and D","venue":null,"work_id":"e0926e9f-efc6-41a5-b160-ca73fe50f9bc","year":2013},"citing_paper":{"arxiv_id":"2412.03750","last_updated":"2025-02-03T18:44:35Z","snapshot_observed_at":"2026-08-15T02:30:19.775240Z","submitted_at":"2024-12-04T22:40:39Z","title":"Alternating snake modules and a determinantal formula","version":2},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-11T22:16:01.912194Z"},"links":{"citing_paper":"/paper/2412.03750"},"observation_digest":"sha256:b64f2780e0d90d626e79da79a505dcf9fda0a1559bd641afa9a0ed44651b4b59","observation_id":"800af78f-9803-40ef-a79b-03e5db7562de","resolution":{"observed_at":"2026-08-11T22:16:02.236057Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T22:16:02.224287Z","title":"Simplicity of heads and socles of tensor products","venue":null,"work_id":"97c9078f-8938-46cc-aee5-e2a491ac6b59","year":2015},"citing_paper":{"arxiv_id":"2412.03750","last_updated":"2025-02-03T18:44:35Z","snapshot_observed_at":"2026-08-15T02:30:19.775240Z","submitted_at":"2024-12-04T22:40:39Z","title":"Alternating snake modules and a determinantal formula","version":2},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-11T22:16:01.916114Z"},"links":{"citing_paper":"/paper/2412.03750"},"observation_digest":"sha256:0b057cf29b1948b418c50b669b90cca37700f2c35878a159b1473ca2044caf75","observation_id":"e10a64da-10a1-48dd-bb4e-ca02cdc72eb8","resolution":{"observed_at":"2026-08-11T22:16:02.227824Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T22:16:02.215984Z","title":"Monoidal categoriﬁcation of cluster algebras","venue":null,"work_id":"b9cb0c4d-d8b9-416c-969b-6ee80c8c3e2e","year":2018},"citing_paper":{"arxiv_id":"2412.03750","last_updated":"2025-02-03T18:44:35Z","snapshot_observed_at":"2026-08-15T02:30:19.775240Z","submitted_at":"2024-12-04T22:40:39Z","title":"Alternating snake modules and a determinantal formula","version":2},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-11T22:16:01.919372Z"},"links":{"citing_paper":"/paper/2412.03750"},"observation_digest":"sha256:634045afe953b137c2753c72023169e4cc2fee86116f7b667cb3993cd4ddc1a7","observation_id":"7b431026-9ffc-45bf-baab-535da2671b03","resolution":{"observed_at":"2026-08-11T22:16:02.218994Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T22:16:02.207440Z","title":"Monoidal categoriﬁcation and quantum aﬃne algebras","venue":null,"work_id":"636d56fd-9e36-4b5b-805f-7e9a16ffecca","year":2020},"citing_paper":{"arxiv_id":"2412.03750","last_updated":"2025-02-03T18:44:35Z","snapshot_observed_at":"2026-08-15T02:30:19.775240Z","submitted_at":"2024-12-04T22:40:39Z","title":"Alternating snake modules and a determinantal formula","version":2},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-11T22:16:01.922701Z"},"links":{"citing_paper":"/paper/2412.03750"},"observation_digest":"sha256:8a1307f27e7714b19688d239bf837988a46a99afd4c219579c311a5b9f66d7af","observation_id":"6a6d456a-52a9-470e-8d0d-1a06b2efc266","resolution":{"observed_at":"2026-08-11T22:16:02.210587Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T22:16:02.198326Z","title":"Cluster algebra structures on module categories over quantum aﬃne algebras","venue":null,"work_id":"1c825a29-c5f6-4af7-a51d-54257afb0f9f","year":2022},"citing_paper":{"arxiv_id":"2412.03750","last_updated":"2025-02-03T18:44:35Z","snapshot_observed_at":"2026-08-15T02:30:19.775240Z","submitted_at":"2024-12-04T22:40:39Z","title":"Alternating snake modules and a determinantal formula","version":2},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-11T22:16:01.925926Z"},"links":{"citing_paper":"/paper/2412.03750"},"observation_digest":"sha256:26a590d9e96ffdeec830a0b4556a3c3b157df9fd0f9ba3d25fd6e2ae400298f4","observation_id":"3d3b0fdd-7b43-4e0a-889c-a68b8792c2f9","resolution":{"observed_at":"2026-08-11T22:16:02.201519Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T22:16:02.189644Z","title":"Monoidal categoriﬁcation and quantum aﬃne algebras II","venue":null,"work_id":"5a52de6f-dcfb-4033-a8f3-b2d65130b2ca","year":2024},"citing_paper":{"arxiv_id":"2412.03750","last_updated":"2025-02-03T18:44:35Z","snapshot_observed_at":"2026-08-15T02:30:19.775240Z","submitted_at":"2024-12-04T22:40:39Z","title":"Alternating snake modules and a determinantal formula","version":2},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-11T22:16:01.929067Z"},"links":{"citing_paper":"/paper/2412.03750"},"observation_digest":"sha256:8e7ec204597bc004e21935da4be553f55c593f8c952014815ee0f1c1c3b1f072","observation_id":"0afe16ea-cb61-4016-a91b-c1eddb85ce87","resolution":{"observed_at":"2026-08-11T22:16:02.192819Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T22:16:02.180933Z","title":"Pbw theory for quantum aﬃne algebras","venue":null,"work_id":"f26a4255-7b64-41aa-bbc7-e9763bf0654e","year":2024},"citing_paper":{"arxiv_id":"2412.03750","last_updated":"2025-02-03T18:44:35Z","snapshot_observed_at":"2026-08-15T02:30:19.775240Z","submitted_at":"2024-12-04T22:40:39Z","title":"Alternating snake modules and a determinantal formula","version":2},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-11T22:16:01.932232Z"},"links":{"citing_paper":"/paper/2412.03750"},"observation_digest":"sha256:a5126154e036216d032e82a12c9dac3ddab5a01e8e52e7a9404e28902b814b22","observation_id":"867ddd36-c57d-4954-a879-00c3267886d6","resolution":{"observed_at":"2026-08-11T22:16:02.183928Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T22:16:02.172304Z","title":"On a determinantal formula of Tadi´ c.American Journal of Mathematics , 136:111–142, 12 2014","venue":null,"work_id":"8feac355-1e27-405a-9c1f-e6dc04906948","year":2014},"citing_paper":{"arxiv_id":"2412.03750","last_updated":"2025-02-03T18:44:35Z","snapshot_observed_at":"2026-08-15T02:30:19.775240Z","submitted_at":"2024-12-04T22:40:39Z","title":"Alternating snake modules and a determinantal formula","version":2},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-11T22:16:01.935379Z"},"links":{"citing_paper":"/paper/2412.03750"},"observation_digest":"sha256:826a0397ded3c8774d9569e0d5572627340fa94b3edc6301c79fd1c024f8ee49","observation_id":"34baefd8-0416-4912-86e4-af35c0a95bf3","resolution":{"observed_at":"2026-08-11T22:16:02.175559Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T22:16:02.163733Z","title":"Geometric conditions for □ -irreducibility of certain representations of the general linear group over a non-archimedean local ﬁeld","venue":null,"work_id":"c0a5120f-b40b-4d3e-b6d6-e6d98bf6df06","year":2018},"citing_paper":{"arxiv_id":"2412.03750","last_updated":"2025-02-03T18:44:35Z","snapshot_observed_at":"2026-08-15T02:30:19.775240Z","submitted_at":"2024-12-04T22:40:39Z","title":"Alternating snake modules and a determinantal formula","version":2},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-11T22:16:01.938570Z"},"links":{"citing_paper":"/paper/2412.03750"},"observation_digest":"sha256:90061eef25476bae21f62c0733b4ddf6b67c4b90a0f5b916cc2352c04947173b","observation_id":"2bb0c173-08e3-4a90-afb7-156ff3ed5922","resolution":{"observed_at":"2026-08-11T22:16:02.166913Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T22:16:02.154099Z","title":"Aﬃne Hecke algebras and their graded ve rsion","venue":null,"work_id":"52fbf9f1-2723-4ecc-a4ac-ff4971398285","year":1989},"citing_paper":{"arxiv_id":"2412.03750","last_updated":"2025-02-03T18:44:35Z","snapshot_observed_at":"2026-08-15T02:30:19.775240Z","submitted_at":"2024-12-04T22:40:39Z","title":"Alternating snake modules and a determinantal formula","version":2},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-11T22:16:01.941686Z"},"links":{"citing_paper":"/paper/2412.03750"},"observation_digest":"sha256:ca145b8e7274d40949ae02c30950a5b17a50245e89d3359f20e3dc7747b7f3ef","observation_id":"bfbb0079-8d77-4261-ab92-2173e2bc1746","resolution":{"observed_at":"2026-08-11T22:16:02.157715Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T22:16:02.145201Z","title":"On the primality of tot ally ordered q-factorization graphs","venue":null,"work_id":"882606c1-514a-4fed-920c-87acddfabfc2","year":2024},"citing_paper":{"arxiv_id":"2412.03750","last_updated":"2025-02-03T18:44:35Z","snapshot_observed_at":"2026-08-15T02:30:19.775240Z","submitted_at":"2024-12-04T22:40:39Z","title":"Alternating snake modules and a determinantal formula","version":2},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-11T22:16:01.944748Z"},"links":{"citing_paper":"/paper/2412.03750"},"observation_digest":"sha256:1e24e0042f876c969fcb593af68c8af0e0e963180ac4bed066645eb4cca1545c","observation_id":"a2162fe3-8625-4088-9f95-bea6d5928b97","resolution":{"observed_at":"2026-08-11T22:16:02.148764Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T22:16:02.136276Z","title":null,"venue":null,"work_id":"bb41f15b-0dab-410d-b597-9039905f63c8","year":2012},"citing_paper":{"arxiv_id":"2412.03750","last_updated":"2025-02-03T18:44:35Z","snapshot_observed_at":"2026-08-15T02:30:19.775240Z","submitted_at":"2024-12-04T22:40:39Z","title":"Alternating snake modules and a determinantal formula","version":2},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-11T22:16:01.948365Z"},"links":{"citing_paper":"/paper/2412.03750"},"observation_digest":"sha256:148bf7c9722115fcc5095a6a29c0ae94a5216187019577494eb0ea925141854f","observation_id":"0f0b39d6-364f-40f4-aaef-1cfa868c2897","resolution":{"observed_at":"2026-08-11T22:16:02.139523Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T22:16:02.127480Z","title":null,"venue":null,"work_id":"f192564c-001a-4396-98fa-1a25dc0847b9","year":2012},"citing_paper":{"arxiv_id":"2412.03750","last_updated":"2025-02-03T18:44:35Z","snapshot_observed_at":"2026-08-15T02:30:19.775240Z","submitted_at":"2024-12-04T22:40:39Z","title":"Alternating snake modules and a determinantal formula","version":2},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-11T22:16:01.951272Z"},"links":{"citing_paper":"/paper/2412.03750"},"observation_digest":"sha256:77de9d8c483051cb58eb65299f3d9daebceadfddd3fadef1e799e402fd00ae8f","observation_id":"7c3804bc-0b5a-4a6a-9e3d-823640f3cb54","resolution":{"observed_at":"2026-08-11T22:16:02.130579Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T22:16:02.117680Z","title":"Strong duality data of type A and extend ed T-systems","venue":null,"work_id":"f05dd1c6-1c49-451c-a52b-757beaa809fa","year":2024},"citing_paper":{"arxiv_id":"2412.03750","last_updated":"2025-02-03T18:44:35Z","snapshot_observed_at":"2026-08-15T02:30:19.775240Z","submitted_at":"2024-12-04T22:40:39Z","title":"Alternating snake modules and a determinantal formula","version":2},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-11T22:16:01.954115Z"},"links":{"citing_paper":"/paper/2412.03750"},"observation_digest":"sha256:e421f730045c76feee4d8a99d2b06552ca4108e782da3e1ea57122be7f379c62","observation_id":"24855057-cffd-4bde-9907-e5349fbc5bcc","resolution":{"observed_at":"2026-08-11T22:16:02.121423Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T22:16:02.108207Z","title":"Triangular bases in quantum cluster algebras a nd monoidal categoriﬁcation conjectures","venue":null,"work_id":"46cf4912-2eb3-4d96-b128-2168301ceb95","year":2017},"citing_paper":{"arxiv_id":"2412.03750","last_updated":"2025-02-03T18:44:35Z","snapshot_observed_at":"2026-08-15T02:30:19.775240Z","submitted_at":"2024-12-04T22:40:39Z","title":"Alternating snake modules and a determinantal formula","version":2},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-11T22:16:01.957369Z"},"links":{"citing_paper":"/paper/2412.03750"},"observation_digest":"sha256:58e788380363e5981bd1cb0ceca9b29c7a3ea09b701b3b765ab9b96b2fe0dc87","observation_id":"4d9023e1-7557-4d31-9fa0-26c2701680b4","resolution":{"observed_at":"2026-08-11T22:16:02.111510Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T22:16:02.098729Z","title":"On characters of irreducible unitary rep resentations of general linear groups","venue":null,"work_id":"acc1f8f9-63e2-4fed-b2ad-0b346d690047","year":1995},"citing_paper":{"arxiv_id":"2412.03750","last_updated":"2025-02-03T18:44:35Z","snapshot_observed_at":"2026-08-15T02:30:19.775240Z","submitted_at":"2024-12-04T22:40:39Z","title":"Alternating snake modules and a determinantal formula","version":2},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-11T22:16:01.960177Z"},"links":{"citing_paper":"/paper/2412.03750"},"observation_digest":"sha256:ef8297502be93c1a9bdbec38b05ea5a95385d28a61539e153a3828fa24ed3c1e","observation_id":"69f31a75-ed88-4f3e-9058-75af1ea01154","resolution":{"observed_at":"2026-08-11T22:16:02.102256Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T22:16:02.088675Z","title":"Standard modules of quantum aﬃne algebras","venue":null,"work_id":"1d90040c-9f46-4243-a345-09ffb34df5e4","year":2002},"citing_paper":{"arxiv_id":"2412.03750","last_updated":"2025-02-03T18:44:35Z","snapshot_observed_at":"2026-08-15T02:30:19.775240Z","submitted_at":"2024-12-04T22:40:39Z","title":"Alternating snake modules and a determinantal formula","version":2},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-11T22:16:01.963841Z"},"links":{"citing_paper":"/paper/2412.03750"},"observation_digest":"sha256:7893f2be435ef835421559db25d72b779643ea13f22d873640d52209c78f87ff","observation_id":"b3e2c2cb-0ce7-43b9-9953-b11dcaac2991","resolution":{"observed_at":"2026-08-11T22:16:02.092061Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T22:16:02.078302Z","title":"Quantum groups and ﬂag varieties","venue":null,"work_id":"3bc2870b-d8ac-412f-b27e-7e9eb7d10aac","year":1992},"citing_paper":{"arxiv_id":"2412.03750","last_updated":"2025-02-03T18:44:35Z","snapshot_observed_at":"2026-08-15T02:30:19.775240Z","submitted_at":"2024-12-04T22:40:39Z","title":"Alternating snake modules and a determinantal formula","version":2},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-11T22:16:01.966754Z"},"links":{"citing_paper":"/paper/2412.03750"},"observation_digest":"sha256:7189c7f515db1fa1089528d4a2d1b43c5315309c8822ea9680382493adb5e706","observation_id":"02e02e48-0014-4f08-9c16-fba72f58e896","resolution":{"observed_at":"2026-08-11T22:16:02.081652Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2412.03750","last_updated":"2025-02-03T18:44:35Z","latest_version":2,"primary_category":"math.RT","snapshot_observed_at":"2026-08-15T02:30:19.775240Z","submitted_at":"2024-12-04T22:40:39Z","title":"Alternating snake modules and a determinantal formula"},"reference_resolution":{"displayed":37,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":3,"verified_exact":1,"verified_fuzzy":33},"total_outbound_references":37},"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":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"thesis":"As of 18 August 2026, this Paper Citation Record lists 37 of 37 outbound references and 1 inbound Pith citation observation for arXiv:2412.03750."}