{"as_of":"2026-08-08T03:43:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:68e1b6638e007cfdc4a2ee131cc61c7d74a0933d1d3455db66d65658867086a2","coverage":[{"denominator":33,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":33,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T00:30:57.805433Z","state":"measured"},{"denominator":34,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":34,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-07T06:34:17.273281+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":"2026-05-10T17:51:57.020010Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"arxiv_reference","source_observed_at":"2026-05-11T05:56:00.103056Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2506.14216","last_updated":"2025-06-17T06:12:13Z","snapshot_observed_at":"2026-08-07T00:15:53.703301Z","submitted_at":"2025-06-17T06:12:13Z","title":"Associative Pentagon Algebras","version":1},"cited_work":{"arxiv_id":"2506.14216","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2506.14216","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Mazzotta and A","venue":null,"work_id":"7d0df872-9258-4684-ae83-90f991960db0","year":2025},"citing_paper":{"arxiv_id":"2604.07231","last_updated":"2026-05-27T11:09:22Z","snapshot_observed_at":"2026-07-13T08:34:35.825322Z","submitted_at":"2026-04-08T15:54:50Z","title":"Multicomponent pentagon maps","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-05-10T17:51:57.020010Z"},"links":{"cited_paper":"/paper/2506.14216","citing_paper":"/paper/2604.07231"},"observation_digest":"sha256:7770105ab8284b4048c61c4ddbb3b5e790f9521233505911469438dc55b73f3b","observation_id":"d4a31e3c-df75-443b-8cff-50871d9b834a","resolution":{"observed_at":"2026-05-11T05:56:00.105875Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2506.14216/citation-record","integrity":"/paper/2506.14216/integrity","json":"/paper/2506.14216/citation-record.json","paper":"/paper/2506.14216"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s40687-025-00513-x","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T00:30:58.100287Z","title":"Agore, A","venue":null,"work_id":"cc40d732-dbcd-45b5-b0c2-8deebd9395e0","year":2025},"citing_paper":{"arxiv_id":"2506.14216","last_updated":"2025-06-17T06:12:13Z","snapshot_observed_at":"2026-08-07T00:15:53.703301Z","submitted_at":"2025-06-17T06:12:13Z","title":"Associative Pentagon Algebras","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-07T00:30:53.972296Z"},"links":{"citing_paper":"/paper/2506.14216"},"observation_digest":"sha256:964f337d265116cf18580bc9d244202a6599e7df34345725d4d44f0db901fd9d","observation_id":"b9f3e952-f0ef-4d55-9b9c-661f98892172","resolution":{"observed_at":"2026-08-07T00:30:58.107679Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T00:30:58.509953Z","title":null,"venue":null,"work_id":"fad9e7fe-7a72-4b05-9d8c-8fc1a9565fae","year":1993},"citing_paper":{"arxiv_id":"2506.14216","last_updated":"2025-06-17T06:12:13Z","snapshot_observed_at":"2026-08-07T00:15:53.703301Z","submitted_at":"2025-06-17T06:12:13Z","title":"Associative Pentagon Algebras","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-07T00:30:54.071417Z"},"links":{"citing_paper":"/paper/2506.14216"},"observation_digest":"sha256:2776eda60991a40ed67fbbb4a4b3b418b52ec1a1f988886ca21cbd01a4549453","observation_id":"ce1351ec-923c-4bbb-9cae-590d552344cb","resolution":{"observed_at":"2026-08-07T00:30:58.513484Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/s0764-4442(99)80090-1","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T00:30:58.083149Z","title":null,"venue":null,"work_id":"b1f7cfe6-67c0-4072-bd1a-2de6b99de35f","year":1998},"citing_paper":{"arxiv_id":"2506.14216","last_updated":"2025-06-17T06:12:13Z","snapshot_observed_at":"2026-08-07T00:15:53.703301Z","submitted_at":"2025-06-17T06:12:13Z","title":"Associative Pentagon Algebras","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-07T00:30:54.097507Z"},"links":{"citing_paper":"/paper/2506.14216"},"observation_digest":"sha256:8fdf9b4ed12b9e675a8d14a8d909cf298d162aa6c65a7f9a9e9948f2840eb61d","observation_id":"729c77a1-0548-45a9-8570-77577628bf5f","resolution":{"observed_at":"2026-08-07T00:30:58.089597Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T00:30:58.498646Z","title":null,"venue":null,"work_id":"29c4ce48-4d2c-47b9-b621-34762996e04e","year":1953},"citing_paper":{"arxiv_id":"2506.14216","last_updated":"2025-06-17T06:12:13Z","snapshot_observed_at":"2026-08-07T00:15:53.703301Z","submitted_at":"2025-06-17T06:12:13Z","title":"Associative Pentagon Algebras","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-07T00:30:54.151442Z"},"links":{"citing_paper":"/paper/2506.14216"},"observation_digest":"sha256:bfb23a3f752d79974d292093d4282816a1365e1efe6957e86d5c3eecb747493c","observation_id":"62efca26-bb9b-41eb-9196-1a38b546065c","resolution":{"observed_at":"2026-08-07T00:30:58.502898Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2404.13758","last_updated":"2024-04-21T19:51:40Z","snapshot_observed_at":"2026-07-06T18:03:24.368197Z","submitted_at":"2024-04-21T19:51:40Z","title":"On commutative set-theoretic solutions of the Pentagon Equation","version":1},"cited_work":{"arxiv_id":"2404.13758","doi":null,"metadata_source":"pith","pith_arxiv_id":"2404.13758","snapshot_observed_at":"2026-08-07T00:30:58.407922Z","title":"On commutative set-theoretic solutions of the Pentagon Equation","venue":"math.QA","work_id":"7f35a10b-9d60-429f-baf3-3378ef3b05d7","year":2024},"citing_paper":{"arxiv_id":"2506.14216","last_updated":"2025-06-17T06:12:13Z","snapshot_observed_at":"2026-08-07T00:15:53.703301Z","submitted_at":"2025-06-17T06:12:13Z","title":"Associative Pentagon Algebras","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-07T00:30:54.299567Z"},"links":{"cited_paper":"/paper/2404.13758","citing_paper":"/paper/2506.14216"},"observation_digest":"sha256:07689d2eae15948aac1ecbd414d7a78eb2bbef656a12c11f329f243eddc3458d","observation_id":"67f66ef5-8933-440b-bf6b-45636a3a252b","resolution":{"observed_at":"2026-08-07T00:30:58.412434Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T00:30:54.394666Z","title":"Catino, M","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2506.14216","last_updated":"2025-06-17T06:12:13Z","snapshot_observed_at":"2026-08-07T00:15:53.703301Z","submitted_at":"2025-06-17T06:12:13Z","title":"Associative Pentagon Algebras","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-07T00:30:54.394666Z"},"links":{"citing_paper":"/paper/2506.14216"},"observation_digest":"sha256:94bb3696ecd638b68f297a5f07dda8285e82a9f1548328f4ae0f149041869b93","observation_id":"3f5812c8-430a-42c0-a17d-31f3fa80e870","resolution":{"observed_at":"2026-08-07T00:30:54.394666Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s00233-020-10100-x","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T00:30:58.060827Z","title":"Catino, M","venue":null,"work_id":"ebb17bab-709c-426f-adec-728ceecb3b63","year":2020},"citing_paper":{"arxiv_id":"2506.14216","last_updated":"2025-06-17T06:12:13Z","snapshot_observed_at":"2026-08-07T00:15:53.703301Z","submitted_at":"2025-06-17T06:12:13Z","title":"Associative Pentagon Algebras","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-07T00:30:54.489679Z"},"links":{"citing_paper":"/paper/2506.14216"},"observation_digest":"sha256:50eb374177b4841f9176172336391760733e8d7566cc8a27874381468fbaf02c","observation_id":"b0ab315b-2318-4b75-9802-91c5463d90a7","resolution":{"observed_at":"2026-08-07T00:30:58.070981Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s00220-020-03862-6","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T00:30:58.042258Z","title":"Colazzo, E","venue":null,"work_id":"d7e1a6b8-6909-47e1-be57-e7cc27e50069","year":2020},"citing_paper":{"arxiv_id":"2506.14216","last_updated":"2025-06-17T06:12:13Z","snapshot_observed_at":"2026-08-07T00:15:53.703301Z","submitted_at":"2025-06-17T06:12:13Z","title":"Associative Pentagon Algebras","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-07T00:30:54.598179Z"},"links":{"citing_paper":"/paper/2506.14216"},"observation_digest":"sha256:637b04da2e4ca948feb652f07524d94db82562ba0b6145005eb91a77054e1c97","observation_id":"4ced3408-ba56-410a-af87-57feb41d5263","resolution":{"observed_at":"2026-08-07T00:30:58.048998Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2405.20406","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T00:30:58.298993Z","title":"Colazzo, J","venue":null,"work_id":"8a96686e-0705-488c-9f4a-7133bc502c66","year":2024},"citing_paper":{"arxiv_id":"2506.14216","last_updated":"2025-06-17T06:12:13Z","snapshot_observed_at":"2026-08-07T00:15:53.703301Z","submitted_at":"2025-06-17T06:12:13Z","title":"Associative Pentagon Algebras","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-07T00:30:54.692159Z"},"links":{"citing_paper":"/paper/2506.14216"},"observation_digest":"sha256:6c5308c2024153c367cdd25a4511fcae64781316198cf565f8bf8309c6a8d1d7","observation_id":"ca7270d4-8be4-4f60-bd26-e89aaba489cc","resolution":{"observed_at":"2026-08-07T00:30:58.305454Z","resolver_source":"raw_fallback","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.3842/sigma.2015.042","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T00:30:58.025398Z","title":"Dimakis, F","venue":null,"work_id":"840d4263-60af-4046-bfc9-bf575406d534","year":2015},"citing_paper":{"arxiv_id":"2506.14216","last_updated":"2025-06-17T06:12:13Z","snapshot_observed_at":"2026-08-07T00:15:53.703301Z","submitted_at":"2025-06-17T06:12:13Z","title":"Associative Pentagon Algebras","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-07T00:30:54.816842Z"},"links":{"citing_paper":"/paper/2506.14216"},"observation_digest":"sha256:c04b38a34ebfd8aa172ffa570ca46191710d4c02d274fb9252b9e0f5b1a2c70e","observation_id":"3b67ce78-1502-4e66-85b0-ad02fe71dd9d","resolution":{"observed_at":"2026-08-07T00:30:58.031552Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1063/1.4882285","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T00:30:57.998140Z","title":"Doliwa, S","venue":null,"work_id":"faf03ed6-bab0-4e12-ab48-80b08159b260","year":2014},"citing_paper":{"arxiv_id":"2506.14216","last_updated":"2025-06-17T06:12:13Z","snapshot_observed_at":"2026-08-07T00:15:53.703301Z","submitted_at":"2025-06-17T06:12:13Z","title":"Associative Pentagon Algebras","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-07T00:30:55.004346Z"},"links":{"citing_paper":"/paper/2506.14216"},"observation_digest":"sha256:6933e829a58ae32afe4f6c337336b801493d01004fec5dec2506500415b31883","observation_id":"3cc38bec-3d67-4386-8fd4-0d9795b6fbd3","resolution":{"observed_at":"2026-08-07T00:30:58.010959Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T00:30:58.488818Z","title":null,"venue":null,"work_id":"854d7edc-d1c5-46ac-ba64-dba1d39a529b","year":1989},"citing_paper":{"arxiv_id":"2506.14216","last_updated":"2025-06-17T06:12:13Z","snapshot_observed_at":"2026-08-07T00:15:53.703301Z","submitted_at":"2025-06-17T06:12:13Z","title":"Associative Pentagon Algebras","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-07T00:30:55.146839Z"},"links":{"citing_paper":"/paper/2506.14216"},"observation_digest":"sha256:db8b2cf6e4e188cc03c41ab11e9daad44dd6631f8c636f9edb2769218517acf8","observation_id":"bd7eee53-1b02-4bef-9c83-558f57e67b2c","resolution":{"observed_at":"2026-08-07T00:30:58.492039Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T00:30:55.335795Z","title":null,"venue":null,"work_id":null,"year":1990},"citing_paper":{"arxiv_id":"2506.14216","last_updated":"2025-06-17T06:12:13Z","snapshot_observed_at":"2026-08-07T00:15:53.703301Z","submitted_at":"2025-06-17T06:12:13Z","title":"Associative Pentagon Algebras","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-07T00:30:55.335795Z"},"links":{"citing_paper":"/paper/2506.14216"},"observation_digest":"sha256:d17887e60deab9093e5dc7c6c020c4aded64d9264d758f8c3e4846a7d04e6dc4","observation_id":"00da12e7-ef86-417f-bc65-4e45c2aa0125","resolution":{"observed_at":"2026-08-07T00:30:55.335795Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1088/1751-8121/ad85b1","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T00:30:57.971849Z","title":"Evripidou, P","venue":null,"work_id":"3ff80aeb-4a3a-4be4-9624-bd053c4ecbd9","year":2024},"citing_paper":{"arxiv_id":"2506.14216","last_updated":"2025-06-17T06:12:13Z","snapshot_observed_at":"2026-08-07T00:15:53.703301Z","submitted_at":"2025-06-17T06:12:13Z","title":"Associative Pentagon Algebras","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-07T00:30:55.502623Z"},"links":{"citing_paper":"/paper/2506.14216"},"observation_digest":"sha256:6419f67736370bf4776ca8431612fbc128f86e56bbc6c023ff50c6cfa8ecb548","observation_id":"154f917a-d575-4b4c-ac6b-cc4c103df7e9","resolution":{"observed_at":"2026-08-07T00:30:57.978114Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T00:30:58.478665Z","title":"Jiang, M","venue":null,"work_id":"49e7233a-1da2-41cb-8633-eed36b564852","year":2005},"citing_paper":{"arxiv_id":"2506.14216","last_updated":"2025-06-17T06:12:13Z","snapshot_observed_at":"2026-08-07T00:15:53.703301Z","submitted_at":"2025-06-17T06:12:13Z","title":"Associative Pentagon Algebras","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-07T00:30:55.592696Z"},"links":{"citing_paper":"/paper/2506.14216"},"observation_digest":"sha256:1c04346841078df1c5ad210e28530f995f2fb8c3f8fbee2f9b0cb638d457e2da","observation_id":"0a602f76-64e7-42b2-b104-c91b62529824","resolution":{"observed_at":"2026-08-07T00:30:58.482535Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T00:30:58.466833Z","title":"Kashaev, Fully noncommutative discrete Liouville equation, in: Infinite analysis 2010– Developments in quantum integrable systems, RIMS Kôkyûroku Bessatsu, B28, Res","venue":null,"work_id":"6da714c3-22d4-4f5d-a58c-41908e57cfdd","year":2010},"citing_paper":{"arxiv_id":"2506.14216","last_updated":"2025-06-17T06:12:13Z","snapshot_observed_at":"2026-08-07T00:15:53.703301Z","submitted_at":"2025-06-17T06:12:13Z","title":"Associative Pentagon Algebras","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-07T00:30:55.749768Z"},"links":{"citing_paper":"/paper/2506.14216"},"observation_digest":"sha256:14b3fd493b3aa9315b56167ee5076c8a92ef864c85a2b31b79ef5a5cb4aaaa8e","observation_id":"e64c3013-8948-4e82-833b-ca5827a3a304","resolution":{"observed_at":"2026-08-07T00:30:58.470884Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1090/conm/433/08330","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T00:30:57.959724Z","title":null,"venue":null,"work_id":"b49daf9b-b7b0-4b97-b371-17b3ffff39a5","year":2007},"citing_paper":{"arxiv_id":"2506.14216","last_updated":"2025-06-17T06:12:13Z","snapshot_observed_at":"2026-08-07T00:15:53.703301Z","submitted_at":"2025-06-17T06:12:13Z","title":"Associative Pentagon Algebras","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-07T00:30:55.840787Z"},"links":{"citing_paper":"/paper/2506.14216"},"observation_digest":"sha256:4783c3728046120673c179c324ee415051b1129046b973cb926d805dd9b4a8fe","observation_id":"4ff79aff-d81b-440a-9cbb-76c1a26945f8","resolution":{"observed_at":"2026-08-07T00:30:57.963684Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s002200050391","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T00:30:57.948852Z","title":null,"venue":null,"work_id":"0ce3781f-1059-4a09-9615-e741e36c97e8","year":1998},"citing_paper":{"arxiv_id":"2506.14216","last_updated":"2025-06-17T06:12:13Z","snapshot_observed_at":"2026-08-07T00:15:53.703301Z","submitted_at":"2025-06-17T06:12:13Z","title":"Associative Pentagon Algebras","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-07T00:30:55.981740Z"},"links":{"citing_paper":"/paper/2506.14216"},"observation_digest":"sha256:32b02abc89095109008cc87a0313f1b34fd67f1dc11aeb5aaceee9692e8c06bd","observation_id":"f1bff4d0-0084-4e68-975b-6c70fa4f4ae5","resolution":{"observed_at":"2026-08-07T00:30:57.952502Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T00:30:58.456284Z","title":"Kassotakis, Matrix factorizations and pentagon maps, Proc","venue":null,"work_id":"1d978d45-6e9c-462b-bc53-26f324613f99","year":2023},"citing_paper":{"arxiv_id":"2506.14216","last_updated":"2025-06-17T06:12:13Z","snapshot_observed_at":"2026-08-07T00:15:53.703301Z","submitted_at":"2025-06-17T06:12:13Z","title":"Associative Pentagon Algebras","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-07T00:30:56.092207Z"},"links":{"citing_paper":"/paper/2506.14216"},"observation_digest":"sha256:ef7a2258707c805bf1a21bb0b50b8626d9d5f9628bf45934d31cbf3ede219364","observation_id":"d2e5f89a-0321-49d9-b5af-e9ea101a2722","resolution":{"observed_at":"2026-08-07T00:30:58.459918Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s11005-010-0413-5","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T00:30:57.936731Z","title":"Kawamura, Pentagon equation arising from state equations of a C*-Bialgebra, Lett","venue":null,"work_id":"75bc7403-9512-431d-841e-7ab57265921a","year":2010},"citing_paper":{"arxiv_id":"2506.14216","last_updated":"2025-06-17T06:12:13Z","snapshot_observed_at":"2026-08-07T00:15:53.703301Z","submitted_at":"2025-06-17T06:12:13Z","title":"Associative Pentagon Algebras","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-07T00:30:56.271932Z"},"links":{"citing_paper":"/paper/2506.14216"},"observation_digest":"sha256:bb84f8a597bb941a8e2cb0d416dfac597d4160f9ed062ec8da55b6535c6abf21","observation_id":"2ec7da73-795c-44d5-9a5b-9c01964f7aec","resolution":{"observed_at":"2026-08-07T00:30:57.940882Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T00:30:58.445442Z","title":"Kimura, The structure of idempotent semigroups I, Pacific J","venue":null,"work_id":"01523486-2a54-4cb4-9921-f6a5361c7b0a","year":1958},"citing_paper":{"arxiv_id":"2506.14216","last_updated":"2025-06-17T06:12:13Z","snapshot_observed_at":"2026-08-07T00:15:53.703301Z","submitted_at":"2025-06-17T06:12:13Z","title":"Associative Pentagon Algebras","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-07T00:30:56.568171Z"},"links":{"citing_paper":"/paper/2506.14216"},"observation_digest":"sha256:a9c77c74afef9dac1bc19946c705c22001915c16b9486097d9b06088b010bcef","observation_id":"92716fe5-6ef4-4f96-aa5a-b03a416b1148","resolution":{"observed_at":"2026-08-07T00:30:58.449794Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2402.16682","last_updated":"2024-02-26T16:01:22Z","snapshot_observed_at":"2026-08-07T09:28:35.669766Z","submitted_at":"2024-02-26T16:01:22Z","title":"Pentagon relation and Biedenharn-Elliott identity","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2402.16682","snapshot_observed_at":"2026-08-07T00:30:56.837870Z","title":"Korablev, Pentagon relation and Biedenharn-Elliott identity, preprint arXiv:2402.16682","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2506.14216","last_updated":"2025-06-17T06:12:13Z","snapshot_observed_at":"2026-08-07T00:15:53.703301Z","submitted_at":"2025-06-17T06:12:13Z","title":"Associative Pentagon Algebras","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-07T00:30:56.837870Z"},"links":{"cited_paper":"/paper/2402.16682","citing_paper":"/paper/2506.14216"},"observation_digest":"sha256:096bb0df9980e4d02e8e92dd5ff2d77fcdad1545a9e8872c2c9941927edcb46c","observation_id":"37197b3b-614b-4b61-8ae6-5dd3a3254e02","resolution":{"observed_at":"2026-08-07T00:30:56.837870Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/0920-5632(91)90136-3","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T00:30:57.926810Z","title":"Maillet, Integrable systems and gauge theories, Nuclear Phys","venue":null,"work_id":"9196e106-4e09-45fc-afb9-1a49dbc5db55","year":1990},"citing_paper":{"arxiv_id":"2506.14216","last_updated":"2025-06-17T06:12:13Z","snapshot_observed_at":"2026-08-07T00:15:53.703301Z","submitted_at":"2025-06-17T06:12:13Z","title":"Associative Pentagon Algebras","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-07T00:30:57.004941Z"},"links":{"citing_paper":"/paper/2506.14216"},"observation_digest":"sha256:fc24c77b0d944c7a50ffe63f0c340ab672a1bde209c4eb4daf9046b23b45b966","observation_id":"b396e89c-c67a-48bf-8b35-e5deed496666","resolution":{"observed_at":"2026-08-07T00:30:57.929679Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s40574-023-00382-8","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T00:30:57.916218Z","title":"Mazzotta, Idempotent set-theoretical solutions of the pentagon equation, Boll","venue":null,"work_id":"3c671840-4ac4-49ae-81cc-81ee83cdb26b","year":2024},"citing_paper":{"arxiv_id":"2506.14216","last_updated":"2025-06-17T06:12:13Z","snapshot_observed_at":"2026-08-07T00:15:53.703301Z","submitted_at":"2025-06-17T06:12:13Z","title":"Associative Pentagon Algebras","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-07T00:30:57.171439Z"},"links":{"citing_paper":"/paper/2506.14216"},"observation_digest":"sha256:9cf5b95a2d61506930d74413adf8c88ff8ffd393ded77e450ebd3b2310bfc76b","observation_id":"27b88a18-c63d-4baa-ad58-ac9d3f8abf92","resolution":{"observed_at":"2026-08-07T00:30:57.919899Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T00:30:58.432853Z","title":"Mazzotta, Set-theoretical solutions to the pentagon equation: a survey, Commun","venue":null,"work_id":"e646ff2c-5c85-442d-9208-85c3b49041e0","year":2025},"citing_paper":{"arxiv_id":"2506.14216","last_updated":"2025-06-17T06:12:13Z","snapshot_observed_at":"2026-08-07T00:15:53.703301Z","submitted_at":"2025-06-17T06:12:13Z","title":"Associative Pentagon Algebras","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-07T00:30:57.280488Z"},"links":{"citing_paper":"/paper/2506.14216"},"observation_digest":"sha256:b978ae6920a117e3f3565e75876668a91cd7e0ffb776d15faaf00414d10eeb1d","observation_id":"6a1b8ff5-57e9-4fdf-9105-d7bd1c48c2b7","resolution":{"observed_at":"2026-08-07T00:30:58.437822Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s00233-024-10421-1","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T00:30:57.903320Z","title":"Mazzotta, V","venue":null,"work_id":"ca2bc70e-6f51-4006-a0e1-46a9eabc1694","year":2024},"citing_paper":{"arxiv_id":"2506.14216","last_updated":"2025-06-17T06:12:13Z","snapshot_observed_at":"2026-08-07T00:15:53.703301Z","submitted_at":"2025-06-17T06:12:13Z","title":"Associative Pentagon Algebras","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-07T00:30:57.361663Z"},"links":{"citing_paper":"/paper/2506.14216"},"observation_digest":"sha256:5104e5802f5f268e2040c0e67923c60fab089efb7dc72e27c045424bcd83a9a4","observation_id":"65da927e-c841-46f6-8873-04758cd9ff45","resolution":{"observed_at":"2026-08-07T00:30:57.908097Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1080/00927879808826329","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T00:30:57.891291Z","title":"Militaru, The Hopf modules category and the Hopf equation, Comm","venue":null,"work_id":"5bd43ef9-e817-41e7-a8e1-cb118fbce373","year":1998},"citing_paper":{"arxiv_id":"2506.14216","last_updated":"2025-06-17T06:12:13Z","snapshot_observed_at":"2026-08-07T00:15:53.703301Z","submitted_at":"2025-06-17T06:12:13Z","title":"Associative Pentagon Algebras","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-07T00:30:57.509708Z"},"links":{"citing_paper":"/paper/2506.14216"},"observation_digest":"sha256:525b16f7261e587ea0f1f5cce16e5fcec4f7be6bcb852b32319b876bd1f32481","observation_id":"3337e7b4-e585-40b5-904e-543d713002f5","resolution":{"observed_at":"2026-08-07T00:30:57.894731Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1112/s0024610703004897","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T00:30:57.880606Z","title":"Militaru, Heisenberg Double, Pentagon Equation, Structure and Classification of Finite- Dimensional Hopf Algebras, J","venue":null,"work_id":"eef0702b-0d40-442f-8678-1845e42525b3","year":2004},"citing_paper":{"arxiv_id":"2506.14216","last_updated":"2025-06-17T06:12:13Z","snapshot_observed_at":"2026-08-07T00:15:53.703301Z","submitted_at":"2025-06-17T06:12:13Z","title":"Associative Pentagon Algebras","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-07T00:30:57.600896Z"},"links":{"citing_paper":"/paper/2506.14216"},"observation_digest":"sha256:8ad9d492c6bc46189b36af66a85793c643e4e710df90b52091481f0969cfb225","observation_id":"dc1d7ac3-c448-4327-bf00-90affb084a21","resolution":{"observed_at":"2026-08-07T00:30:57.884125Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T00:30:57.663077Z","title":"Moore, N","venue":null,"work_id":null,"year":1989},"citing_paper":{"arxiv_id":"2506.14216","last_updated":"2025-06-17T06:12:13Z","snapshot_observed_at":"2026-08-07T00:15:53.703301Z","submitted_at":"2025-06-17T06:12:13Z","title":"Associative Pentagon Algebras","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-07T00:30:57.663077Z"},"links":{"citing_paper":"/paper/2506.14216"},"observation_digest":"sha256:8e7cc5f411a60ca65c3eb89bb35faccfec141b149c8af8b6a8d9b9c2b889fef4","observation_id":"2e354468-c661-4431-bc39-5bf1af0e4ee8","resolution":{"observed_at":"2026-08-07T00:30:57.663077Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.3842/sigma.2024.051","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T00:30:57.868667Z","title":"Müller-Hoissen, On the structure of set-theoretic polygon equations, SIGMA Symmetry Integrability Geom","venue":null,"work_id":"8b9fc46d-9d52-463a-8d4f-022ab6442383","year":2024},"citing_paper":{"arxiv_id":"2506.14216","last_updated":"2025-06-17T06:12:13Z","snapshot_observed_at":"2026-08-07T00:15:53.703301Z","submitted_at":"2025-06-17T06:12:13Z","title":"Associative Pentagon Algebras","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-07T00:30:57.742048Z"},"links":{"citing_paper":"/paper/2506.14216"},"observation_digest":"sha256:869001ffcfea25781ba35fc0bab71d942be6e52793470aeb5e07ec83079df9a5","observation_id":"c8f559e6-a5cf-4440-a6c0-76aa6eaee194","resolution":{"observed_at":"2026-08-07T00:30:57.872639Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1142/s0129167x96000086","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T00:30:57.857844Z","title":null,"venue":null,"work_id":"286217d3-2723-4a87-99d0-c0dfd60e9059","year":1996},"citing_paper":{"arxiv_id":"2506.14216","last_updated":"2025-06-17T06:12:13Z","snapshot_observed_at":"2026-08-07T00:15:53.703301Z","submitted_at":"2025-06-17T06:12:13Z","title":"Associative Pentagon Algebras","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-07T00:30:57.747776Z"},"links":{"citing_paper":"/paper/2506.14216"},"observation_digest":"sha256:06a6b871beafb2c49089bfac839567b19c993263559e2721989782b182624d7c","observation_id":"68a2404b-df54-4de4-97f2-7920476a08e3","resolution":{"observed_at":"2026-08-07T00:30:57.861487Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T00:30:58.420962Z","title":"Yamada, Exclusive semigroups, J","venue":null,"work_id":"2af81051-c979-4d96-9025-31a8b617ce7b","year":1973},"citing_paper":{"arxiv_id":"2506.14216","last_updated":"2025-06-17T06:12:13Z","snapshot_observed_at":"2026-08-07T00:15:53.703301Z","submitted_at":"2025-06-17T06:12:13Z","title":"Associative Pentagon Algebras","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-07T00:30:57.784632Z"},"links":{"citing_paper":"/paper/2506.14216"},"observation_digest":"sha256:37f9cdb8cf735f37360a0c03ce842b92bbcb85ffeb9748ce5a356e048fd2ed2a","observation_id":"fb798103-02da-4a79-922c-2196bdbdafc2","resolution":{"observed_at":"2026-08-07T00:30:58.424561Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/bf00429998","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T00:30:57.843948Z","title":"Zakrzewski, Poisson Lie groups and pentagonal transformations, Lett","venue":null,"work_id":"5001669f-4851-428d-bc60-8872add4deb6","year":1992},"citing_paper":{"arxiv_id":"2506.14216","last_updated":"2025-06-17T06:12:13Z","snapshot_observed_at":"2026-08-07T00:15:53.703301Z","submitted_at":"2025-06-17T06:12:13Z","title":"Associative Pentagon Algebras","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-07T00:30:57.805433Z"},"links":{"citing_paper":"/paper/2506.14216"},"observation_digest":"sha256:b5a8abde977a8dfbebde6a4605767420bb1202df4535e4c59a1236c25053d718","observation_id":"fbc2f41a-19d0-4fde-95c4-e160b4df8838","resolution":{"observed_at":"2026-08-07T00:30:57.849470Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2506.14216","last_updated":"2025-06-17T06:12:13Z","latest_version":1,"primary_category":"math.RA","snapshot_observed_at":"2026-08-07T00:15:53.703301Z","submitted_at":"2025-06-17T06:12:13Z","title":"Associative Pentagon Algebras"},"reference_resolution":{"displayed":33,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":7,"verified_exact":20,"verified_fuzzy":6},"total_outbound_references":33},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"thesis":"As of 8 August 2026, this Paper Citation Record lists 33 of 33 outbound references and 1 inbound Pith citation observation for arXiv:2506.14216."}