{"as_of":"2026-08-17T23:24:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:117813528aa727b3e60b81b7fdcae9ce8b1e883f2ff5e0cbe1d7f95b235049c3","coverage":[{"denominator":59,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":59,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-15T18:05:55.697667Z","state":"measured"},{"denominator":59,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":59,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-17T06:30:58.91139+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2507.19306/citation-record","integrity":"/paper/2507.19306/integrity","json":"/paper/2507.19306/citation-record.json","paper":"/paper/2507.19306"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:05:56.808577Z","title":"Clifford modules","venue":null,"work_id":"a55c5592-2bbb-4397-991d-8863940a38bd","year":1964},"citing_paper":{"arxiv_id":"2507.19306","last_updated":"2025-07-25T14:22:18Z","snapshot_observed_at":"2026-08-15T17:53:10.101189Z","submitted_at":"2025-07-25T14:22:18Z","title":"Transverse Spheres in Flag Manifolds","version":1},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-08-15T18:05:55.396782Z"},"links":{"citing_paper":"/paper/2507.19306"},"observation_digest":"sha256:2ce8df475cfeed496de0ee91301d5da68ed3227ff0769386118dfa11f8a703e0","observation_id":"0d829d19-f331-4b8a-be5a-38662fbd2af6","resolution":{"observed_at":"2026-08-15T18:05:56.813599Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:05:56.791991Z","title":null,"venue":null,"work_id":"56998643-9e87-4c7d-8778-a7aa4bcab78f","year":1960},"citing_paper":{"arxiv_id":"2507.19306","last_updated":"2025-07-25T14:22:18Z","snapshot_observed_at":"2026-08-15T17:53:10.101189Z","submitted_at":"2025-07-25T14:22:18Z","title":"Transverse Spheres in Flag Manifolds","version":1},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-08-15T18:05:55.402598Z"},"links":{"citing_paper":"/paper/2507.19306"},"observation_digest":"sha256:8ef86f156725579a956d2cce3c6000115141da8ca4c7721a14b39f40ded7b1b9","observation_id":"aae3eec3-2162-4e21-ac49-4d1df736981d","resolution":{"observed_at":"2026-08-15T18:05:56.797418Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:05:56.776579Z","title":"The Octonions","venue":null,"work_id":"1cfeeb2c-5e1c-4991-a51d-f59b74f8411e","year":2002},"citing_paper":{"arxiv_id":"2507.19306","last_updated":"2025-07-25T14:22:18Z","snapshot_observed_at":"2026-08-15T17:53:10.101189Z","submitted_at":"2025-07-25T14:22:18Z","title":"Transverse Spheres in Flag Manifolds","version":1},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-08-15T18:05:55.407584Z"},"links":{"citing_paper":"/paper/2507.19306"},"observation_digest":"sha256:4d1440087e9c3e77d7d16e36655189fa4ac43ea0ed1614260d70267ae14e0ab2","observation_id":"48257418-a8c9-4968-bde0-3fc17c94e5e5","resolution":{"observed_at":"2026-08-15T18:05:56.781585Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:05:56.759776Z","title":"Baez and John Huerta","venue":null,"work_id":"162f367e-5b8d-4c46-b71c-83a52b4febc8","year":2014},"citing_paper":{"arxiv_id":"2507.19306","last_updated":"2025-07-25T14:22:18Z","snapshot_observed_at":"2026-08-15T17:53:10.101189Z","submitted_at":"2025-07-25T14:22:18Z","title":"Transverse Spheres in Flag Manifolds","version":1},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-08-15T18:05:55.413685Z"},"links":{"citing_paper":"/paper/2507.19306"},"observation_digest":"sha256:aa0bccbc6de547e4e492adedd600694d15538aa7c4e526dea4205f54791e6922","observation_id":"83d8d7ea-6df8-4657-97fb-d8bdcc79b1fa","resolution":{"observed_at":"2026-08-15T18:05:56.765973Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:05:55.418922Z","title":"H ^ p,q -convex cocompactness and higher higher Teichm\\\"uller spaces","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2507.19306","last_updated":"2025-07-25T14:22:18Z","snapshot_observed_at":"2026-08-15T17:53:10.101189Z","submitted_at":"2025-07-25T14:22:18Z","title":"Transverse Spheres in Flag Manifolds","version":1},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-08-15T18:05:55.418922Z"},"links":{"citing_paper":"/paper/2507.19306"},"observation_digest":"sha256:ef7f4efe3c75aa6889472eaa40dec59705327e575cac5f433646e394b0aea6a4","observation_id":"b4e5795b-ac46-49af-99b6-33d1b33526cf","resolution":{"observed_at":"2026-08-15T18:05:55.418922Z","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":"2026-08-15T18:05:56.744679Z","title":"Bourbaki","venue":null,"work_id":"8495fd79-ed8f-447f-a0e0-9c613ebc189b","year":2005},"citing_paper":{"arxiv_id":"2507.19306","last_updated":"2025-07-25T14:22:18Z","snapshot_observed_at":"2026-08-15T17:53:10.101189Z","submitted_at":"2025-07-25T14:22:18Z","title":"Transverse Spheres in Flag Manifolds","version":1},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-08-15T18:05:55.425039Z"},"links":{"citing_paper":"/paper/2507.19306"},"observation_digest":"sha256:5bdccfd9206b0546faa9065eb0f9abaf00f1512a76d3a81b2ff827a95eb57688","observation_id":"296cb8ba-3547-4ac1-94bc-a33ea841875c","resolution":{"observed_at":"2026-08-15T18:05:56.749392Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:05:56.729450Z","title":"Topology and Geometry","venue":null,"work_id":"773ba49e-fbfc-48b4-8134-4e2a00c40a72","year":1993},"citing_paper":{"arxiv_id":"2507.19306","last_updated":"2025-07-25T14:22:18Z","snapshot_observed_at":"2026-08-15T17:53:10.101189Z","submitted_at":"2025-07-25T14:22:18Z","title":"Transverse Spheres in Flag Manifolds","version":1},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-08-15T18:05:55.430712Z"},"links":{"citing_paper":"/paper/2507.19306"},"observation_digest":"sha256:db2cea49db9a286a403e7994bbd69eb352baf1304eb67fad15ecffb0c475d60c","observation_id":"c53704d2-3302-4913-8f16-6e403eaa27aa","resolution":{"observed_at":"2026-08-15T18:05:56.734235Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2011.05568","last_updated":"2020-11-09T15:19:33Z","snapshot_observed_at":"2026-08-16T19:07:09.478802Z","submitted_at":"2020-11-09T15:19:33Z","title":"Notes on spinors in low dimension","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2011.05568","snapshot_observed_at":"2026-08-15T18:05:55.438968Z","title":null,"venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2507.19306","last_updated":"2025-07-25T14:22:18Z","snapshot_observed_at":"2026-08-15T17:53:10.101189Z","submitted_at":"2025-07-25T14:22:18Z","title":"Transverse Spheres in Flag Manifolds","version":1},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-08-15T18:05:55.438968Z"},"links":{"cited_paper":"/paper/2011.05568","citing_paper":"/paper/2507.19306"},"observation_digest":"sha256:29460984a7846e27973d39beead298999c0504f50d269b00587c0febc561407e","observation_id":"a2b32275-cd4b-4b32-82db-6108f517c64e","resolution":{"observed_at":"2026-08-15T18:05:55.438968Z","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":"2026-08-15T18:05:56.710456Z","title":"Maximal surfaces and the universal T eichm \\\"u ller space","venue":null,"work_id":"7d35e250-77a4-4d2a-ac2c-0b944123d33c","year":2010},"citing_paper":{"arxiv_id":"2507.19306","last_updated":"2025-07-25T14:22:18Z","snapshot_observed_at":"2026-08-15T17:53:10.101189Z","submitted_at":"2025-07-25T14:22:18Z","title":"Transverse Spheres in Flag Manifolds","version":1},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-08-15T18:05:55.444643Z"},"links":{"citing_paper":"/paper/2507.19306"},"observation_digest":"sha256:b767b04dae31ef494828c6b1b03251963b3ea7574606cd6f1fff241f9e410cb8","observation_id":"0b7babf2-7b5b-49c1-b78b-c56ea0fcd17c","resolution":{"observed_at":"2026-08-15T18:05:56.717656Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:05:56.692003Z","title":"Les groupes r\\'eels simples, finis et continus","venue":null,"work_id":"c56bf52d-ac5e-44c0-9eb5-6b7534145873","year":1914},"citing_paper":{"arxiv_id":"2507.19306","last_updated":"2025-07-25T14:22:18Z","snapshot_observed_at":"2026-08-15T17:53:10.101189Z","submitted_at":"2025-07-25T14:22:18Z","title":"Transverse Spheres in Flag Manifolds","version":1},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-08-15T18:05:55.449239Z"},"links":{"citing_paper":"/paper/2507.19306"},"observation_digest":"sha256:590434c231b5f2124952f0585c5b43e3270059fc60fc01cf7ffaf671b346507f","observation_id":"044e0c16-5c09-42fe-87e7-edd334966650","resolution":{"observed_at":"2026-08-15T18:05:56.697296Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:05:56.675924Z","title":"Topological restrictions on Anosov representations","venue":null,"work_id":"5dba9654-48b4-4bfa-9ee8-e0d5520e54e9","year":2020},"citing_paper":{"arxiv_id":"2507.19306","last_updated":"2025-07-25T14:22:18Z","snapshot_observed_at":"2026-08-15T17:53:10.101189Z","submitted_at":"2025-07-25T14:22:18Z","title":"Transverse Spheres in Flag Manifolds","version":1},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-08-15T18:05:55.454488Z"},"links":{"citing_paper":"/paper/2507.19306"},"observation_digest":"sha256:d3d84db2e1697977dff438b49ed1414a5ebd52a094f0968983541a7b65d6bea5","observation_id":"69e29074-b3f5-480a-974e-ffeb84352348","resolution":{"observed_at":"2026-08-15T18:05:56.681126Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:05:56.659169Z","title":"Holomorphic curves in the 6-pseudosphere and cyclic surfaces","venue":null,"work_id":"0cbb740d-14f2-410c-b846-b6b9b7b3b81c","year":2024},"citing_paper":{"arxiv_id":"2507.19306","last_updated":"2025-07-25T14:22:18Z","snapshot_observed_at":"2026-08-15T17:53:10.101189Z","submitted_at":"2025-07-25T14:22:18Z","title":"Transverse Spheres in Flag Manifolds","version":1},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-08-15T18:05:55.460299Z"},"links":{"citing_paper":"/paper/2507.19306"},"observation_digest":"sha256:153573d89e81c06ca02a16b2d7fed73d5426ca813dbfefb02cd73e962d3236fb","observation_id":"f4ad323f-6395-49b2-a072-7e838ea2ef29","resolution":{"observed_at":"2026-08-15T18:05:56.664751Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:05:56.642947Z","title":"Geometric structures for SO_0(p,p+1) and G_2' -representations (to appear), 2025","venue":null,"work_id":"3e8c0b10-2085-4d84-b3e9-9d0f4f5cb649","year":2025},"citing_paper":{"arxiv_id":"2507.19306","last_updated":"2025-07-25T14:22:18Z","snapshot_observed_at":"2026-08-15T17:53:10.101189Z","submitted_at":"2025-07-25T14:22:18Z","title":"Transverse Spheres in Flag Manifolds","version":1},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-08-15T18:05:55.465925Z"},"links":{"citing_paper":"/paper/2507.19306"},"observation_digest":"sha256:354467042c8d585700e75b8ecab6d8d5000aa9e861a8c141378ce8d8e1ca1ef9","observation_id":"c3a6ef9e-365b-40b7-bc5c-f8b233a51d2a","resolution":{"observed_at":"2026-08-15T18:05:56.648441Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:05:56.626793Z","title":"On Borel Anosov subgroups of SL(d, R )","venue":null,"work_id":"37b5b912-5636-4dfc-9552-1ccf2c73b35f","year":2025},"citing_paper":{"arxiv_id":"2507.19306","last_updated":"2025-07-25T14:22:18Z","snapshot_observed_at":"2026-08-15T17:53:10.101189Z","submitted_at":"2025-07-25T14:22:18Z","title":"Transverse Spheres in Flag Manifolds","version":1},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-08-15T18:05:55.470887Z"},"links":{"citing_paper":"/paper/2507.19306"},"observation_digest":"sha256:5fa14667b26bbfdb749f1357a041b3886460d945a936b6df06aa1a5fb330e5dd","observation_id":"b72cdced-6d4b-495a-93ee-4f57ba9621f6","resolution":{"observed_at":"2026-08-15T18:05:56.631939Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:05:55.476226Z","title":"Convex cocompactness in pseudo- R iemannian hyperbolic spaces","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2507.19306","last_updated":"2025-07-25T14:22:18Z","snapshot_observed_at":"2026-08-15T17:53:10.101189Z","submitted_at":"2025-07-25T14:22:18Z","title":"Transverse Spheres in Flag Manifolds","version":1},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-08-15T18:05:55.476226Z"},"links":{"citing_paper":"/paper/2507.19306"},"observation_digest":"sha256:5e56306a40c793daa2a54d627b4052a4414c549a13c9b991c5d8d18624b04c86","observation_id":"7a0b0cce-d75a-4e14-955f-d4f584f94064","resolution":{"observed_at":"2026-08-15T18:05:55.476226Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1704.08711","last_updated":"2023-04-18T07:04:05Z","snapshot_observed_at":"2026-08-14T21:04:13.068620Z","submitted_at":"2017-04-27T18:40:37Z","title":"Convex cocompact actions in real projective geometry","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1704.08711","snapshot_observed_at":"2026-08-15T18:05:55.481277Z","title":"Convex cocompact actions in real projective geometry","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2507.19306","last_updated":"2025-07-25T14:22:18Z","snapshot_observed_at":"2026-08-15T17:53:10.101189Z","submitted_at":"2025-07-25T14:22:18Z","title":"Transverse Spheres in Flag Manifolds","version":1},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-08-15T18:05:55.481277Z"},"links":{"cited_paper":"/paper/1704.08711","citing_paper":"/paper/2507.19306"},"observation_digest":"sha256:69a2b3c04e50a431c68abd7fd9849ee42ebcc1a07cb7956d1fd1c5495d7c83db","observation_id":"09c7afeb-2b50-4a3b-b3ea-c3c94edb46da","resolution":{"observed_at":"2026-08-15T18:05:55.481277Z","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":"2026-08-15T18:05:56.598101Z","title":"Maxwell Riestenberg","venue":null,"work_id":"77c37eb6-62d7-4291-8ea9-0835a434f538","year":2024},"citing_paper":{"arxiv_id":"2507.19306","last_updated":"2025-07-25T14:22:18Z","snapshot_observed_at":"2026-08-15T17:53:10.101189Z","submitted_at":"2025-07-25T14:22:18Z","title":"Transverse Spheres in Flag Manifolds","version":1},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-08-15T18:05:55.486551Z"},"links":{"citing_paper":"/paper/2507.19306"},"observation_digest":"sha256:ffacb30a3b447050a693753a1b1b5ce1d6203d6f41b800957837a5c54a3f4f39","observation_id":"a28899b8-e2f0-4989-b2d5-af24ecf46e31","resolution":{"observed_at":"2026-08-15T18:05:56.603437Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:05:56.581898Z","title":"Klein–Maskit combination theorem for Anosov subgroups: free products","venue":null,"work_id":"74fe8e6d-9619-48b4-bc1b-51b1fc27d9e6","year":2023},"citing_paper":{"arxiv_id":"2507.19306","last_updated":"2025-07-25T14:22:18Z","snapshot_observed_at":"2026-08-15T17:53:10.101189Z","submitted_at":"2025-07-25T14:22:18Z","title":"Transverse Spheres in Flag Manifolds","version":1},"reference_index":18,"source":"arxiv_source","source_observed_at":"2026-08-15T18:05:55.491471Z"},"links":{"citing_paper":"/paper/2507.19306"},"observation_digest":"sha256:1f807bd5d7942852b09a31ca142b0e2a999ea249045b8cdb53964350c2b5d7ff","observation_id":"d2ee842f-c343-44e4-800f-d206863d247d","resolution":{"observed_at":"2026-08-15T18:05:56.587300Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2504.07586","last_updated":"2025-04-10T09:28:50Z","snapshot_observed_at":"2026-08-16T12:42:26.607021Z","submitted_at":"2025-04-10T09:28:50Z","title":"A perspective on totally geodesic submanifolds of the symmetric space $G_2/SO(4)$","version":1},"cited_work":{"arxiv_id":"2504.07586","doi":null,"metadata_source":"pith","pith_arxiv_id":"2504.07586","snapshot_observed_at":"2026-08-15T18:05:55.879439Z","title":"A perspective on totally geodesic submanifolds of the symmetric space $G_2/SO(4)$","venue":"math.DG","work_id":"d03d900b-81a0-4b46-9c02-da64eda3818a","year":2025},"citing_paper":{"arxiv_id":"2507.19306","last_updated":"2025-07-25T14:22:18Z","snapshot_observed_at":"2026-08-15T17:53:10.101189Z","submitted_at":"2025-07-25T14:22:18Z","title":"Transverse Spheres in Flag Manifolds","version":1},"reference_index":19,"source":"arxiv_source","source_observed_at":"2026-08-15T18:05:55.496328Z"},"links":{"cited_paper":"/paper/2504.07586","citing_paper":"/paper/2507.19306"},"observation_digest":"sha256:1289d35546d77c2467acb81bddcad038217e95c32848a0229ac0f68ddf5913fe","observation_id":"7fd6c021-c53b-4748-b096-5f293322d758","resolution":{"observed_at":"2026-08-15T18:05:55.885491Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:05:56.564446Z","title":"Notes on G _2 : The Lie algebra and the Lie group","venue":null,"work_id":"fe0dc3b5-8942-48de-afaf-eb5d49757c31","year":2018},"citing_paper":{"arxiv_id":"2507.19306","last_updated":"2025-07-25T14:22:18Z","snapshot_observed_at":"2026-08-15T17:53:10.101189Z","submitted_at":"2025-07-25T14:22:18Z","title":"Transverse Spheres in Flag Manifolds","version":1},"reference_index":20,"source":"arxiv_source","source_observed_at":"2026-08-15T18:05:55.503911Z"},"links":{"citing_paper":"/paper/2507.19306"},"observation_digest":"sha256:6b9710cd68921b8092227d4a219319cbd6f4924f58c80c21acc4f557f0599d05","observation_id":"ce91b85f-3a6e-4173-b167-502167fb599b","resolution":{"observed_at":"2026-08-15T18:05:56.570140Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:05:56.548190Z","title":"Affine actions with Hitchin linear part","venue":null,"work_id":"33e1ad72-f77f-4148-be03-f84208456019","year":2019},"citing_paper":{"arxiv_id":"2507.19306","last_updated":"2025-07-25T14:22:18Z","snapshot_observed_at":"2026-08-15T17:53:10.101189Z","submitted_at":"2025-07-25T14:22:18Z","title":"Transverse Spheres in Flag Manifolds","version":1},"reference_index":21,"source":"arxiv_source","source_observed_at":"2026-08-15T18:05:55.508772Z"},"links":{"citing_paper":"/paper/2507.19306"},"observation_digest":"sha256:04dfedecbc9fa53a0a442a237e73e91f446e9a9a6584b46a5dc938538862b16e","observation_id":"0e6f8c06-1327-4f5e-8887-5fd29a2aa840","resolution":{"observed_at":"2026-08-15T18:05:56.553104Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:05:56.532013Z","title":"Eberlein","venue":null,"work_id":"4206d0d2-dd73-46a9-940c-8baa7964503a","year":1996},"citing_paper":{"arxiv_id":"2507.19306","last_updated":"2025-07-25T14:22:18Z","snapshot_observed_at":"2026-08-15T17:53:10.101189Z","submitted_at":"2025-07-25T14:22:18Z","title":"Transverse Spheres in Flag Manifolds","version":1},"reference_index":22,"source":"arxiv_source","source_observed_at":"2026-08-15T18:05:55.514602Z"},"links":{"citing_paper":"/paper/2507.19306"},"observation_digest":"sha256:57724b6305008af5103c9896fa7f2fd1dfbda87e06ab4ee9e6c78e8ec579e51e","observation_id":"f04f6d0d-d02e-4dbc-874f-0f567745519c","resolution":{"observed_at":"2026-08-15T18:05:56.536761Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:05:56.515863Z","title":"Eschenburg","venue":null,"work_id":"baa70732-42b6-490c-9f0e-69852658dfde","year":2018},"citing_paper":{"arxiv_id":"2507.19306","last_updated":"2025-07-25T14:22:18Z","snapshot_observed_at":"2026-08-15T17:53:10.101189Z","submitted_at":"2025-07-25T14:22:18Z","title":"Transverse Spheres in Flag Manifolds","version":1},"reference_index":23,"source":"arxiv_source","source_observed_at":"2026-08-15T18:05:55.520118Z"},"links":{"citing_paper":"/paper/2507.19306"},"observation_digest":"sha256:f120fdbff538825f8a16fe428dabd00140d83bac0c16423ff8151a3c0e94ce0c","observation_id":"d19d5bac-3c69-4f9c-b215-4398a5018330","resolution":{"observed_at":"2026-08-15T18:05:56.521303Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:05:56.499918Z","title":"Geometry of G _2' -Harmonic Maps and Representations","venue":null,"work_id":"32d22f1e-ca30-4839-b493-e36db07cf47d","year":2024},"citing_paper":{"arxiv_id":"2507.19306","last_updated":"2025-07-25T14:22:18Z","snapshot_observed_at":"2026-08-15T17:53:10.101189Z","submitted_at":"2025-07-25T14:22:18Z","title":"Transverse Spheres in Flag Manifolds","version":1},"reference_index":24,"source":"arxiv_source","source_observed_at":"2026-08-15T18:05:55.525230Z"},"links":{"citing_paper":"/paper/2507.19306"},"observation_digest":"sha256:bf440a7a9a542623ff5ac6cd7be094c5f12975ec88e1db181f97a9f1cdcffa40","observation_id":"87a4494f-66c3-4a29-aa47-1feb07ed25bd","resolution":{"observed_at":"2026-08-15T18:05:56.505424Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2208.14409","last_updated":"2024-04-24T00:34:13Z","snapshot_observed_at":"2026-08-16T16:35:52.825229Z","submitted_at":"2022-08-30T17:20:30Z","title":"Polynomial Almost-Complex Curves in $\\hat{\\mathbb{S}}^{2,4}$","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2208.14409","snapshot_observed_at":"2026-08-15T18:05:55.530128Z","title":"Polynomial almost-complex curves in S ^ 2,4 , 2024","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2507.19306","last_updated":"2025-07-25T14:22:18Z","snapshot_observed_at":"2026-08-15T17:53:10.101189Z","submitted_at":"2025-07-25T14:22:18Z","title":"Transverse Spheres in Flag Manifolds","version":1},"reference_index":25,"source":"arxiv_source","source_observed_at":"2026-08-15T18:05:55.530128Z"},"links":{"cited_paper":"/paper/2208.14409","citing_paper":"/paper/2507.19306"},"observation_digest":"sha256:7d3ac90d0e553a82a12d6dde5a7000b64da240009417133504f6c6418371680a","observation_id":"e9768134-5c07-4318-9cb8-6dd1d79bae27","resolution":{"observed_at":"2026-08-15T18:05:55.530128Z","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":"2026-08-15T18:05:56.478730Z","title":"Fock and A","venue":null,"work_id":"d1df2799-c09a-4ff4-9612-3e2eb65d75b0","year":2006},"citing_paper":{"arxiv_id":"2507.19306","last_updated":"2025-07-25T14:22:18Z","snapshot_observed_at":"2026-08-15T17:53:10.101189Z","submitted_at":"2025-07-25T14:22:18Z","title":"Transverse Spheres in Flag Manifolds","version":1},"reference_index":26,"source":"arxiv_source","source_observed_at":"2026-08-15T18:05:55.535212Z"},"links":{"citing_paper":"/paper/2507.19306"},"observation_digest":"sha256:bb7ef54957c39919b676f025320f4147ebcb2fada9d6c31b8531fc6074497d45","observation_id":"7d0e63cc-be9f-4c05-9cf4-d3074a257a25","resolution":{"observed_at":"2026-08-15T18:05:56.486895Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:05:56.462801Z","title":"Frobenius","venue":null,"work_id":"f65200b6-5d18-4071-9d84-2e942c3a4208","year":null},"citing_paper":{"arxiv_id":"2507.19306","last_updated":"2025-07-25T14:22:18Z","snapshot_observed_at":"2026-08-15T17:53:10.101189Z","submitted_at":"2025-07-25T14:22:18Z","title":"Transverse Spheres in Flag Manifolds","version":1},"reference_index":27,"source":"arxiv_source","source_observed_at":"2026-08-15T18:05:55.540069Z"},"links":{"citing_paper":"/paper/2507.19306"},"observation_digest":"sha256:4e39950260d2f27cfbf9bdd050a037b373f2b22f3b86d5757b5a0f13d73afff4","observation_id":"b78c7086-88c8-4821-be3a-f994eb530646","resolution":{"observed_at":"2026-08-15T18:05:56.467789Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:05:55.545753Z","title":"Anosov representations and proper actions","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2507.19306","last_updated":"2025-07-25T14:22:18Z","snapshot_observed_at":"2026-08-15T17:53:10.101189Z","submitted_at":"2025-07-25T14:22:18Z","title":"Transverse Spheres in Flag Manifolds","version":1},"reference_index":28,"source":"arxiv_source","source_observed_at":"2026-08-15T18:05:55.545753Z"},"links":{"citing_paper":"/paper/2507.19306"},"observation_digest":"sha256:5f3e12680b7d1056ecb7b1e4da32d1f5c2603844b5cd3a95acdc34722516934e","observation_id":"b760ad0f-1f07-4c8e-bf72-89d972d7224a","resolution":{"observed_at":"2026-08-15T18:05:55.545753Z","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":"2026-08-15T18:05:56.435967Z","title":"The number of connected components in double B ruhat cells for nonsimply-laced groups","venue":null,"work_id":"cf2abede-0d20-44de-ba3d-3e1083fe1b3f","year":2003},"citing_paper":{"arxiv_id":"2507.19306","last_updated":"2025-07-25T14:22:18Z","snapshot_observed_at":"2026-08-15T17:53:10.101189Z","submitted_at":"2025-07-25T14:22:18Z","title":"Transverse Spheres in Flag Manifolds","version":1},"reference_index":29,"source":"arxiv_source","source_observed_at":"2026-08-15T18:05:55.550336Z"},"links":{"citing_paper":"/paper/2507.19306"},"observation_digest":"sha256:707bac4be471a28530ece1c9153d89bf95afc6619a4b0d90267b75fd5bcabbf8","observation_id":"8e761220-fa73-4fdd-824a-c86a4b69bc84","resolution":{"observed_at":"2026-08-15T18:05:56.440723Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:05:55.555015Z","title":"Anosov representations: domains of discontinuity and applications","venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2507.19306","last_updated":"2025-07-25T14:22:18Z","snapshot_observed_at":"2026-08-15T17:53:10.101189Z","submitted_at":"2025-07-25T14:22:18Z","title":"Transverse Spheres in Flag Manifolds","version":1},"reference_index":30,"source":"arxiv_source","source_observed_at":"2026-08-15T18:05:55.555015Z"},"links":{"citing_paper":"/paper/2507.19306"},"observation_digest":"sha256:9ddee5a32533886ae3fadd98796af80dba6828b1d449eee69c07329cb0e67a58","observation_id":"a511111f-af2b-4ebb-8fef-36aec196a306","resolution":{"observed_at":"2026-08-15T18:05:55.555015Z","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":"2026-08-15T18:05:56.408964Z","title":"Vector Bundles and K -theory, 2017","venue":null,"work_id":"b9d7cef0-e7d1-4764-b1ca-8058f4ef6c78","year":2017},"citing_paper":{"arxiv_id":"2507.19306","last_updated":"2025-07-25T14:22:18Z","snapshot_observed_at":"2026-08-15T17:53:10.101189Z","submitted_at":"2025-07-25T14:22:18Z","title":"Transverse Spheres in Flag Manifolds","version":1},"reference_index":31,"source":"arxiv_source","source_observed_at":"2026-08-15T18:05:55.559423Z"},"links":{"citing_paper":"/paper/2507.19306"},"observation_digest":"sha256:4955727e5b8d65d22ff06c1835e145676e03de681bb2d152b6c653fd558c66fd","observation_id":"06e3a112-8f70-482f-bfd5-735ee5356135","resolution":{"observed_at":"2026-08-15T18:05:56.414061Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:05:56.392846Z","title":"askyl\\\"a Department of Mathematics and Statistics . University of Jyv\\","venue":null,"work_id":"a41d0aea-f106-4f67-93d1-7e3975be64ed","year":2005},"citing_paper":{"arxiv_id":"2507.19306","last_updated":"2025-07-25T14:22:18Z","snapshot_observed_at":"2026-08-15T17:53:10.101189Z","submitted_at":"2025-07-25T14:22:18Z","title":"Transverse Spheres in Flag Manifolds","version":1},"reference_index":32,"source":"arxiv_source","source_observed_at":"2026-08-15T18:05:55.563994Z"},"links":{"citing_paper":"/paper/2507.19306"},"observation_digest":"sha256:920f861ff340eb9fb59357485f937fea3ef0962a9a412105472576bd90353c48","observation_id":"56047d0e-e3be-45be-a684-1325e028a3af","resolution":{"observed_at":"2026-08-15T18:05:56.397687Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:05:56.377389Z","title":"Blaine Lawson","venue":null,"work_id":"9b40e36f-9072-4b66-9567-6bbd9931e93f","year":1982},"citing_paper":{"arxiv_id":"2507.19306","last_updated":"2025-07-25T14:22:18Z","snapshot_observed_at":"2026-08-15T17:53:10.101189Z","submitted_at":"2025-07-25T14:22:18Z","title":"Transverse Spheres in Flag Manifolds","version":1},"reference_index":33,"source":"arxiv_source","source_observed_at":"2026-08-15T18:05:55.568528Z"},"links":{"citing_paper":"/paper/2507.19306"},"observation_digest":"sha256:a951cd1bfae52ed1c63fadd51c59d534a4a94705d131a54395975ba74c408fbc","observation_id":"c68265f2-52dd-469b-a1de-b68c3f19ff47","resolution":{"observed_at":"2026-08-15T18:05:56.382131Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:05:56.360800Z","title":"Ueber die Composition der quadratischen Formen von belibig vielen Variablen","venue":null,"work_id":"5d0904a2-bfa9-4c4f-84ab-59cfc6405c25","year":null},"citing_paper":{"arxiv_id":"2507.19306","last_updated":"2025-07-25T14:22:18Z","snapshot_observed_at":"2026-08-15T17:53:10.101189Z","submitted_at":"2025-07-25T14:22:18Z","title":"Transverse Spheres in Flag Manifolds","version":1},"reference_index":34,"source":"arxiv_source","source_observed_at":"2026-08-15T18:05:55.577713Z"},"links":{"citing_paper":"/paper/2507.19306"},"observation_digest":"sha256:e11c0e3397e1cf2d67e5881ea9f233aa5e0dee6a5ebebca452f5c7164e68ba24","observation_id":"cf08f6b4-8a3d-4c46-8c10-63ba4c259bb2","resolution":{"observed_at":"2026-08-15T18:05:56.366236Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:05:56.344525Z","title":null,"venue":null,"work_id":"6aa34235-9f1f-4468-ade6-af49451031ee","year":1953},"citing_paper":{"arxiv_id":"2507.19306","last_updated":"2025-07-25T14:22:18Z","snapshot_observed_at":"2026-08-15T17:53:10.101189Z","submitted_at":"2025-07-25T14:22:18Z","title":"Transverse Spheres in Flag Manifolds","version":1},"reference_index":35,"source":"arxiv_source","source_observed_at":"2026-08-15T18:05:55.583102Z"},"links":{"citing_paper":"/paper/2507.19306"},"observation_digest":"sha256:755ec3587aeabfcd740dc350d30bf020dc489710fc61a16a9f3cce4b761cda06","observation_id":"6e3555d3-1db2-4ab6-8cb8-b9e4d145fc33","resolution":{"observed_at":"2026-08-15T18:05:56.349489Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:05:56.327549Z","title":"Introduction to G_2 geometry , pages 3--50","venue":null,"work_id":"22aa7f4d-ea74-422c-9ca1-9d3e7bdb0dc6","year":2020},"citing_paper":{"arxiv_id":"2507.19306","last_updated":"2025-07-25T14:22:18Z","snapshot_observed_at":"2026-08-15T17:53:10.101189Z","submitted_at":"2025-07-25T14:22:18Z","title":"Transverse Spheres in Flag Manifolds","version":1},"reference_index":36,"source":"arxiv_source","source_observed_at":"2026-08-15T18:05:55.587776Z"},"links":{"citing_paper":"/paper/2507.19306"},"observation_digest":"sha256:66df1f9c748c172c924744d6433098fcc588c967ae870ad7115f819fbb902263","observation_id":"8f987a53-64dd-4559-9928-849a64cae564","resolution":{"observed_at":"2026-08-15T18:05:56.332559Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:05:55.591872Z","title":"Anosov subgroups: dynamical and geometric characterizations","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2507.19306","last_updated":"2025-07-25T14:22:18Z","snapshot_observed_at":"2026-08-15T17:53:10.101189Z","submitted_at":"2025-07-25T14:22:18Z","title":"Transverse Spheres in Flag Manifolds","version":1},"reference_index":37,"source":"arxiv_source","source_observed_at":"2026-08-15T18:05:55.591872Z"},"links":{"citing_paper":"/paper/2507.19306"},"observation_digest":"sha256:1382a2053d0b4b7414be43c0db6be67c16876c2e5da53a7c9388abbe530b114e","observation_id":"d6f37167-f37d-47c6-9383-7dbb5f34ed35","resolution":{"observed_at":"2026-08-15T18:05:55.591872Z","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":"2026-08-15T18:05:56.298595Z","title":"A M orse lemma for quasigeodesics in symmetric spaces and euclidean buildings","venue":null,"work_id":"b6f73569-0381-47aa-aa63-9bb5b2f5b2da","year":2018},"citing_paper":{"arxiv_id":"2507.19306","last_updated":"2025-07-25T14:22:18Z","snapshot_observed_at":"2026-08-15T17:53:10.101189Z","submitted_at":"2025-07-25T14:22:18Z","title":"Transverse Spheres in Flag Manifolds","version":1},"reference_index":38,"source":"arxiv_source","source_observed_at":"2026-08-15T18:05:55.596378Z"},"links":{"citing_paper":"/paper/2507.19306"},"observation_digest":"sha256:377214e5cc867d332dffe92faeed3d5e946c03c564a2bbb20dc37328dc5038e7","observation_id":"aabf9c02-ceb7-461d-8d7d-4caa921156dd","resolution":{"observed_at":"2026-08-15T18:05:56.304774Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:05:55.600844Z","title":"Eigenvalue gaps for hyperbolic groups and semigroups","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2507.19306","last_updated":"2025-07-25T14:22:18Z","snapshot_observed_at":"2026-08-15T17:53:10.101189Z","submitted_at":"2025-07-25T14:22:18Z","title":"Transverse Spheres in Flag Manifolds","version":1},"reference_index":39,"source":"arxiv_source","source_observed_at":"2026-08-15T18:05:55.600844Z"},"links":{"citing_paper":"/paper/2507.19306"},"observation_digest":"sha256:8f63dcb87d38cfb69c6d730bee05378e7ad159faee7c7b62c7f3ce5bbf2c77be","observation_id":"5be0590d-4df7-45e8-bfda-9c3769e2ddbd","resolution":{"observed_at":"2026-08-15T18:05:55.600844Z","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":"2026-08-15T18:05:56.271455Z","title":"Orbits and representations associated with symmetric spaces","venue":null,"work_id":"57083524-4ecb-4cda-ab94-d0ee6afce5a8","year":1971},"citing_paper":{"arxiv_id":"2507.19306","last_updated":"2025-07-25T14:22:18Z","snapshot_observed_at":"2026-08-15T17:53:10.101189Z","submitted_at":"2025-07-25T14:22:18Z","title":"Transverse Spheres in Flag Manifolds","version":1},"reference_index":40,"source":"arxiv_source","source_observed_at":"2026-08-15T18:05:55.606194Z"},"links":{"citing_paper":"/paper/2507.19306"},"observation_digest":"sha256:758ac0b0bbcc6a2a5034e7d6468fcb42a6749a52f05dc165b93009f2be49a723","observation_id":"afa4b4fc-aca9-407a-9f6b-6e3ed1c71984","resolution":{"observed_at":"2026-08-15T18:05:56.276368Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:05:55.610906Z","title":"Connected components of the space of triples of transverse partial flags in SO_0(p,q) and A nosov representations, 2024","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2507.19306","last_updated":"2025-07-25T14:22:18Z","snapshot_observed_at":"2026-08-15T17:53:10.101189Z","submitted_at":"2025-07-25T14:22:18Z","title":"Transverse Spheres in Flag Manifolds","version":1},"reference_index":41,"source":"arxiv_source","source_observed_at":"2026-08-15T18:05:55.610906Z"},"links":{"citing_paper":"/paper/2507.19306"},"observation_digest":"sha256:0c9bf4d051ab4af0f2baff3a9a1c17d98fda94341c396039a48d23a520a72191","observation_id":"a32da182-3949-49e2-8ed0-3ab028310b39","resolution":{"observed_at":"2026-08-15T18:05:55.610906Z","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":"2026-08-15T18:05:55.615521Z","title":"Anosov flows, surface groups and curves in projective space","venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2507.19306","last_updated":"2025-07-25T14:22:18Z","snapshot_observed_at":"2026-08-15T17:53:10.101189Z","submitted_at":"2025-07-25T14:22:18Z","title":"Transverse Spheres in Flag Manifolds","version":1},"reference_index":42,"source":"arxiv_source","source_observed_at":"2026-08-15T18:05:55.615521Z"},"links":{"citing_paper":"/paper/2507.19306"},"observation_digest":"sha256:d1577420ca11406784e0a83ad095e933d27e8d1bee01b3e11df76d7526bcad31","observation_id":"1f601027-14a9-458c-bb92-6490d0d4c138","resolution":{"observed_at":"2026-08-15T18:05:55.615521Z","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":"2026-08-15T18:05:56.244961Z","title":"Orthogonal complex structures on S ^6","venue":null,"work_id":"d57ed973-cc23-4ae8-8dae-f2c7eada0b5b","year":1987},"citing_paper":{"arxiv_id":"2507.19306","last_updated":"2025-07-25T14:22:18Z","snapshot_observed_at":"2026-08-15T17:53:10.101189Z","submitted_at":"2025-07-25T14:22:18Z","title":"Transverse Spheres in Flag Manifolds","version":1},"reference_index":43,"source":"arxiv_source","source_observed_at":"2026-08-15T18:05:55.620437Z"},"links":{"citing_paper":"/paper/2507.19306"},"observation_digest":"sha256:42bc91d347c8605a6cb1f921570f50f1d802bb273ff0ebe0d3973fc0aa697364","observation_id":"88a46715-96cb-41bc-b16e-a0b9045401e3","resolution":{"observed_at":"2026-08-15T18:05:56.249924Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:05:56.227492Z","title":"Blaine Lawson and Marie-Louise Michelsohn","venue":null,"work_id":"57f42989-dd31-4ffe-9d32-f296c0af27bb","year":1989},"citing_paper":{"arxiv_id":"2507.19306","last_updated":"2025-07-25T14:22:18Z","snapshot_observed_at":"2026-08-15T17:53:10.101189Z","submitted_at":"2025-07-25T14:22:18Z","title":"Transverse Spheres in Flag Manifolds","version":1},"reference_index":44,"source":"arxiv_source","source_observed_at":"2026-08-15T18:05:55.625728Z"},"links":{"citing_paper":"/paper/2507.19306"},"observation_digest":"sha256:b99e4fe010dac3dbd8d39d4c39f3827a2448ef1c64fa5a33d2667250e858dd30","observation_id":"99f3e901-fcf9-4cb7-b013-df7eba0c6dc2","resolution":{"observed_at":"2026-08-15T18:05:56.232954Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:05:56.210734Z","title":"Lorentz spacetimes of constant curvature","venue":null,"work_id":"a9777da1-e226-4f6b-b6b8-6b9226ec023d","year":2007},"citing_paper":{"arxiv_id":"2507.19306","last_updated":"2025-07-25T14:22:18Z","snapshot_observed_at":"2026-08-15T17:53:10.101189Z","submitted_at":"2025-07-25T14:22:18Z","title":"Transverse Spheres in Flag Manifolds","version":1},"reference_index":45,"source":"arxiv_source","source_observed_at":"2026-08-15T18:05:55.630402Z"},"links":{"citing_paper":"/paper/2507.19306"},"observation_digest":"sha256:52ca361d997b494d54581408fdfa355d51a9819d215d341606183e38d41548ea","observation_id":"a18cbed7-9c9c-4bf2-befd-ec9a97e976e5","resolution":{"observed_at":"2026-08-15T18:05:56.215565Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:05:56.193817Z","title":"The Geometry of Marked Contact Engel Structures","venue":null,"work_id":"1dee8b43-9b4f-41c2-9659-49b847fd043c","year":2021},"citing_paper":{"arxiv_id":"2507.19306","last_updated":"2025-07-25T14:22:18Z","snapshot_observed_at":"2026-08-15T17:53:10.101189Z","submitted_at":"2025-07-25T14:22:18Z","title":"Transverse Spheres in Flag Manifolds","version":1},"reference_index":46,"source":"arxiv_source","source_observed_at":"2026-08-15T18:05:55.635192Z"},"links":{"citing_paper":"/paper/2507.19306"},"observation_digest":"sha256:519781b3c41b43d12ec9402151cf7f6f3dfcd6a58359e26cc536cd428c9225e6","observation_id":"d43007a4-654a-4576-88a4-61742f358d5f","resolution":{"observed_at":"2026-08-15T18:05:56.198753Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:05:56.177288Z","title":null,"venue":null,"work_id":"54f04226-8471-421d-ab59-d4c30ac8ddb1","year":1955},"citing_paper":{"arxiv_id":"2507.19306","last_updated":"2025-07-25T14:22:18Z","snapshot_observed_at":"2026-08-15T17:53:10.101189Z","submitted_at":"2025-07-25T14:22:18Z","title":"Transverse Spheres in Flag Manifolds","version":1},"reference_index":47,"source":"arxiv_source","source_observed_at":"2026-08-15T18:05:55.640696Z"},"links":{"citing_paper":"/paper/2507.19306"},"observation_digest":"sha256:9465873534ceb14857f19ffc6b159de04fa9d1a1cfb29916ee1ea1342b076dd0","observation_id":"c92ba54b-b152-429e-a42f-1539edc00aee","resolution":{"observed_at":"2026-08-15T18:05:56.182195Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:05:56.161155Z","title":null,"venue":null,"work_id":"0dbab4c1-5017-4ec0-9529-9b30db74210d","year":2002},"citing_paper":{"arxiv_id":"2507.19306","last_updated":"2025-07-25T14:22:18Z","snapshot_observed_at":"2026-08-15T17:53:10.101189Z","submitted_at":"2025-07-25T14:22:18Z","title":"Transverse Spheres in Flag Manifolds","version":1},"reference_index":48,"source":"arxiv_source","source_observed_at":"2026-08-15T18:05:55.645760Z"},"links":{"citing_paper":"/paper/2507.19306"},"observation_digest":"sha256:6669724c131cc9889d80f2783f8c2ba924e4fa650e57a3dda3c807b1cd1c0066","observation_id":"66b1581a-4cc2-4ab3-8266-629b0a9b8cf2","resolution":{"observed_at":"2026-08-15T18:05:56.166255Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:05:56.144744Z","title":"Cyclic H iggs bundles and minimal surfaces in pseudo-hyperbolic spaces","venue":null,"work_id":"f2d015ce-c411-4db9-b90b-4a03ba71f75b","year":2024},"citing_paper":{"arxiv_id":"2507.19306","last_updated":"2025-07-25T14:22:18Z","snapshot_observed_at":"2026-08-15T17:53:10.101189Z","submitted_at":"2025-07-25T14:22:18Z","title":"Transverse Spheres in Flag Manifolds","version":1},"reference_index":49,"source":"arxiv_source","source_observed_at":"2026-08-15T18:05:55.650651Z"},"links":{"citing_paper":"/paper/2507.19306"},"observation_digest":"sha256:1fe2e5daefa3da99d9d78ff2c959eb00f953a84ec5b94e758c02e53cf7d16c08","observation_id":"82d3466b-d5d5-471a-8ddc-a2502b3f8546","resolution":{"observed_at":"2026-08-15T18:05:56.149828Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:05:55.655311Z","title":"Conformality for a robust class of non-conformal attractors","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2507.19306","last_updated":"2025-07-25T14:22:18Z","snapshot_observed_at":"2026-08-15T17:53:10.101189Z","submitted_at":"2025-07-25T14:22:18Z","title":"Transverse Spheres in Flag Manifolds","version":1},"reference_index":50,"source":"arxiv_source","source_observed_at":"2026-08-15T18:05:55.655311Z"},"links":{"citing_paper":"/paper/2507.19306"},"observation_digest":"sha256:ab0b86327e0df88c1d086a9d1f3c8d3633375e7b319e165709f2adc9025a5200","observation_id":"d40b9f45-35e4-456a-97be-9f0dea571c8a","resolution":{"observed_at":"2026-08-15T18:05:55.655311Z","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":"2026-08-15T18:05:56.116983Z","title":"On projective A nosov subgroups of symplectic groups","venue":null,"work_id":"52507815-46f0-437f-83ef-991b6d816abc","year":2024},"citing_paper":{"arxiv_id":"2507.19306","last_updated":"2025-07-25T14:22:18Z","snapshot_observed_at":"2026-08-15T17:53:10.101189Z","submitted_at":"2025-07-25T14:22:18Z","title":"Transverse Spheres in Flag Manifolds","version":1},"reference_index":51,"source":"arxiv_source","source_observed_at":"2026-08-15T18:05:55.660123Z"},"links":{"citing_paper":"/paper/2507.19306"},"observation_digest":"sha256:ba4715960ad772ec10db025beccd01f1d71f8afbe2a15ecc2ac6674e40b55a76","observation_id":"8b5b9935-fcfc-4183-bd2b-08b2d7c4a28a","resolution":{"observed_at":"2026-08-15T18:05:56.122444Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2505.16203","last_updated":"2025-05-22T04:11:13Z","snapshot_observed_at":"2026-08-14T17:27:56.674756Z","submitted_at":"2025-05-22T04:11:13Z","title":"Explicit Families of Spinor Representations","version":1},"cited_work":{"arxiv_id":"2505.16203","doi":null,"metadata_source":"pith","pith_arxiv_id":"2505.16203","snapshot_observed_at":"2026-08-15T18:05:55.763276Z","title":"Explicit Families of Spinor Representations","venue":"math.DG","work_id":"945c9be7-5e6d-4703-952b-8d064f8ca611","year":2025},"citing_paper":{"arxiv_id":"2507.19306","last_updated":"2025-07-25T14:22:18Z","snapshot_observed_at":"2026-08-15T17:53:10.101189Z","submitted_at":"2025-07-25T14:22:18Z","title":"Transverse Spheres in Flag Manifolds","version":1},"reference_index":52,"source":"arxiv_source","source_observed_at":"2026-08-15T18:05:55.665666Z"},"links":{"cited_paper":"/paper/2505.16203","citing_paper":"/paper/2507.19306"},"observation_digest":"sha256:eec0c344dc47465b6c3b3d7a1b6b5ccbd0c5ffd0fa3871125a9c82d9a4b5a34d","observation_id":"d370c41f-671f-4c44-ad4e-128c05efd3d2","resolution":{"observed_at":"2026-08-15T18:05:55.769290Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:05:56.099867Z","title":null,"venue":null,"work_id":"beba61ff-ba7e-4632-80b0-adb7d954fe57","year":1995},"citing_paper":{"arxiv_id":"2507.19306","last_updated":"2025-07-25T14:22:18Z","snapshot_observed_at":"2026-08-15T17:53:10.101189Z","submitted_at":"2025-07-25T14:22:18Z","title":"Transverse Spheres in Flag Manifolds","version":1},"reference_index":53,"source":"arxiv_source","source_observed_at":"2026-08-15T18:05:55.670657Z"},"links":{"citing_paper":"/paper/2507.19306"},"observation_digest":"sha256:9ce967f272dcb6af9759166f115b551b1d22f99a2aa02f69b4e522abe222497c","observation_id":"64e5ec62-31c7-4adc-909f-8ab95b79a077","resolution":{"observed_at":"2026-08-15T18:05:56.105425Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:05:56.082260Z","title":null,"venue":null,"work_id":"58c19c36-636a-4dd3-a077-b54e19ba7a2b","year":1971},"citing_paper":{"arxiv_id":"2507.19306","last_updated":"2025-07-25T14:22:18Z","snapshot_observed_at":"2026-08-15T17:53:10.101189Z","submitted_at":"2025-07-25T14:22:18Z","title":"Transverse Spheres in Flag Manifolds","version":1},"reference_index":54,"source":"arxiv_source","source_observed_at":"2026-08-15T18:05:55.675383Z"},"links":{"citing_paper":"/paper/2507.19306"},"observation_digest":"sha256:9a5b1d469df89b5c6029711a5ecf98aa0c7586e27a37440e6b68f079ed0a36b7","observation_id":"90abd54e-3f60-4190-bc91-e63e37f5ea0e","resolution":{"observed_at":"2026-08-15T18:05:56.087553Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:05:56.063157Z","title":"On Borel Anosov representations in even dimensions","venue":null,"work_id":"1b44c837-f7af-4895-9aee-891c03474e6c","year":2020},"citing_paper":{"arxiv_id":"2507.19306","last_updated":"2025-07-25T14:22:18Z","snapshot_observed_at":"2026-08-15T17:53:10.101189Z","submitted_at":"2025-07-25T14:22:18Z","title":"Transverse Spheres in Flag Manifolds","version":1},"reference_index":55,"source":"arxiv_source","source_observed_at":"2026-08-15T18:05:55.679769Z"},"links":{"citing_paper":"/paper/2507.19306"},"observation_digest":"sha256:e81aeff39a75edcb1df8569783661742ce83400cf247d6ae2f90437c6a590b33","observation_id":"94ebf372-9bf1-4e66-8ad9-4167250f455a","resolution":{"observed_at":"2026-08-15T18:05:56.070297Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2401.03050","last_updated":"2024-09-06T15:03:31Z","snapshot_observed_at":"2026-08-17T22:26:37.264314Z","submitted_at":"2024-01-05T20:00:19Z","title":"Topological restrictions on relatively Anosov representations","version":2},"cited_work":{"arxiv_id":"2401.03050","doi":null,"metadata_source":"pith","pith_arxiv_id":"2401.03050","snapshot_observed_at":"2026-08-15T18:05:55.737324Z","title":"Topological restrictions on relatively Anosov representations","venue":"math.GR","work_id":"07b2a686-4fd8-4e21-adb2-e152d0d51a64","year":2024},"citing_paper":{"arxiv_id":"2507.19306","last_updated":"2025-07-25T14:22:18Z","snapshot_observed_at":"2026-08-15T17:53:10.101189Z","submitted_at":"2025-07-25T14:22:18Z","title":"Transverse Spheres in Flag Manifolds","version":1},"reference_index":56,"source":"arxiv_source","source_observed_at":"2026-08-15T18:05:55.684083Z"},"links":{"cited_paper":"/paper/2401.03050","citing_paper":"/paper/2507.19306"},"observation_digest":"sha256:00cbf23394b896f7204b225a6b9a2775754e69f75aa199fffc7c5ecc6bdfd707","observation_id":"ca0b6272-f8a8-4cb4-860f-cffe3fd4706c","resolution":{"observed_at":"2026-08-15T18:05:55.744451Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:05:56.045247Z","title":"Non-compact simple Lie group G_2' of type G_2","venue":null,"work_id":"88e41d4f-9eda-4788-b98d-59ebad147005","year":1977},"citing_paper":{"arxiv_id":"2507.19306","last_updated":"2025-07-25T14:22:18Z","snapshot_observed_at":"2026-08-15T17:53:10.101189Z","submitted_at":"2025-07-25T14:22:18Z","title":"Transverse Spheres in Flag Manifolds","version":1},"reference_index":57,"source":"arxiv_source","source_observed_at":"2026-08-15T18:05:55.688929Z"},"links":{"citing_paper":"/paper/2507.19306"},"observation_digest":"sha256:a46d2d67f3fc711154660508c8eddb4be4c7ddf199a734cbb7c363c06c7977d6","observation_id":"33fa6330-18cd-4fe0-8e57-d5ea4d2ceb4f","resolution":{"observed_at":"2026-08-15T18:05:56.051276Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:05:56.026520Z","title":"Connected Components of Double Bruhat Cells","venue":null,"work_id":"dc5ddc38-534e-402a-8e00-6d0aabea388c","year":2000},"citing_paper":{"arxiv_id":"2507.19306","last_updated":"2025-07-25T14:22:18Z","snapshot_observed_at":"2026-08-15T17:53:10.101189Z","submitted_at":"2025-07-25T14:22:18Z","title":"Transverse Spheres in Flag Manifolds","version":1},"reference_index":58,"source":"arxiv_source","source_observed_at":"2026-08-15T18:05:55.693070Z"},"links":{"citing_paper":"/paper/2507.19306"},"observation_digest":"sha256:6eac66b1dbb8001f19b410a1a8167fc2655e759f6d9234a4f94fc2ba7fd17c33","observation_id":"41a7f490-5813-432f-859b-f82002287604","resolution":{"observed_at":"2026-08-15T18:05:56.032643Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:05:56.008776Z","title":"Theorie der alternativen ringe","venue":null,"work_id":"61be649a-a12b-4b64-9a8a-54c9019dac0e","year":1931},"citing_paper":{"arxiv_id":"2507.19306","last_updated":"2025-07-25T14:22:18Z","snapshot_observed_at":"2026-08-15T17:53:10.101189Z","submitted_at":"2025-07-25T14:22:18Z","title":"Transverse Spheres in Flag Manifolds","version":1},"reference_index":59,"source":"arxiv_source","source_observed_at":"2026-08-15T18:05:55.697667Z"},"links":{"citing_paper":"/paper/2507.19306"},"observation_digest":"sha256:385d379e27ec9c7ef4ffbf242bdee4d27f2273764d85a04824e96e49fe07fa6f","observation_id":"caadac4c-2c36-41f8-b16a-819883768761","resolution":{"observed_at":"2026-08-15T18:05:56.013347Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2507.19306","last_updated":"2025-07-25T14:22:18Z","latest_version":1,"primary_category":"math.GT","snapshot_observed_at":"2026-08-15T17:53:10.101189Z","submitted_at":"2025-07-25T14:22:18Z","title":"Transverse Spheres in Flag Manifolds"},"reference_resolution":{"displayed":59,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":18,"verified_exact":3,"verified_fuzzy":38},"total_outbound_references":59},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"thesis":"As of 17 August 2026, this Paper Citation Record lists 59 of 59 outbound references and 0 inbound Pith citation observations for arXiv:2507.19306."}