{"as_of":"2026-08-19T16:41:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:c2511e359e422458269b6eb959408a70f64a1e766c724b7662c03f6212bc83ca","coverage":[{"denominator":20,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":20,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-16T05:15:28.669546Z","state":"measured"},{"denominator":20,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":20,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-19T06:32:44.657259+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/2504.21180/citation-record","integrity":"/paper/2504.21180/integrity","json":"/paper/2504.21180/citation-record.json","paper":"/paper/2504.21180"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T05:15:28.842712Z","title":"Four-Dimensional N ilpotent Diassociative Algebras Journal of Generalized Lie Theory and Applications, V ol","venue":null,"work_id":"75d0de77-6705-45cc-91d5-e676b1fe0a61","year":2015},"citing_paper":{"arxiv_id":"2504.21180","last_updated":"2025-04-29T21:14:19Z","snapshot_observed_at":"2026-08-19T02:46:21.761726Z","submitted_at":"2025-04-29T21:14:19Z","title":"Derivations, Centroids and Iner-Derivations of $\\textbf{5}$-Dimensional Nilpotent Complex Associative Algebras","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-16T05:15:28.549599Z"},"links":{"citing_paper":"/paper/2504.21180"},"observation_digest":"sha256:c70fdc57c01b32cf7d6bac126c570c9c3dc501cc10785e4287fbd5e76e865ce0","observation_id":"98951f53-e49b-4d14-8616-d64f9de46026","resolution":{"observed_at":"2026-08-16T05:15:28.845799Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-16T05:15:28.834663Z","title":"´El´ ements de math´ ematiques, Alg` ebre, Hermann ( (1959))","venue":null,"work_id":"c3a8d30c-5792-490e-9437-f4fc60629282","year":1959},"citing_paper":{"arxiv_id":"2504.21180","last_updated":"2025-04-29T21:14:19Z","snapshot_observed_at":"2026-08-19T02:46:21.761726Z","submitted_at":"2025-04-29T21:14:19Z","title":"Derivations, Centroids and Iner-Derivations of $\\textbf{5}$-Dimensional Nilpotent Complex Associative Algebras","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-16T05:15:28.553441Z"},"links":{"citing_paper":"/paper/2504.21180"},"observation_digest":"sha256:f4e8151d4484ac8f2ba2fe7e5eaf097fdf7acb99620907d96beaf0dc596404ab","observation_id":"aa86de02-e2c3-464c-b93d-6c653f3d2ae9","resolution":{"observed_at":"2026-08-16T05:15:28.837606Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-16T05:15:28.826834Z","title":null,"venue":null,"work_id":"49cdce2e-9a3f-477c-8adc-94494fb16166","year":2017},"citing_paper":{"arxiv_id":"2504.21180","last_updated":"2025-04-29T21:14:19Z","snapshot_observed_at":"2026-08-19T02:46:21.761726Z","submitted_at":"2025-04-29T21:14:19Z","title":"Derivations, Centroids and Iner-Derivations of $\\textbf{5}$-Dimensional Nilpotent Complex Associative Algebras","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-16T05:15:28.556673Z"},"links":{"citing_paper":"/paper/2504.21180"},"observation_digest":"sha256:695d7d69b08849d4c38d781fd3af94e116a6f074593493081c3a256adcce2eb5","observation_id":"6aabed08-30c0-4f7d-9cc5-bbccb25537dd","resolution":{"observed_at":"2026-08-16T05:15:28.829667Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-16T05:15:28.818549Z","title":"Indecomposable representations","venue":null,"work_id":"b18305b7-8e07-4a04-9d0e-13e40f74f5e9","year":1974},"citing_paper":{"arxiv_id":"2504.21180","last_updated":"2025-04-29T21:14:19Z","snapshot_observed_at":"2026-08-19T02:46:21.761726Z","submitted_at":"2025-04-29T21:14:19Z","title":"Derivations, Centroids and Iner-Derivations of $\\textbf{5}$-Dimensional Nilpotent Complex Associative Algebras","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-16T05:15:28.559654Z"},"links":{"citing_paper":"/paper/2504.21180"},"observation_digest":"sha256:ad5cb3aff77729ebeea3c68ca7be1f1fd0a7a763177432706da9152c807512da","observation_id":"a9c862ea-e3cb-4443-85c9-e309a99de8fd","resolution":{"observed_at":"2026-08-16T05:15:28.821283Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-16T05:15:28.810911Z","title":null,"venue":null,"work_id":"b87dcadf-471b-4e81-97d8-2e04a40c8635","year":1964},"citing_paper":{"arxiv_id":"2504.21180","last_updated":"2025-04-29T21:14:19Z","snapshot_observed_at":"2026-08-19T02:46:21.761726Z","submitted_at":"2025-04-29T21:14:19Z","title":"Derivations, Centroids and Iner-Derivations of $\\textbf{5}$-Dimensional Nilpotent Complex Associative Algebras","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-16T05:15:28.562647Z"},"links":{"citing_paper":"/paper/2504.21180"},"observation_digest":"sha256:fe02ad741b3e858cd7fd4d9f091cafa84c37c40311736e1d24b67928d76f6dbf","observation_id":"aec27755-b6aa-4eb8-826b-a159c7041150","resolution":{"observed_at":"2026-08-16T05:15:28.813709Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-16T05:15:28.802323Z","title":"and Khakimdjanov Y","venue":null,"work_id":"b535fa6f-9001-4a18-8a14-f49a2aec73ad","year":1996},"citing_paper":{"arxiv_id":"2504.21180","last_updated":"2025-04-29T21:14:19Z","snapshot_observed_at":"2026-08-19T02:46:21.761726Z","submitted_at":"2025-04-29T21:14:19Z","title":"Derivations, Centroids and Iner-Derivations of $\\textbf{5}$-Dimensional Nilpotent Complex Associative Algebras","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-16T05:15:28.565612Z"},"links":{"citing_paper":"/paper/2504.21180"},"observation_digest":"sha256:1c7dae68a1b6591e63cc918bd4c559858a0057b720832c11cc4d4e6c188908fb","observation_id":"3d3df211-5b23-4793-bd7d-885c70f79200","resolution":{"observed_at":"2026-08-16T05:15:28.805541Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-16T05:15:28.794482Z","title":"A, lassiﬁcation of nilpotent associative alge bras of small dimension, C","venue":null,"work_id":"037a4b08-9880-4fad-9527-c49d7aac8d9d","year":2007},"citing_paper":{"arxiv_id":"2504.21180","last_updated":"2025-04-29T21:14:19Z","snapshot_observed_at":"2026-08-19T02:46:21.761726Z","submitted_at":"2025-04-29T21:14:19Z","title":"Derivations, Centroids and Iner-Derivations of $\\textbf{5}$-Dimensional Nilpotent Complex Associative Algebras","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-16T05:15:28.568524Z"},"links":{"citing_paper":"/paper/2504.21180"},"observation_digest":"sha256:9b5c9567f3f5d69a471c8249a4b19b25bf9c12ed41c5c31bdaef3da51b9760bb","observation_id":"395b470e-b4d7-402e-9b70-9c25adea8128","resolution":{"observed_at":"2026-08-16T05:15:28.797388Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-16T05:15:28.786758Z","title":null,"venue":null,"work_id":"e6d5f526-f676-4e6c-a2ba-5fa90837db26","year":1990},"citing_paper":{"arxiv_id":"2504.21180","last_updated":"2025-04-29T21:14:19Z","snapshot_observed_at":"2026-08-19T02:46:21.761726Z","submitted_at":"2025-04-29T21:14:19Z","title":"Derivations, Centroids and Iner-Derivations of $\\textbf{5}$-Dimensional Nilpotent Complex Associative Algebras","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-16T05:15:28.571278Z"},"links":{"citing_paper":"/paper/2504.21180"},"observation_digest":"sha256:8a12736b350e4fa2dd352331e210ce5aed0d9eee704068699de8a24f910e9486","observation_id":"1919867f-a3db-44e2-bfe1-df32afe2882a","resolution":{"observed_at":"2026-08-16T05:15:28.789555Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-16T05:15:28.778542Z","title":"The g eometric classiﬁcation of 2-step nilpotent algebras and ap plica- tions.Linear and Multilinear Algebra, 70(8), 1553–1570","venue":null,"work_id":"cbab1c9b-1081-477c-8e82-45ccf7dc1774","year":2022},"citing_paper":{"arxiv_id":"2504.21180","last_updated":"2025-04-29T21:14:19Z","snapshot_observed_at":"2026-08-19T02:46:21.761726Z","submitted_at":"2025-04-29T21:14:19Z","title":"Derivations, Centroids and Iner-Derivations of $\\textbf{5}$-Dimensional Nilpotent Complex Associative Algebras","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-16T05:15:28.573940Z"},"links":{"citing_paper":"/paper/2504.21180"},"observation_digest":"sha256:4c40c9bc18755305e9a8f2d3bc6045a2c56911a26995d86021ac62695dc7efe7","observation_id":"ea2554ca-0bdb-411f-8dca-97a2e2ec492d","resolution":{"observed_at":"2026-08-16T05:15:28.781637Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2303.01905","last_updated":"2025-05-20T11:42:46Z","snapshot_observed_at":"2026-08-16T15:51:03.707194Z","submitted_at":"2023-03-03T13:05:43Z","title":"Classification of five-dimensional symmetric Leibniz algebras","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2303.01905","snapshot_observed_at":"2026-08-16T05:15:28.576611Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2504.21180","last_updated":"2025-04-29T21:14:19Z","snapshot_observed_at":"2026-08-19T02:46:21.761726Z","submitted_at":"2025-04-29T21:14:19Z","title":"Derivations, Centroids and Iner-Derivations of $\\textbf{5}$-Dimensional Nilpotent Complex Associative Algebras","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-16T05:15:28.576611Z"},"links":{"cited_paper":"/paper/2303.01905","citing_paper":"/paper/2504.21180"},"observation_digest":"sha256:b267c444a7df6263b50f6d349f8811b67d63a677ff0416a5a38f16cf53e04e83","observation_id":"e203e9a3-2515-4771-bd02-de557fce6f35","resolution":{"observed_at":"2026-08-16T05:15:28.576611Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T05:15:28.770725Z","title":"Lie algebras","venue":null,"work_id":"f67d720f-1d9a-46f6-810b-7828bd23c3b3","year":1962},"citing_paper":{"arxiv_id":"2504.21180","last_updated":"2025-04-29T21:14:19Z","snapshot_observed_at":"2026-08-19T02:46:21.761726Z","submitted_at":"2025-04-29T21:14:19Z","title":"Derivations, Centroids and Iner-Derivations of $\\textbf{5}$-Dimensional Nilpotent Complex Associative Algebras","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-16T05:15:28.579798Z"},"links":{"citing_paper":"/paper/2504.21180"},"observation_digest":"sha256:172c17e6a315cef6442993b578ed7f86d95adf9789491ac0aa25acd3b3f2ba9a","observation_id":"e028af49-3af6-4e84-9a35-01edbc6f45f7","resolution":{"observed_at":"2026-08-16T05:15:28.773465Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-16T05:15:28.762768Z","title":null,"venue":null,"work_id":"6c23464c-4080-4c0f-ae36-fee2491f3ed0","year":1980},"citing_paper":{"arxiv_id":"2504.21180","last_updated":"2025-04-29T21:14:19Z","snapshot_observed_at":"2026-08-19T02:46:21.761726Z","submitted_at":"2025-04-29T21:14:19Z","title":"Derivations, Centroids and Iner-Derivations of $\\textbf{5}$-Dimensional Nilpotent Complex Associative Algebras","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-16T05:15:28.582374Z"},"links":{"citing_paper":"/paper/2504.21180"},"observation_digest":"sha256:78e3d8331b2fd67bdcb02ac085147e8aa3e1aa61dbd9df9a2c4ae6c611d5c9ad","observation_id":"0300e960-f59d-4a94-92bc-53d3feaaf382","resolution":{"observed_at":"2026-08-16T05:15:28.765597Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-16T05:15:28.753760Z","title":"In Paul Dubreil and Marie-Paule Malliavin Algebra Seminar (pp","venue":null,"work_id":"14ee7476-6ea5-4fa7-a82b-f7815032d3f4","year":1979},"citing_paper":{"arxiv_id":"2504.21180","last_updated":"2025-04-29T21:14:19Z","snapshot_observed_at":"2026-08-19T02:46:21.761726Z","submitted_at":"2025-04-29T21:14:19Z","title":"Derivations, Centroids and Iner-Derivations of $\\textbf{5}$-Dimensional Nilpotent Complex Associative Algebras","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-16T05:15:28.649896Z"},"links":{"citing_paper":"/paper/2504.21180"},"observation_digest":"sha256:ace176804e1a7d6e8ea8de4bcf1a6a3ad5458326de030395eaac83eed861ef13","observation_id":"74ede6e6-3d4c-409c-bb04-1aefcbf62876","resolution":{"observed_at":"2026-08-16T05:15:28.757524Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-16T05:15:28.653090Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2504.21180","last_updated":"2025-04-29T21:14:19Z","snapshot_observed_at":"2026-08-19T02:46:21.761726Z","submitted_at":"2025-04-29T21:14:19Z","title":"Derivations, Centroids and Iner-Derivations of $\\textbf{5}$-Dimensional Nilpotent Complex Associative Algebras","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-16T05:15:28.653090Z"},"links":{"citing_paper":"/paper/2504.21180"},"observation_digest":"sha256:115115e7ec47846ea97f4314ce34f150e9ab2cd0e4f0d95a652dd8ab260c1f32","observation_id":"b2a14732-a433-4caf-ab6c-86bf849d5a5c","resolution":{"observed_at":"2026-08-16T05:15:28.653090Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T05:15:28.745338Z","title":null,"venue":null,"work_id":"60de4280-079a-475e-b421-e20e4fcbaa70","year":2020},"citing_paper":{"arxiv_id":"2504.21180","last_updated":"2025-04-29T21:14:19Z","snapshot_observed_at":"2026-08-19T02:46:21.761726Z","submitted_at":"2025-04-29T21:14:19Z","title":"Derivations, Centroids and Iner-Derivations of $\\textbf{5}$-Dimensional Nilpotent Complex Associative Algebras","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-16T05:15:28.656065Z"},"links":{"citing_paper":"/paper/2504.21180"},"observation_digest":"sha256:a3936b8c2e6d08bd7b09751fd2eed20f75b93c7ca1c3d1ba249ea37083714071","observation_id":"43f920ad-cf96-47e6-bfec-0b67a5941e72","resolution":{"observed_at":"2026-08-16T05:15:28.748239Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-16T05:15:28.735667Z","title":"The algebraic and geomeric classiﬁcation o f associative algebras of dimension ﬁve, Mathematica, V ol","venue":null,"work_id":"8d84ac9b-0821-4abe-b528-4ab9de8f91ae","year":1979},"citing_paper":{"arxiv_id":"2504.21180","last_updated":"2025-04-29T21:14:19Z","snapshot_observed_at":"2026-08-19T02:46:21.761726Z","submitted_at":"2025-04-29T21:14:19Z","title":"Derivations, Centroids and Iner-Derivations of $\\textbf{5}$-Dimensional Nilpotent Complex Associative Algebras","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-16T05:15:28.658727Z"},"links":{"citing_paper":"/paper/2504.21180"},"observation_digest":"sha256:1fe47d77c5e00b57f8948e6ecb369ac35c77e5eb90579208206f36131defc6f9","observation_id":"30a5bf25-1669-43de-9df2-773358c65049","resolution":{"observed_at":"2026-08-16T05:15:28.739445Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-16T05:15:28.727234Z","title":null,"venue":null,"work_id":"ca172416-e20d-4599-8240-20a86f0fcfe3","year":1966},"citing_paper":{"arxiv_id":"2504.21180","last_updated":"2025-04-29T21:14:19Z","snapshot_observed_at":"2026-08-19T02:46:21.761726Z","submitted_at":"2025-04-29T21:14:19Z","title":"Derivations, Centroids and Iner-Derivations of $\\textbf{5}$-Dimensional Nilpotent Complex Associative Algebras","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-16T05:15:28.661487Z"},"links":{"citing_paper":"/paper/2504.21180"},"observation_digest":"sha256:2c31d7ea40d8263bb87bd73f826f0b35ba050bc9c888f5c2f6fb4bf9b66005e0","observation_id":"cbae817e-fd46-4b7f-84e4-388d95316306","resolution":{"observed_at":"2026-08-16T05:15:28.730127Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-16T05:15:28.718835Z","title":null,"venue":null,"work_id":"516486ea-f292-485b-b65d-401a0c32c46f","year":null},"citing_paper":{"arxiv_id":"2504.21180","last_updated":"2025-04-29T21:14:19Z","snapshot_observed_at":"2026-08-19T02:46:21.761726Z","submitted_at":"2025-04-29T21:14:19Z","title":"Derivations, Centroids and Iner-Derivations of $\\textbf{5}$-Dimensional Nilpotent Complex Associative Algebras","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-16T05:15:28.664154Z"},"links":{"citing_paper":"/paper/2504.21180"},"observation_digest":"sha256:8014b960da81d7ba32a695c6bccfc3db8b6f8092abe36390d132f5aa1feb207d","observation_id":"a554738f-73c6-455b-becf-a19ed2d63f35","resolution":{"observed_at":"2026-08-16T05:15:28.721621Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-16T05:15:28.709957Z","title":null,"venue":null,"work_id":"9f677e35-57ee-469c-af64-f99fb8516ce4","year":1966},"citing_paper":{"arxiv_id":"2504.21180","last_updated":"2025-04-29T21:14:19Z","snapshot_observed_at":"2026-08-19T02:46:21.761726Z","submitted_at":"2025-04-29T21:14:19Z","title":"Derivations, Centroids and Iner-Derivations of $\\textbf{5}$-Dimensional Nilpotent Complex Associative Algebras","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-16T05:15:28.666862Z"},"links":{"citing_paper":"/paper/2504.21180"},"observation_digest":"sha256:b6c07484bfc278132b01f3c878b39afc552acbc2871f672511230b95d539e3d9","observation_id":"cbdf1ee1-98bb-4019-ab3d-0508b4ce8af9","resolution":{"observed_at":"2026-08-16T05:15:28.712899Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-16T05:15:28.700421Z","title":null,"venue":null,"work_id":"adff6aad-5491-44b0-b04a-7910aaafefb9","year":2023},"citing_paper":{"arxiv_id":"2504.21180","last_updated":"2025-04-29T21:14:19Z","snapshot_observed_at":"2026-08-19T02:46:21.761726Z","submitted_at":"2025-04-29T21:14:19Z","title":"Derivations, Centroids and Iner-Derivations of $\\textbf{5}$-Dimensional Nilpotent Complex Associative Algebras","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-16T05:15:28.669546Z"},"links":{"citing_paper":"/paper/2504.21180"},"observation_digest":"sha256:4ec0ffea188977371eb7d1b2fe163729c36ef0e2c5ff7058e41e506e5f52ecf3","observation_id":"f294aebc-97b8-4c5a-be16-e4d8e52090e1","resolution":{"observed_at":"2026-08-16T05:15:28.704255Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2504.21180","last_updated":"2025-04-29T21:14:19Z","latest_version":1,"primary_category":"math.RA","snapshot_observed_at":"2026-08-19T02:46:21.761726Z","submitted_at":"2025-04-29T21:14:19Z","title":"Derivations, Centroids and Iner-Derivations of $\\textbf{5}$-Dimensional Nilpotent Complex Associative Algebras"},"reference_resolution":{"displayed":20,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":11,"verified_exact":0,"verified_fuzzy":9},"total_outbound_references":20},"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":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"thesis":"As of 19 August 2026, this Paper Citation Record lists 20 of 20 outbound references and 0 inbound Pith citation observations for arXiv:2504.21180."}