{"as_of":"2026-08-18T07:21:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:86ee74045d87fc05971bfbd649948b74fa17d24c91a299b62e5c31c7e2c45326","coverage":[{"denominator":26,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":26,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-16T04:34:09.418664Z","state":"measured"},{"denominator":28,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":28,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-18T06:34:40.430872+00:00","state":"measured"},{"denominator":2,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":2,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T11:30:36.357282Z","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":"2026-07-02T00:46:23.573283Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2505.01173","last_updated":"2025-07-28T06:04:45Z","snapshot_observed_at":"2026-08-16T04:22:14.207185Z","submitted_at":"2025-05-02T10:31:01Z","title":"Dual canonical bases and embeddings of symmetric spaces","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2505.01173","snapshot_observed_at":"2026-08-07T11:30:36.357282Z","title":"Certains schémas de groupes semi-simples","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2506.02638","last_updated":"2025-06-03T08:53:56Z","snapshot_observed_at":"2026-08-14T04:57:39.246719Z","submitted_at":"2025-06-03T08:53:56Z","title":"Toroidal embedding of Chevalley groups over $\\mathbb{Z}$","version":1},"reference_index":2025,"source":"pdf_text","source_observed_at":"2026-08-07T11:30:36.357282Z"},"links":{"cited_paper":"/paper/2505.01173","citing_paper":"/paper/2506.02638"},"observation_digest":"sha256:9abb05e87505eba310d62784ab4cebdb8f98dba6e64a8e0e9f6f432457b99720","observation_id":"5cc64439-7485-4af0-9485-173aa2a43658","resolution":{"observed_at":"2026-08-07T11:30:36.357282Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2505.01173","last_updated":"2025-07-28T06:04:45Z","snapshot_observed_at":"2026-08-16T04:22:14.207185Z","submitted_at":"2025-05-02T10:31:01Z","title":"Dual canonical bases and embeddings of symmetric spaces","version":2},"cited_work":{"arxiv_id":"2505.01173","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2505.01173","snapshot_observed_at":"2026-07-02T00:46:23.573283Z","title":"Dual canonical bases and embeddings of symmetric spaces","venue":null,"work_id":"e2193249-aa45-4731-ac51-aa66379ec174","year":2025},"citing_paper":{"arxiv_id":"2607.00322","last_updated":"2026-07-01T01:42:53Z","snapshot_observed_at":"2026-08-10T11:28:10.219237Z","submitted_at":"2026-07-01T01:42:53Z","title":"Reductive monoids over general base","version":1},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-07-02T00:41:51.151546Z"},"links":{"cited_paper":"/paper/2505.01173","citing_paper":"/paper/2607.00322"},"observation_digest":"sha256:981a7889dc8c05c527cc3aebc636f88a1af01d438247bbdb7b50c46a1887926b","observation_id":"d8f2baf7-0c8c-40aa-869a-f4d86c6c90d8","resolution":{"observed_at":"2026-07-02T00:46:23.575275Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2505.01173/citation-record","integrity":"/paper/2505.01173/integrity","json":"/paper/2505.01173/citation-record.json","paper":"/paper/2505.01173"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T04:34:09.116321Z","title":null,"venue":null,"work_id":null,"year":1986},"citing_paper":{"arxiv_id":"2505.01173","last_updated":"2025-07-28T06:04:45Z","snapshot_observed_at":"2026-08-16T04:22:14.207185Z","submitted_at":"2025-05-02T10:31:01Z","title":"Dual canonical bases and embeddings of symmetric spaces","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-16T04:34:09.116321Z"},"links":{"citing_paper":"/paper/2505.01173"},"observation_digest":"sha256:d3006cd5f6254d6008d4713dceaa04828a88de7039fd8d4496d05fdf18793f4b","observation_id":"4e0957de-5fcd-4fcf-9b22-0babff3b94ab","resolution":{"observed_at":"2026-08-16T04:34:09.116321Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2212.13426","last_updated":"2022-12-27T09:42:08Z","snapshot_observed_at":"2026-08-16T16:05:51.678803Z","submitted_at":"2022-12-27T09:42:08Z","title":"Symmetric subgroup schemes, Frobenius splittings, and quantum symmetric pairs","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2212.13426","snapshot_observed_at":"2026-08-16T04:34:09.127364Z","title":null,"venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2505.01173","last_updated":"2025-07-28T06:04:45Z","snapshot_observed_at":"2026-08-16T04:22:14.207185Z","submitted_at":"2025-05-02T10:31:01Z","title":"Dual canonical bases and embeddings of symmetric spaces","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-16T04:34:09.127364Z"},"links":{"cited_paper":"/paper/2212.13426","citing_paper":"/paper/2505.01173"},"observation_digest":"sha256:9e24822a1b9096565e835d55fad6d446a4f1dd98c134583add9a209a393384d4","observation_id":"0816686a-9560-421f-8127-0678b8ef2a19","resolution":{"observed_at":"2026-08-16T04:34:09.127364Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2402.08258","last_updated":"2024-02-13T07:17:21Z","snapshot_observed_at":"2026-08-16T14:19:05.857726Z","submitted_at":"2024-02-13T07:17:21Z","title":"Coordinate rings on symmetric spaces","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2402.08258","snapshot_observed_at":"2026-08-16T04:34:09.142562Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2505.01173","last_updated":"2025-07-28T06:04:45Z","snapshot_observed_at":"2026-08-16T04:22:14.207185Z","submitted_at":"2025-05-02T10:31:01Z","title":"Dual canonical bases and embeddings of symmetric spaces","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-16T04:34:09.142562Z"},"links":{"cited_paper":"/paper/2402.08258","citing_paper":"/paper/2505.01173"},"observation_digest":"sha256:5d8bf36dee384d9d516daa414c31bd0ec48bb9da360195b3630322f0130691b5","observation_id":"a995b9a7-7454-4395-8f00-48c5ebc1fd9e","resolution":{"observed_at":"2026-08-16T04:34:09.142562Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T04:34:09.154055Z","title":null,"venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2505.01173","last_updated":"2025-07-28T06:04:45Z","snapshot_observed_at":"2026-08-16T04:22:14.207185Z","submitted_at":"2025-05-02T10:31:01Z","title":"Dual canonical bases and embeddings of symmetric spaces","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-16T04:34:09.154055Z"},"links":{"citing_paper":"/paper/2505.01173"},"observation_digest":"sha256:976b6105ac72fc5056992e4d3ceb02000c1107c690b06813176984985b680deb","observation_id":"dfc94f75-7f64-45cb-9c07-7c56e7fa472c","resolution":{"observed_at":"2026-08-16T04:34:09.154055Z","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":"2026-08-16T04:34:10.709111Z","title":"Cox, John B","venue":null,"work_id":"9bac5463-9928-425b-913a-f04ff1a6761e","year":2011},"citing_paper":{"arxiv_id":"2505.01173","last_updated":"2025-07-28T06:04:45Z","snapshot_observed_at":"2026-08-16T04:22:14.207185Z","submitted_at":"2025-05-02T10:31:01Z","title":"Dual canonical bases and embeddings of symmetric spaces","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-16T04:34:09.163957Z"},"links":{"citing_paper":"/paper/2505.01173"},"observation_digest":"sha256:166f139d2b86e816ed469fdccc016fccecf8904135059c375ce8f95476f7391d","observation_id":"8a7c0a47-b102-4643-8c5d-af97bbebb965","resolution":{"observed_at":"2026-08-16T04:34:10.719425Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-16T04:34:10.668165Z","title":"Mumford, J","venue":null,"work_id":"f2f9c600-4cf6-49eb-ac24-3f83500b5da3","year":1994},"citing_paper":{"arxiv_id":"2505.01173","last_updated":"2025-07-28T06:04:45Z","snapshot_observed_at":"2026-08-16T04:22:14.207185Z","submitted_at":"2025-05-02T10:31:01Z","title":"Dual canonical bases and embeddings of symmetric spaces","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-16T04:34:09.174643Z"},"links":{"citing_paper":"/paper/2505.01173"},"observation_digest":"sha256:aca49690646083fd08f280f3dd17d24e9e023f528c48b802d5bcfbf45f6a6fff","observation_id":"3e83d857-f52f-46d8-ba96-2dd00f22f495","resolution":{"observed_at":"2026-08-16T04:34:10.677882Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-16T04:34:09.185524Z","title":"De Concini and C","venue":null,"work_id":null,"year":1982},"citing_paper":{"arxiv_id":"2505.01173","last_updated":"2025-07-28T06:04:45Z","snapshot_observed_at":"2026-08-16T04:22:14.207185Z","submitted_at":"2025-05-02T10:31:01Z","title":"Dual canonical bases and embeddings of symmetric spaces","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-16T04:34:09.185524Z"},"links":{"citing_paper":"/paper/2505.01173"},"observation_digest":"sha256:fe42031aa096cba55bc3b895bd6aa2637ff15ae808b6267cc4bf9c8595a7f89b","observation_id":"7cb9c317-3563-4777-9816-af4c61b7030a","resolution":{"observed_at":"2026-08-16T04:34:09.185524Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T04:34:09.198529Z","title":"De Concini and T","venue":null,"work_id":null,"year":1999},"citing_paper":{"arxiv_id":"2505.01173","last_updated":"2025-07-28T06:04:45Z","snapshot_observed_at":"2026-08-16T04:22:14.207185Z","submitted_at":"2025-05-02T10:31:01Z","title":"Dual canonical bases and embeddings of symmetric spaces","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-16T04:34:09.198529Z"},"links":{"citing_paper":"/paper/2505.01173"},"observation_digest":"sha256:22759c997ff8d6eda6ed742c3d35c32cdb41614a9403aa8212bc4655c73cbdde","observation_id":"dbe3bbbd-94b3-4d9b-972d-267894cd999b","resolution":{"observed_at":"2026-08-16T04:34:09.198529Z","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/s10114-018-7162-2","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T04:34:09.885936Z","title":null,"venue":null,"work_id":"81cd2122-376f-4e84-868f-b723c009bef6","year":2018},"citing_paper":{"arxiv_id":"2505.01173","last_updated":"2025-07-28T06:04:45Z","snapshot_observed_at":"2026-08-16T04:22:14.207185Z","submitted_at":"2025-05-02T10:31:01Z","title":"Dual canonical bases and embeddings of symmetric spaces","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-16T04:34:09.207337Z"},"links":{"citing_paper":"/paper/2505.01173"},"observation_digest":"sha256:9129a8ec451ff490ab7b00978b2c7c6332f036112754909fa93cff799a5c91e7","observation_id":"057ff585-ba79-4a16-8531-49559c89b222","resolution":{"observed_at":"2026-08-16T04:34:09.905174Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/bf01231884","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T04:34:09.826498Z","title":"Grosshans, Contractions of the actions of reductive algebraic groups in arbi- trary characteristic, Invent","venue":null,"work_id":"1df3715e-8da0-491a-93af-371929f55964","year":1992},"citing_paper":{"arxiv_id":"2505.01173","last_updated":"2025-07-28T06:04:45Z","snapshot_observed_at":"2026-08-16T04:22:14.207185Z","submitted_at":"2025-05-02T10:31:01Z","title":"Dual canonical bases and embeddings of symmetric spaces","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-16T04:34:09.218037Z"},"links":{"citing_paper":"/paper/2505.01173"},"observation_digest":"sha256:4302cfb8148884787e70f82cb6d25af836ce58fce0842dc5763090c61a3e97c0","observation_id":"acab446b-4bc6-4ae5-8b91-38d3dbf4e834","resolution":{"observed_at":"2026-08-16T04:34:09.835029Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/bf01237251","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T04:34:09.773686Z","title":"Groups 6 (2001), no","venue":null,"work_id":"34151564-c034-434c-ac1d-0f8f6dd006ca","year":2001},"citing_paper":{"arxiv_id":"2505.01173","last_updated":"2025-07-28T06:04:45Z","snapshot_observed_at":"2026-08-16T04:22:14.207185Z","submitted_at":"2025-05-02T10:31:01Z","title":"Dual canonical bases and embeddings of symmetric spaces","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-16T04:34:09.229496Z"},"links":{"citing_paper":"/paper/2505.01173"},"observation_digest":"sha256:ddc676bad95d306d14acd9a3d548465ecfced8930d133f90e17c8f255d38a91a","observation_id":"543d5af6-1659-4cf6-a0f7-a1d77d76d142","resolution":{"observed_at":"2026-08-16T04:34:09.787383Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-16T04:34:10.636226Z","title":null,"venue":null,"work_id":"1c6b3106-507d-424f-91c8-c18d85a1a35d","year":1977},"citing_paper":{"arxiv_id":"2505.01173","last_updated":"2025-07-28T06:04:45Z","snapshot_observed_at":"2026-08-16T04:22:14.207185Z","submitted_at":"2025-05-02T10:31:01Z","title":"Dual canonical bases and embeddings of symmetric spaces","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-16T04:34:09.235677Z"},"links":{"citing_paper":"/paper/2505.01173"},"observation_digest":"sha256:02c98b4a67134f19f12f5021aec30c844fad3ca213f98600977795548e483f54","observation_id":"f1d4b47e-1f1b-4931-832e-1c48cfa53cc3","resolution":{"observed_at":"2026-08-16T04:34:10.644970Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-16T04:34:10.588699Z","title":"Kac, Infinite-dimensional Lie algebras, 3rd ed., Cambridge University Press, Cam- bridge, 1990","venue":null,"work_id":"93f7022c-bfa0-4d57-8ea4-9b849250c19a","year":1990},"citing_paper":{"arxiv_id":"2505.01173","last_updated":"2025-07-28T06:04:45Z","snapshot_observed_at":"2026-08-16T04:22:14.207185Z","submitted_at":"2025-05-02T10:31:01Z","title":"Dual canonical bases and embeddings of symmetric spaces","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-16T04:34:09.245162Z"},"links":{"citing_paper":"/paper/2505.01173"},"observation_digest":"sha256:2e10050ba4dc9f9dc0b4fa7a01dcbedf710f1ab74d5cd155a6aa5ab139e0aaf7","observation_id":"734dcb8b-aa1a-4363-8fb2-00143e632536","resolution":{"observed_at":"2026-08-16T04:34:10.615345Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-16T04:34:10.536199Z","title":null,"venue":null,"work_id":"7e43ddb9-46e6-429f-b991-4de5be3264a1","year":1989},"citing_paper":{"arxiv_id":"2505.01173","last_updated":"2025-07-28T06:04:45Z","snapshot_observed_at":"2026-08-16T04:22:14.207185Z","submitted_at":"2025-05-02T10:31:01Z","title":"Dual canonical bases and embeddings of symmetric spaces","version":2},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-16T04:34:09.256516Z"},"links":{"citing_paper":"/paper/2505.01173"},"observation_digest":"sha256:f5dd5f29cce4fd8a274856969bb452818337f9e3cad1888879efed78c325ca9c","observation_id":"d54fe3a2-bd6b-49aa-ae28-28d6dc3b5a6f","resolution":{"observed_at":"2026-08-16T04:34:10.546368Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1090/s0894-0347-08-00603-6","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T04:34:09.729880Z","title":null,"venue":null,"work_id":"4e128b9f-f64a-467d-8a1b-c6681bcd4e6c","year":2009},"citing_paper":{"arxiv_id":"2505.01173","last_updated":"2025-07-28T06:04:45Z","snapshot_observed_at":"2026-08-16T04:22:14.207185Z","submitted_at":"2025-05-02T10:31:01Z","title":"Dual canonical bases and embeddings of symmetric spaces","version":2},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-16T04:34:09.267472Z"},"links":{"citing_paper":"/paper/2505.01173"},"observation_digest":"sha256:090bdcbe2c33e8945e5bdce8ef0c7e39c5651c1c6aeeb14aaa1fe2b6990c7475","observation_id":"f73c7df4-9a60-4e8d-9320-a98ca929b728","resolution":{"observed_at":"2026-08-16T04:34:09.758452Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-16T04:34:10.477193Z","title":"8, Cambridge University Press, Cambridge, 1989","venue":null,"work_id":"e9e9a5a9-7b0a-44db-9663-d9d579f508ff","year":1989},"citing_paper":{"arxiv_id":"2505.01173","last_updated":"2025-07-28T06:04:45Z","snapshot_observed_at":"2026-08-16T04:22:14.207185Z","submitted_at":"2025-05-02T10:31:01Z","title":"Dual canonical bases and embeddings of symmetric spaces","version":2},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-16T04:34:09.277759Z"},"links":{"citing_paper":"/paper/2505.01173"},"observation_digest":"sha256:75c8d7cecdb106de566c3ee726a4fb10cea5fb35c4ee30194d8778a40217d1ec","observation_id":"7c0429c2-bcc0-44c8-a69c-b7d9916e8274","resolution":{"observed_at":"2026-08-16T04:34:10.494674Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-16T04:34:09.293322Z","title":null,"venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2505.01173","last_updated":"2025-07-28T06:04:45Z","snapshot_observed_at":"2026-08-16T04:22:14.207185Z","submitted_at":"2025-05-02T10:31:01Z","title":"Dual canonical bases and embeddings of symmetric spaces","version":2},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-16T04:34:09.293322Z"},"links":{"citing_paper":"/paper/2505.01173"},"observation_digest":"sha256:6a50aa38a111e0df67eb185708fb60aec674eb6155bda854e4b7e9a92966f08d","observation_id":"e454bacd-ceaa-438d-9f56-c1c23abcad58","resolution":{"observed_at":"2026-08-16T04:34:09.293322Z","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":"10.5802/ccirm.3","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T04:34:09.643294Z","title":"6–10 avril 2009, 2010, pp","venue":null,"work_id":"d69d072a-7497-4ceb-b5ce-866b4000526e","year":2009},"citing_paper":{"arxiv_id":"2505.01173","last_updated":"2025-07-28T06:04:45Z","snapshot_observed_at":"2026-08-16T04:22:14.207185Z","submitted_at":"2025-05-02T10:31:01Z","title":"Dual canonical bases and embeddings of symmetric spaces","version":2},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-16T04:34:09.315758Z"},"links":{"citing_paper":"/paper/2505.01173"},"observation_digest":"sha256:64e10398b826066c95aa8cd8c24a2d0723c8c4b291150fd19688fd157af3ba84","observation_id":"a9336c8a-9294-482b-b9bc-2b6bf9913c6e","resolution":{"observed_at":"2026-08-16T04:34:09.652534Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-16T04:34:09.330213Z","title":"Rittatore, Algebraic monoids and group embeddings, Transform","venue":null,"work_id":null,"year":1998},"citing_paper":{"arxiv_id":"2505.01173","last_updated":"2025-07-28T06:04:45Z","snapshot_observed_at":"2026-08-16T04:22:14.207185Z","submitted_at":"2025-05-02T10:31:01Z","title":"Dual canonical bases and embeddings of symmetric spaces","version":2},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-16T04:34:09.330213Z"},"links":{"citing_paper":"/paper/2505.01173"},"observation_digest":"sha256:9ae44b158fefc6323973ae3418a42ecf3eaf1b7b5d6f568c35ae7984522e5632","observation_id":"5224f71e-3104-44b7-a675-259ef5debea8","resolution":{"observed_at":"2026-08-16T04:34:09.330213Z","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":"2026-08-16T04:34:10.424178Z","title":null,"venue":null,"work_id":"a9faa8ae-a0b0-4315-9dbd-e6aa680eb30c","year":1987},"citing_paper":{"arxiv_id":"2505.01173","last_updated":"2025-07-28T06:04:45Z","snapshot_observed_at":"2026-08-16T04:22:14.207185Z","submitted_at":"2025-05-02T10:31:01Z","title":"Dual canonical bases and embeddings of symmetric spaces","version":2},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-16T04:34:09.342343Z"},"links":{"citing_paper":"/paper/2505.01173"},"observation_digest":"sha256:6969abedc42038d8e5328aec0096b2bbe50045bc1c80e82162021c5735b9d654","observation_id":"2781a418-cab1-4c92-b4a3-94ec119cb3ab","resolution":{"observed_at":"2026-08-16T04:34:10.436650Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-16T04:34:10.376442Z","title":"MR3764130","venue":null,"work_id":"0fc527b8-7698-4ffa-b5bc-dfc0262128ed","year":2017},"citing_paper":{"arxiv_id":"2505.01173","last_updated":"2025-07-28T06:04:45Z","snapshot_observed_at":"2026-08-16T04:22:14.207185Z","submitted_at":"2025-05-02T10:31:01Z","title":"Dual canonical bases and embeddings of symmetric spaces","version":2},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-16T04:34:09.360921Z"},"links":{"citing_paper":"/paper/2505.01173"},"observation_digest":"sha256:c859a5d319546fa81b3d869d1a18ce12ef07eb1596aef2ccb1e073d44559ba98","observation_id":"4ae536e6-504e-498a-89bd-59a63053c547","resolution":{"observed_at":"2026-08-16T04:34:10.395497Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-16T04:34:10.335746Z","title":null,"venue":null,"work_id":"20e08bff-32cc-4e06-a559-1fbcd873315c","year":null},"citing_paper":{"arxiv_id":"2505.01173","last_updated":"2025-07-28T06:04:45Z","snapshot_observed_at":"2026-08-16T04:22:14.207185Z","submitted_at":"2025-05-02T10:31:01Z","title":"Dual canonical bases and embeddings of symmetric spaces","version":2},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-16T04:34:09.372664Z"},"links":{"citing_paper":"/paper/2505.01173"},"observation_digest":"sha256:16904c437df9bc13d400393fff90c0f22cf96b1cd8337bed1a89436544060148","observation_id":"9052d068-36e4-40f8-8689-552d4455ed0d","resolution":{"observed_at":"2026-08-16T04:34:10.343131Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s00209-017-1897-9","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T04:34:09.567888Z","title":null,"venue":null,"work_id":"1bc815cd-fb44-4646-9f6a-e8da19bd5ef9","year":2018},"citing_paper":{"arxiv_id":"2505.01173","last_updated":"2025-07-28T06:04:45Z","snapshot_observed_at":"2026-08-16T04:22:14.207185Z","submitted_at":"2025-05-02T10:31:01Z","title":"Dual canonical bases and embeddings of symmetric spaces","version":2},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-16T04:34:09.380694Z"},"links":{"citing_paper":"/paper/2505.01173"},"observation_digest":"sha256:f8a2ef5642c9717c54b018eeb99aa37bcb7e4263cde81c3f7d994c9467605e68","observation_id":"13985eaa-4c2b-445d-bdf1-103bb99fe0fc","resolution":{"observed_at":"2026-08-16T04:34:09.590254Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1090/trans2/169/10","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T04:34:09.492218Z","title":null,"venue":null,"work_id":"a48a3a52-eb77-41be-ad64-fb24778c0e49","year":1995},"citing_paper":{"arxiv_id":"2505.01173","last_updated":"2025-07-28T06:04:45Z","snapshot_observed_at":"2026-08-16T04:22:14.207185Z","submitted_at":"2025-05-02T10:31:01Z","title":"Dual canonical bases and embeddings of symmetric spaces","version":2},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-16T04:34:09.394599Z"},"links":{"citing_paper":"/paper/2505.01173"},"observation_digest":"sha256:bee46c9b553caef2c6c3521ebd98e63f346a29c7490f6b3c2f76b2c66da306c1","observation_id":"3699c0f9-61b8-47c5-a838-c00c58a9b1d0","resolution":{"observed_at":"2026-08-16T04:34:09.507896Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-16T04:34:10.262776Z","title":"Math., vol","venue":null,"work_id":"087c7750-a60c-4814-8ca2-8f22495bbf08","year":1993},"citing_paper":{"arxiv_id":"2505.01173","last_updated":"2025-07-28T06:04:45Z","snapshot_observed_at":"2026-08-16T04:22:14.207185Z","submitted_at":"2025-05-02T10:31:01Z","title":"Dual canonical bases and embeddings of symmetric spaces","version":2},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-16T04:34:09.407726Z"},"links":{"citing_paper":"/paper/2505.01173"},"observation_digest":"sha256:bfe0cd936e9a512d3652d4088364d4dc820709e33795fbb0d204bea3911419a8","observation_id":"8cc2e126-7216-4521-a989-e1ece08d015a","resolution":{"observed_at":"2026-08-16T04:34:10.282471Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-16T04:34:10.222890Z","title":"Scuola Norm","venue":null,"work_id":"120a522b-3c4d-4f73-b7b2-6580df1919de","year":1990},"citing_paper":{"arxiv_id":"2505.01173","last_updated":"2025-07-28T06:04:45Z","snapshot_observed_at":"2026-08-16T04:22:14.207185Z","submitted_at":"2025-05-02T10:31:01Z","title":"Dual canonical bases and embeddings of symmetric spaces","version":2},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-16T04:34:09.418664Z"},"links":{"citing_paper":"/paper/2505.01173"},"observation_digest":"sha256:de1a3f57723d8f1a6cdcf7cf2d7b16fc94f1561f27480c12fb8536913c4cdf60","observation_id":"41e998bc-fa12-4129-9b89-841647e61d60","resolution":{"observed_at":"2026-08-16T04:34:10.232293Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2505.01173","last_updated":"2025-07-28T06:04:45Z","latest_version":2,"primary_category":"math.RT","snapshot_observed_at":"2026-08-16T04:22:14.207185Z","submitted_at":"2025-05-02T10:31:01Z","title":"Dual canonical bases and embeddings of symmetric spaces"},"reference_resolution":{"displayed":26,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":12,"verified_exact":7,"verified_fuzzy":7},"total_outbound_references":26},"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":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"thesis":"As of 18 August 2026, this Paper Citation Record lists 26 of 26 outbound references and 2 inbound Pith citation observations for arXiv:2505.01173."}