{"as_of":"2026-08-08T20:04:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:a153cd6c32d14a183c7d3218c7b89337aaf4fa326d7753189ebedf5170969ecd","coverage":[{"denominator":23,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":23,"source":"paper_references, paper_reference_links","source_observed_at":"2026-06-25T20:18:17.874109Z","state":"measured"},{"denominator":24,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":24,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-08T06:32:00.761636+00:00","state":"measured"},{"denominator":1,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":1,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-02T01:48:53.125869Z","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":[{"citation":{"cited_paper":{"arxiv_id":"2606.25516","last_updated":"2026-06-24T07:48:19Z","snapshot_observed_at":"2026-08-06T12:03:54.604657Z","submitted_at":"2026-06-24T07:48:19Z","title":"Total positivity and symmetric spaces","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2606.25516","snapshot_observed_at":"2026-08-02T01:48:53.125869Z","title":"Bao,Total positive and symmetric spaces(2026), available athttps://arxiv.org/abs/ 2606.25516","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.14634","last_updated":"2026-07-16T06:59:14Z","snapshot_observed_at":"2026-08-02T01:48:51.999866Z","submitted_at":"2026-07-16T06:59:14Z","title":"Cluster structures on $SL_n/SO_n$","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-02T01:48:53.125869Z"},"links":{"cited_paper":"/paper/2606.25516","citing_paper":"/paper/2607.14634"},"observation_digest":"sha256:15801a8c0fce55a61d40c6f9815dd353f47cb4510e4012ef7401b09ef4f7f9c0","observation_id":"d387ce89-a202-4fa2-af8c-ab5b5077a9cd","resolution":{"observed_at":"2026-08-02T01:48:53.125869Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2606.25516/citation-record","integrity":"/paper/2606.25516/integrity","json":"/paper/2606.25516/citation-record.json","paper":"/paper/2606.25516"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-25T20:18:17.874109Z","title":null,"venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2606.25516","last_updated":"2026-06-24T07:48:19Z","snapshot_observed_at":"2026-08-06T12:03:54.604657Z","submitted_at":"2026-06-24T07:48:19Z","title":"Total positivity and symmetric spaces","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-06-25T20:18:17.874109Z"},"links":{"citing_paper":"/paper/2606.25516"},"observation_digest":"sha256:49cca87e81bce238e2d176fcd2a314f560ba1a08996f31a56737b70cbf5696ac","observation_id":"d90db1e8-be4d-4d4a-9541-5f2d6ec5a4ac","resolution":{"observed_at":"2026-06-25T20:18:17.874109Z","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":"10.2140/ant.2021.15.2037","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"8, 2037– 2069, DOI 10.2140/ant.2021.15.2037","venue":"Algebra & Number Theory","work_id":"7dda207b-66ff-4e11-9101-d15f00d51137","year":2021},"citing_paper":{"arxiv_id":"2606.25516","last_updated":"2026-06-24T07:48:19Z","snapshot_observed_at":"2026-08-06T12:03:54.604657Z","submitted_at":"2026-06-24T07:48:19Z","title":"Total positivity and symmetric spaces","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-06-25T20:18:17.874109Z"},"links":{"citing_paper":"/paper/2606.25516"},"observation_digest":"sha256:b6d829ef69cd0c59aa92710563df2ae320c46ae4914164105fc2ba63eccc7b4f","observation_id":"820b6c11-16fc-4414-871b-cf9d427db9f1","resolution":{"observed_at":"2026-06-27T03:40:28.624501Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2211.11168","last_updated":"2024-02-23T01:09:06Z","snapshot_observed_at":"2026-07-06T14:20:58.769163Z","submitted_at":"2022-11-21T03:51:53Z","title":"Total positivity in twisted product of flag varieties","version":2},"cited_work":{"arxiv_id":"2211.11168","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2211.11168","snapshot_observed_at":"2026-07-04T20:20:07.591894Z","title":"Bao and X","venue":null,"work_id":"e6528123-91b0-4c44-aa03-83a4373fbeb1","year":2022},"citing_paper":{"arxiv_id":"2606.25516","last_updated":"2026-06-24T07:48:19Z","snapshot_observed_at":"2026-08-06T12:03:54.604657Z","submitted_at":"2026-06-24T07:48:19Z","title":"Total positivity and symmetric spaces","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-06-25T20:18:17.874109Z"},"links":{"cited_paper":"/paper/2211.11168","citing_paper":"/paper/2606.25516"},"observation_digest":"sha256:8789943d39c4e57800f0e17f7c1a91243f15ba7801bc25ca3ee7fb7bf3f73e0f","observation_id":"e9f201c4-6ec1-43c9-863a-159bd30888af","resolution":{"observed_at":"2026-07-04T20:20:07.593938Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s00222-024-01256-2","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Math.237(2024), no","venue":"Inventiones mathematicae","work_id":"afeacd89-f638-404d-9a4c-9c253ab4f5b0","year":2024},"citing_paper":{"arxiv_id":"2606.25516","last_updated":"2026-06-24T07:48:19Z","snapshot_observed_at":"2026-08-06T12:03:54.604657Z","submitted_at":"2026-06-24T07:48:19Z","title":"Total positivity and symmetric spaces","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-06-25T20:18:17.874109Z"},"links":{"citing_paper":"/paper/2606.25516"},"observation_digest":"sha256:d77f236fd9e9913f6eb29552f6b2187c02f0e14a4dde94800e6dce46c7e6610e","observation_id":"2f267d19-0a05-4d29-9d2d-879da8fe3487","resolution":{"observed_at":"2026-06-27T03:40:28.619287Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2402.08258","last_updated":"2024-02-13T07:17:21Z","snapshot_observed_at":"2026-08-01T16:40:47.797451Z","submitted_at":"2024-02-13T07:17:21Z","title":"Coordinate rings on symmetric spaces","version":1},"cited_work":{"arxiv_id":"2402.08258","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2402.08258","snapshot_observed_at":"2026-07-04T20:20:07.595228Z","title":null,"venue":null,"work_id":"d94b1e59-6d0e-4a0c-8b8f-129ab29c3df7","year":2024},"citing_paper":{"arxiv_id":"2606.25516","last_updated":"2026-06-24T07:48:19Z","snapshot_observed_at":"2026-08-06T12:03:54.604657Z","submitted_at":"2026-06-24T07:48:19Z","title":"Total positivity and symmetric spaces","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-06-25T20:18:17.874109Z"},"links":{"cited_paper":"/paper/2402.08258","citing_paper":"/paper/2606.25516"},"observation_digest":"sha256:0db8e087d7a36c06287be61f0c6f3603a76cc3f891f4af92139be90ce45119ba","observation_id":"dc53147b-a1f6-46cb-ba7d-50730d4aae4c","resolution":{"observed_at":"2026-07-04T20:20:07.596894Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2212.13426","last_updated":"2022-12-27T09:42:08Z","snapshot_observed_at":"2026-07-06T14:35:14.315578Z","submitted_at":"2022-12-27T09:42:08Z","title":"Symmetric subgroup schemes, Frobenius splittings, and quantum symmetric pairs","version":1},"cited_work":{"arxiv_id":"2212.13426","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2212.13426","snapshot_observed_at":"2026-07-04T20:20:07.600823Z","title":null,"venue":null,"work_id":"684db9c4-ebb0-4a00-83c1-0370244b5eec","year":2022},"citing_paper":{"arxiv_id":"2606.25516","last_updated":"2026-06-24T07:48:19Z","snapshot_observed_at":"2026-08-06T12:03:54.604657Z","submitted_at":"2026-06-24T07:48:19Z","title":"Total positivity and symmetric spaces","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-06-25T20:18:17.874109Z"},"links":{"cited_paper":"/paper/2212.13426","citing_paper":"/paper/2606.25516"},"observation_digest":"sha256:941983464613b8bdf5bc8ccab544ffcae4706cb1281f1a0f8c7ea777139686f9","observation_id":"890d34b5-3963-4dc7-8c60-4c63dade1ab6","resolution":{"observed_at":"2026-07-04T20:20:07.602442Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1610.09271","last_updated":"2018-04-09T17:53:58Z","snapshot_observed_at":"2026-07-06T05:16:33.346094Z","submitted_at":"2016-10-28T15:32:17Z","title":"Canonical bases arising from quantum symmetric pairs","version":2},"cited_work":{"arxiv_id":"1610.09271","doi":null,"metadata_source":"pith","pith_arxiv_id":"1610.09271","snapshot_observed_at":"2026-07-04T20:20:07.598218Z","title":"Canonical bases arising from quantum symmetric pairs","venue":"math.QA","work_id":"20cd0103-461e-4049-ba68-244f2ae3e06d","year":2016},"citing_paper":{"arxiv_id":"2606.25516","last_updated":"2026-06-24T07:48:19Z","snapshot_observed_at":"2026-08-06T12:03:54.604657Z","submitted_at":"2026-06-24T07:48:19Z","title":"Total positivity and symmetric spaces","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-06-25T20:18:17.874109Z"},"links":{"cited_paper":"/paper/1610.09271","citing_paper":"/paper/2606.25516"},"observation_digest":"sha256:ab30857a3435632bcca6b7a8048f29d4032ddf23a1a02c83efd781109581b8c2","observation_id":"f5c349f6-7196-40b3-aa87-38dd14cf5e8e","resolution":{"observed_at":"2026-07-04T20:20:07.599550Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s00031-","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T16:32:22.753484Z","title":"Calculating thep-canonical basis of Hecke algebras","venue":null,"work_id":"bb9959ae-7097-4f85-b08a-431bfd1bac71","year":2017},"citing_paper":{"arxiv_id":"2606.25516","last_updated":"2026-06-24T07:48:19Z","snapshot_observed_at":"2026-08-06T12:03:54.604657Z","submitted_at":"2026-06-24T07:48:19Z","title":"Total positivity and symmetric spaces","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-06-25T20:18:17.874109Z"},"links":{"citing_paper":"/paper/2606.25516"},"observation_digest":"sha256:4c4206b397542efc1d5816f55637097ab5b4840371dd3b73dd75acceb6a4d955","observation_id":"d6e51aac-8d37-4725-9f13-84f90c937eac","resolution":{"observed_at":"2026-06-27T03:40:28.622911Z","resolver_source":"doi_truncated","status":"malformed_identifier"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-06-25T20:18:17.874109Z","title":"996, Springer, Berlin, 1983, pp","venue":null,"work_id":null,"year":1982},"citing_paper":{"arxiv_id":"2606.25516","last_updated":"2026-06-24T07:48:19Z","snapshot_observed_at":"2026-08-06T12:03:54.604657Z","submitted_at":"2026-06-24T07:48:19Z","title":"Total positivity and symmetric spaces","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-06-25T20:18:17.874109Z"},"links":{"citing_paper":"/paper/2606.25516"},"observation_digest":"sha256:fa11bd5a356612cc52f7d639b4c1e75a8441fb63d45940563e2615b2c5ed0a85","observation_id":"4014ef9f-2a88-4b9e-9d91-544d4d9ebf45","resolution":{"observed_at":"2026-06-25T20:18:17.874109Z","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":"2026-06-25T20:18:17.874109Z","title":null,"venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2606.25516","last_updated":"2026-06-24T07:48:19Z","snapshot_observed_at":"2026-08-06T12:03:54.604657Z","submitted_at":"2026-06-24T07:48:19Z","title":"Total positivity and symmetric spaces","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-06-25T20:18:17.874109Z"},"links":{"citing_paper":"/paper/2606.25516"},"observation_digest":"sha256:7b6097c54cf9c6ce9d382b2c9972bc013190110ac54afe839af9f609f53a4238","observation_id":"75afce81-86f3-43b3-b728-be4b0aee01e6","resolution":{"observed_at":"2026-06-25T20:18:17.874109Z","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":"10.1090/jams/983","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Karp, and Thomas Lam","venue":"Journal of the American Mathematical Society","work_id":"b7a461d9-1cd5-49d0-9738-744f710f2570","year":2022},"citing_paper":{"arxiv_id":"2606.25516","last_updated":"2026-06-24T07:48:19Z","snapshot_observed_at":"2026-08-06T12:03:54.604657Z","submitted_at":"2026-06-24T07:48:19Z","title":"Total positivity and symmetric spaces","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-06-25T20:18:17.874109Z"},"links":{"citing_paper":"/paper/2606.25516"},"observation_digest":"sha256:9bd057e1dd5c464df14764d6d28631a967df106005940c8849bce3078781fcec","observation_id":"0f4297f5-74d1-493a-9c38-7a7930531615","resolution":{"observed_at":"2026-06-27T03:40:28.628025Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/j.indag.2014.07.011","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":null,"venue":"Indagationes Mathematicae","work_id":"dd55f46e-36e0-4e16-b1aa-31e903e8d613","year":2014},"citing_paper":{"arxiv_id":"2606.25516","last_updated":"2026-06-24T07:48:19Z","snapshot_observed_at":"2026-08-06T12:03:54.604657Z","submitted_at":"2026-06-24T07:48:19Z","title":"Total positivity and symmetric spaces","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-06-25T20:18:17.874109Z"},"links":{"citing_paper":"/paper/2606.25516"},"observation_digest":"sha256:2709100291d17dc0ffb5745cf68e763fb524734a9046820f051521274ae1128c","observation_id":"a1ae480b-29bc-45b0-9863-b549415bc009","resolution":{"observed_at":"2026-06-27T03:40:28.626154Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-06-25T20:18:17.874109Z","title":null,"venue":null,"work_id":null,"year":1994},"citing_paper":{"arxiv_id":"2606.25516","last_updated":"2026-06-24T07:48:19Z","snapshot_observed_at":"2026-08-06T12:03:54.604657Z","submitted_at":"2026-06-24T07:48:19Z","title":"Total positivity and symmetric spaces","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-06-25T20:18:17.874109Z"},"links":{"citing_paper":"/paper/2606.25516"},"observation_digest":"sha256:6767ea07d9fa3220d8c3782e2847c871960999eb9645d385528a45d89e54b7b4","observation_id":"17e7b477-605f-4e62-8f24-156463f1b169","resolution":{"observed_at":"2026-06-25T20:18:17.874109Z","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":"2026-06-25T20:18:17.874109Z","title":null,"venue":null,"work_id":null,"year":1998},"citing_paper":{"arxiv_id":"2606.25516","last_updated":"2026-06-24T07:48:19Z","snapshot_observed_at":"2026-08-06T12:03:54.604657Z","submitted_at":"2026-06-24T07:48:19Z","title":"Total positivity and symmetric spaces","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-06-25T20:18:17.874109Z"},"links":{"citing_paper":"/paper/2606.25516"},"observation_digest":"sha256:af40982383c8f2de976acde41369bdd81abe36c22be91c22738b2826be0cbf5a","observation_id":"37a03293-3d1b-4bd2-a838-a6cce7c58216","resolution":{"observed_at":"2026-06-25T20:18:17.874109Z","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":"10.1090/ert/628","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Theory26(2022), 1025–1046, DOI 10.1090/ert/628, available atarXiv:2107.13447","venue":"Representation Theory of the American Mathematical Society","work_id":"8f23ba25-724a-43d2-9d03-b01761e89472","year":2022},"citing_paper":{"arxiv_id":"2606.25516","last_updated":"2026-06-24T07:48:19Z","snapshot_observed_at":"2026-08-06T12:03:54.604657Z","submitted_at":"2026-06-24T07:48:19Z","title":"Total positivity and symmetric spaces","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-06-25T20:18:17.874109Z"},"links":{"citing_paper":"/paper/2606.25516"},"observation_digest":"sha256:faf011230ea3c3692f02b892865d84fd0574af903e70f85e12190d1902d2cafc","observation_id":"6bc25149-15ec-4f60-b2e5-9a5441128886","resolution":{"observed_at":"2026-06-27T03:40:28.620943Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"math/0307017","last_updated":"2004-04-15T08:16:44Z","snapshot_observed_at":"2026-08-05T21:13:01.911256Z","submitted_at":"2003-07-02T12:09:54Z","title":"Parametrizations of flag varieties","version":2},"cited_work":{"arxiv_id":"math/0307017","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"math/0307017","snapshot_observed_at":"2026-07-04T20:20:07.580864Z","title":null,"venue":null,"work_id":"a9350d2a-9ac1-4f61-bfdd-af78cf49a6f6","year":2004},"citing_paper":{"arxiv_id":"2606.25516","last_updated":"2026-06-24T07:48:19Z","snapshot_observed_at":"2026-08-06T12:03:54.604657Z","submitted_at":"2026-06-24T07:48:19Z","title":"Total positivity and symmetric spaces","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-06-25T20:18:17.874109Z"},"links":{"cited_paper":"/paper/math/0307017","citing_paper":"/paper/2606.25516"},"observation_digest":"sha256:a8120f61f24ff54ba98e0c950becd3745170745eaf3dc093c4e9a5a5727cc03d","observation_id":"3ea59c7b-291f-4a4b-b762-7de34d29ca21","resolution":{"observed_at":"2026-07-04T20:20:07.584123Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/0019-3577(92)90028-j","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":null,"venue":"Indagationes Mathematicae","work_id":"8edf234b-a967-4b94-8dc5-ebb58e5984ca","year":1992},"citing_paper":{"arxiv_id":"2606.25516","last_updated":"2026-06-24T07:48:19Z","snapshot_observed_at":"2026-08-06T12:03:54.604657Z","submitted_at":"2026-06-24T07:48:19Z","title":"Total positivity and symmetric spaces","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-06-25T20:18:17.874109Z"},"links":{"citing_paper":"/paper/2606.25516"},"observation_digest":"sha256:85765e4b094b76e84a8e1aabc86fa7071a0420494c6568aba1009ae8e692e6e7","observation_id":"008bdce4-2663-44f1-b63a-3a498a377712","resolution":{"observed_at":"2026-06-27T03:40:28.620677Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-06-25T20:18:17.874109Z","title":null,"venue":null,"work_id":null,"year":1990},"citing_paper":{"arxiv_id":"2606.25516","last_updated":"2026-06-24T07:48:19Z","snapshot_observed_at":"2026-08-06T12:03:54.604657Z","submitted_at":"2026-06-24T07:48:19Z","title":"Total positivity and symmetric spaces","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-06-25T20:18:17.874109Z"},"links":{"citing_paper":"/paper/2606.25516"},"observation_digest":"sha256:7ac5d5be5d2438fb886bc030d7b23b136240ad70274fb65952e015261d319363","observation_id":"b72588b8-062f-4013-b01e-9077f3f586fe","resolution":{"observed_at":"2026-06-25T20:18:17.874109Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"math/0509137","last_updated":"2005-11-10T16:20:40Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2005-09-06T21:42:00Z","title":"Closure relations for totally nonnegative cells in G/P","version":2},"cited_work":{"arxiv_id":"math/0509137","doi":null,"metadata_source":"pith","pith_arxiv_id":"math/0509137","snapshot_observed_at":"2026-07-04T20:20:07.587918Z","title":"Closure relations for totally nonnegative cells in G/P","venue":"math.AG","work_id":"1a890eda-e61d-4f7a-a6c6-ce84112304f1","year":2005},"citing_paper":{"arxiv_id":"2606.25516","last_updated":"2026-06-24T07:48:19Z","snapshot_observed_at":"2026-08-06T12:03:54.604657Z","submitted_at":"2026-06-24T07:48:19Z","title":"Total positivity and symmetric spaces","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-06-25T20:18:17.874109Z"},"links":{"cited_paper":"/paper/math/0509137","citing_paper":"/paper/2606.25516"},"observation_digest":"sha256:2f7c62a70b84b72687ef1bc87a6bcb138624badfd9b19a0a737cbb27421aa102","observation_id":"7119ca8b-f00e-488c-829e-a9ea2baa28b8","resolution":{"observed_at":"2026-07-04T20:20:07.590279Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2512.01398","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-04T20:20:07.584890Z","title":null,"venue":null,"work_id":"afdb209d-3112-432a-8ede-77570cf28763","year":2025},"citing_paper":{"arxiv_id":"2606.25516","last_updated":"2026-06-24T07:48:19Z","snapshot_observed_at":"2026-08-06T12:03:54.604657Z","submitted_at":"2026-06-24T07:48:19Z","title":"Total positivity and symmetric spaces","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-06-25T20:18:17.874109Z"},"links":{"citing_paper":"/paper/2606.25516"},"observation_digest":"sha256:98a862e900b86ae9456fc584ec8950c3dcd3d067b79455249131a2fb6844a7dd","observation_id":"9dc13805-eb9d-4193-aea1-8bfb6f9e96d1","resolution":{"observed_at":"2026-07-04T20:20:07.587263Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-06-25T20:18:17.874109Z","title":null,"venue":null,"work_id":null,"year":1998},"citing_paper":{"arxiv_id":"2606.25516","last_updated":"2026-06-24T07:48:19Z","snapshot_observed_at":"2026-08-06T12:03:54.604657Z","submitted_at":"2026-06-24T07:48:19Z","title":"Total positivity and symmetric spaces","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-06-25T20:18:17.874109Z"},"links":{"citing_paper":"/paper/2606.25516"},"observation_digest":"sha256:eac8ee51088a505d3a01b133233653bcbd22f0c7520c671ea6ceea83908d5210","observation_id":"4e9551e2-d904-4281-a34c-00edda6fe266","resolution":{"observed_at":"2026-06-25T20:18:17.874109Z","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":"2026-06-25T20:18:17.874109Z","title":null,"venue":null,"work_id":null,"year":1985},"citing_paper":{"arxiv_id":"2606.25516","last_updated":"2026-06-24T07:48:19Z","snapshot_observed_at":"2026-08-06T12:03:54.604657Z","submitted_at":"2026-06-24T07:48:19Z","title":"Total positivity and symmetric spaces","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-06-25T20:18:17.874109Z"},"links":{"citing_paper":"/paper/2606.25516"},"observation_digest":"sha256:f4f89ff4386cbbda4747af58ab8d401d842ad331ff9192785ff9d0c37906d9b4","observation_id":"6c9022ab-747e-48e5-9832-6cb1512c1a55","resolution":{"observed_at":"2026-06-25T20:18:17.874109Z","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":"2026-06-25T20:18:17.874109Z","title":"Wikipedia,https://en.wikipedia.org/wiki/ Satake_diagram","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2606.25516","last_updated":"2026-06-24T07:48:19Z","snapshot_observed_at":"2026-08-06T12:03:54.604657Z","submitted_at":"2026-06-24T07:48:19Z","title":"Total positivity and symmetric spaces","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-06-25T20:18:17.874109Z"},"links":{"citing_paper":"/paper/2606.25516"},"observation_digest":"sha256:358280e9a4ed8a5e7281310cbdfb075f7abf0b4f93c0908343e50147fd5a2f49","observation_id":"9fd397d0-28f7-4997-b406-fd68872f9f1b","resolution":{"observed_at":"2026-06-25T20:18:17.874109Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2606.25516","last_updated":"2026-06-24T07:48:19Z","latest_version":1,"primary_category":"math.RT","snapshot_observed_at":"2026-08-06T12:03:54.604657Z","submitted_at":"2026-06-24T07:48:19Z","title":"Total positivity and symmetric spaces"},"reference_resolution":{"displayed":23,"state_counts":{"malformed_identifier":1,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":9,"verified_exact":13,"verified_fuzzy":0},"total_outbound_references":23},"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":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"thesis":"As of 8 August 2026, this Paper Citation Record lists 23 of 23 outbound references and 1 inbound Pith citation observation for arXiv:2606.25516."}